Embryo editing for intelligence

A cost-benefit analysis of CRISPR-based editing for intelligence with 2015-2016 state-of-the-art
decision-theory, biology, psychology, statistics, transhumanism, R, power-analysis, Bayes, IQ
2016-01-222019-04-04 in progress certainty: likely importance: 10


Embryo editing

One approach not dis­cussed in Shul­man & Bostrom is embryo edit­ing, which has com­pelling advan­tages over selec­tion:

  1. Embryo selec­tion must be done col­lec­tively for any mean­ing­ful gains, so one must score all viable embryos; while edit­ing can poten­tially be done singly, edit­ing only the embryo being implant­ed, and no more if that embryo yields a birth.

  2. Fur­ther, a failed implan­ta­tion is a dis­as­ter for embryo selec­tion, since it means one must set­tle for a pos­si­bly much lower scor­ing embryo with lit­tle or no gain while still hav­ing paid upfront for selec­tion; on the other hand, the edit gains will be largely uni­form across all embryos and so the loss of the first embryo is unfor­tu­nate (since it means another set of edits and an implan­ta­tion will be nec­es­sary) but not a major set­back.

  3. Embryo selec­tion suf­fers from the curse of thin tails and being unable to start from a higher mean (ex­cept as part of a mul­ti­-­gen­er­a­tional scheme): one takes 2 steps back for every 3 steps for­ward, so for larger gains, one must brute-­force them with a steeply esca­lat­ing num­ber of embryos.

  4. Embryo selec­tion is con­strained by the broad­-sense her­i­tabil­i­ty, and the num­ber of avail­able embryos.

    • No mat­ter how many GWASes are done on whole-genomes or fancy algo­rithms are applied, embryo selec­tion will never sur­pass the upper bound set by a broad­-sense her­i­tabil­ity 0.8; while the effects of edit­ing has no known upper bound either in terms of exist­ing pop­u­la­tion vari­a­tion, as there appear to be thou­sands of vari­ants inclu­sive of all genetic changes, and evo­lu­tion­ar­ily novel changes could the­o­ret­i­cally be made as well1 (a bac­te­ria or a chim­panzee is, after all, not sim­ply a small human who refuses to talk).
    • Edit­ing is also largely inde­pen­dent of the num­ber of embryos, since each embryo can be edited about as much as any oth­er, and as long as one has enough embryos to expect a birth, more embryos make no dif­fer­ence.
  5. Edit­ing scales lin­early and smoothly by going to the root of the prob­lem, rather than dif­fi­culty increas­ing expo­nen­tially in gain - an exam­ple:

    as cal­cu­lated above, the Rietveld et al 2013 poly­genic score can yield a gain no greater than 2.58 IQ points with 1-in-10 selec­tion, and in prac­tice, we can hardly expect more than 0.14-0.56 IQ points in prac­tice due to fewer than 10 embryos usu­ally being viable etc. But with edit­ing, we can do bet­ter: the same study reported 3 SNP hits (rs9320913, rs11584700, rs4851266) each pre­dict­ing +1 month of school­ing, the largest effects trans­lat­ing to ~0.5IQ points (the edu­ca­tion proxy makes the exact value a lit­tle tricky but we can cross-check with other GWASes which regressed directly on fluid intel­li­gence, like Davies et al 2015’s whose largest hit, rs10457441, does indeed have a reported beta of -0.0324SD or -0.486) with fairly even bal­anced fre­quen­cies around 50% as well.2 So one can see imme­di­ately that if an embryo is sequenced & found to have the bad vari­ant on any of those SNPs, a sin­gle edit has the same gain as the entire embryo selec­tion process! Unlike embryo selec­tion, there is no inher­ent rea­son an edit­ing process must stop at one edit - and with two edits, one does­n’t even need to sequence in the first place, as the fre­quency means that the expected value of edit­ing the SNP is 0.25 points and so two blind edits would have the same gain! Con­tin­u­ing, the gains can stack; tak­ing the 15 top hits from Davies et al 2015’s Sup­ple­men­tary Table S3, 15 edits would yield 6.35 points and yes, com­bined with the next 15 after that would yield ~14 points, blow­ing past the SNP embryo selec­tion upper bounds. While on aver­age any embryo would not need half of those edits, that just means that an edit­ing pro­ce­dure will go down another entry down the list and edit that instead (given a bud­get of 15 edits, one might wind up edit­ing, say #30). Since the esti­mated effects do not decline too fast and fre­quen­cies are high, this is sim­i­lar to if we skipped every other edit and so the gains are still sub­stan­tial:

    davies2015 <- data.frame(Beta=c(-0.0324, 0.0321, -0.0446, -0.032, 0.0329, 0.0315, 0.0312, 0.0312, -0.0311, -0.0315, -0.0314, 0.0305,
     0.0309, 0.0306, 0.0305, 0.0293, -0.0292, -0.0292, -0.0292, 0.0292, -0.0292, 0.0292, -0.0291, -0.0293, -0.0293, 0.0292, -0.0296,
     -0.0293, -0.0291, 0.0296, -0.0313, -0.047, -0.0295, 0.0295, -0.0292, -0.028, -0.0287, -0.029, 0.0289, 0.0302, -0.0289, 0.0289,
     -0.0281, -0.028, 0.028, -0.028, 0.0281, -0.028, 0.0281, 0.028, 0.028, 0.028, -0.029, 0.029, 0.028, -0.0279, -0.029, 0.0279,
     -0.0289, -0.027, 0.0289, -0.0282, -0.0286, -0.0278, -0.0279, 0.0289, -0.0288, 0.0278, 0.0314, -0.0324, -0.0288, 0.0278, 0.0287,
     0.0278, 0.0277, -0.0287, -0.0268, -0.0287, -0.0287, -0.0272, -0.0277, 0.0277, -0.0286, -0.0276, -0.0267, 0.0276, -0.0277, 0.0284,
     0.0277, -0.0276, 0.0337, 0.0276, 0.0286, -0.0279, 0.0282, 0.0275, -0.0269, -0.0277),
                  Frequency=c(0.4797, 0.5199, 0.2931, 0.4803, 0.5256, 0.4858, 0.484, 0.4858, 0.4791, 0.4802, 0.4805, 0.487, 0.528,
                  0.5018, 0.5196, 0.5191, 0.481, 0.481, 0.4807, 0.5191, 0.4808, 0.5221, 0.4924, 0.3898, 0.3897, 0.5196, 0.3901,
                  0.3897, 0.4755, 0.4861, 0.6679, 0.1534, 0.3653, 0.6351, 0.6266, 0.4772, 0.3747, 0.3714, 0.6292, 0.6885, 0.668,
                  0.3319, 0.3703, 0.3696, 0.6307, 0.3695, 0.6255, 0.3695, 0.3559, 0.6306, 0.6305, 0.6309, 0.316, 0.684, 0.631,
                  0.3692, 0.3143, 0.631, 0.316, 0.4493, 0.6856, 0.6491, 0.6681, 0.3694, 0.3686, 0.6845, 0.3155, 0.6314, 0.2421,
                  0.7459, 0.3142, 0.3606, 0.6859, 0.6315, 0.6305, 0.3157, 0.5364, 0.3144, 0.3141, 0.5876, 0.3686, 0.6314, 0.3227,
                  0.3695, 0.5359, 0.6305, 0.3728, 0.3318, 0.3551, 0.3695, 0.2244, 0.6304, 0.6856, 0.6482, 0.6304, 0.6304, 0.4498, 0.6469))
    davies2015$Beta <- abs(davies2015$Beta)
    sum(head(davies2015$Beta,n=30))*15
    # [1] 13.851
    editSample <- function(editBudget) { head(Filter(function(x){rbinom(1, 1, prob=davies2015$Frequency)}, davies2015$Beta), n=editBudget) }
    mean(replicate(1000, sum(editSample(30) * 15)))
    # [1] 13.534914
  6. Edit­ing can be done on low-fre­quency or rare vari­ants, whose effects are known but will not be avail­able in the embryos in most selec­tion instances.

    For exam­ple, George Church lists 10 rare muta­tions of large effect that may be worth edit­ing into peo­ple:

    1. G171V/+ Extra-strong bones3
    2. -/- Lean mus­cles
    3. -/- Insen­si­tiv­ity to pain
    4. -/- Low Odor pro­duc­tion
    5. , -/- Virus resis­tance
    6. -/- Low coro­nary dis­ease
    7. A673T/+ Low Alzheimer’s
    8. , GH -/- Low can­cer
    9. -/+ Low T2 Dia­betes
    10. E627X/+ Low T1 Dia­betes

    To which I would add: sleep dura­tion, qual­i­ty, morn­ing­ness-evening­ness, and resis­tance to sleep depri­va­tion () are, like most traits, her­i­ta­ble. The extreme case is that of “short­-sleep­ers”, the ~1% of the pop­u­la­tion who nor­mally sleep 3-6h; they often men­tion a par­ent who was also a short­-sleep­er, short sleep start­ing in child­hood, that ‘over’ sleep­ing is & they do not fall asleep faster & don’t sleep exces­sively more on week­ends (indi­cat­ing they are not merely chron­i­cally sleep­-de­prived), and are anec­do­tally described as highly ener­getic mul­ti­-­taskers, thin, with pos­i­tive atti­tudes & high pain thresh­olds (Monk et al 2001) with­out any known health effects or down­sides in humans4 or mice (aside from, pre­sum­ably, greater caloric expen­di­ture).

    Some instances of short­-sleep­ers are due to , with a vari­ant found in short­-sleep­ers vs con­trols (6.25h vs 8.37h, -127m) and the effect con­firmed by knock­out-mice (); another short­-sleep vari­ant was iden­ti­fied in a dis­cor­dant twin pair with an effect of -64m (). DEC2/BHLHE41 SNPs are also rare (for exam­ple, 3 such SNPs have fre­quen­cies of 0.08%, 3%, & 5%). Hence, selec­tion would be almost entirely inef­fec­tive, but edit­ing is easy.

    As far as costs and ben­e­fits go, we can observe that being able to stay awake an addi­tional 127 min­utes a day is equiv­a­lent to being able to live an addi­tional 7 years, 191 min­utes to 11 years; to negate that, any side-­ef­fect would have to be tan­ta­mount to life­long smok­ing of tobac­co.

The largest dis­ad­van­tage of edit­ing, and the largest advan­tage of embryo selec­tion, is that selec­tion relies on proven, well-un­der­stood known-priced PGD tech­nol­ogy already in use for other pur­pos­es; while the for­mer has­n’t existed and has been sci­ence fic­tion, not fact.

Genome synthesis

The cost of CRISPR edit­ing will scale roughly as the num­ber of edits: 100 edits will cost 10x 10 edits. It may also scale super­lin­early if each edit makes the next edit more dif­fi­cult. This poses chal­lenges to prof­itable edit­ing since the mar­ginal gain of each edit will keep decreas­ing as the SNPs with largest effect sizes are edited first - it’s hard to see how 500 or 1000 edits would be prof­itable. Sim­i­lar to the daunt­ing cost of iter­ated embryo selec­tion, where the IES is done only once or a few times and then gametes are dis­trib­uted en masse to prospec­tive par­ents to amor­tize per-child costs to small amounts, one could imag­ine doing the same thing for a heav­ily CRISPR-edited embryo.

But at some point, doing many edits raises the ques­tion of why you are both­er­ing with the wild type genome? Could­n’t you just cre­ate a whole from scratch incor­po­rat­ing every pos­si­ble edit? Syn­the­size a whole genome’s DNA and incor­po­rate all edits one wish­es; in the design phase, take the GWASes for a wide vari­ety of traits and set each SNP, no mat­ter how weakly esti­mat­ed, to the pos­i­tive direc­tion; in copy­ing in the data of regions with rare vari­ants, they are prob­a­bly harm­ful and can be erased with the modal human base-­pairs at those posi­tions, for sys­tem­atic health ben­e­fits across most dis­eases; or to imi­tate iter­a­tive embryo selec­tion, which exploits the tag­ging power of SNPs to pull in the ben­e­fi­cial rare vari­ants, copy over the hap­lo­types for ben­e­fi­cial SNPs which might be tag­ging a rare vari­ant. Between the eras­ing of muta­tion load and exploit­ing all com­mon vari­ants simul­ta­ne­ous­ly, the results could be a stag­ger­ing phe­no­type.

DNA syn­the­sis, syn­the­siz­ing a strand of DNA by base-­pair, has long been done, but gen­er­ally lim­ited to a few hun­dred BPs, which is much less than the 23 human chro­mo­somes’ col­lec­tive ~3.3 bil­lion BP. Past work in syn­the­siz­ing genomes has included Craig Ven­ter’s min­i­mal bac­terium in 2008 with 582,970 BP; http://www.nature.com/news/2008/080124/full/news.2008.522.html 1.1 mil­lion BP in 2010 http://www.nature.com/news/2010/100520/full/news.2010.253.html 483,000 BP and 531,000 BP in 2016 http://www.nature.com/news/minimal-cell-raises-stakes-in-race-to-harness-synthetic-life-1.19633 (spend­ing some­where ~$40m on these pro­jects) 272,871 in 2014 (1 yeast chro­mo­some; 90k BP cost­ing $50k at the time) and plans for syn­the­siz­ing the whole yeast genome in 5 years http://www.nature.com/news/first-synthetic-yeast-chromosome-revealed-1.14941 http://science.sciencemag.org/content/290/5498/1972 http://science.sciencemag.org/content/329/5987/52 http://science.sciencemag.org/content/342/6156/357 http://science.sciencemag.org/content/333/6040/348 2,750,000 BP in 2016 for E. coli http://www.nature.com/news/radically-rewritten-bacterial-genome-unveiled-1.20451 “Design, syn­the­sis, and test­ing toward a 57-­codon genome”, Ostrov et al 2016 http://science.sciencemag.org/content/353/6301/819

https://www.quora.com/How-many-base-pairs-of-DNA-can-I-synthesize-for-1-dollar

The biggest chro­mo­some is #1, with 8.1% of the base-­pairs or 249,250,621; the small­est is #21, 1.6%, or 48,129,895. DNA syn­the­sis prices drop each year in an expo­nen­tial decline (if not remotely as fast as the DNA sequenc­ing cost curve), and so 2016 syn­the­siz­ing costs have reached <$0.3; let’s say $0.25/BP.

Chro­mo­some Length in base-­pairs Frac­tion Syn­the­sis cost at $0.25/BP
1 249,250,621 0.081 $62,312,655
2 243,199,373 0.079 $60,799,843
3 198,022,430 0.064 $49,505,608
4 191,154,276 0.062 $47,788,569
5 180,915,260 0.058 $45,228,815
6 171,115,067 0.055 $42,778,767
7 159,138,663 0.051 $39,784,666
8 146,364,022 0.047 $36,591,006
9 141,213,431 0.046 $35,303,358
10 135,534,747 0.044 $33,883,687
11 135,006,516 0.044 $33,751,629
12 133,851,895 0.043 $33,462,974
13 115,169,878 0.037 $28,792,470
14 107,349,540 0.035 $26,837,385
15 102,531,392 0.033 $25,632,848
16 90,354,753 0.029 $22,588,688
17 81,195,210 0.026 $20,298,802
18 78,077,248 0.025 $19,519,312
19 59,128,983 0.019 $14,782,246
20 63,025,520 0.020 $15,756,380
21 48,129,895 0.016 $12,032,474
22 51,304,566 0.017 $12,826,142
X 155,270,560 0.050 $38,817,640
Y 59,373,566 0.019 $14,843,392
total 3,095,693,981 1.000 $773,923,495

So the syn­the­sis of one genome in 2016, assum­ing no economies of scale or fur­ther improve­ment, would come in at ~$773m. This is a stag­ger­ing but finite and even fea­si­ble amount: the orig­i­nal cost ~$3b, and other large sci­ence projects like the LHC, Man­hat­tan Pro­ject, ITER, Apollo Pro­gram, ISS, the National Chil­dren’s Study etc have cost many times what 1 human genome would.

https://en.wikipedia.org/wiki/Human_Genome_Project_-_Write http://www.nature.com/news/plan-to-synthesize-human-genome-triggers-mixed-response-1.20028 http://science.sciencemag.org/content/early/2016/06/01/science.aaf6850.full http://science.sciencemag.org/content/sci/suppl/2016/06/01/science.aaf6850.DC1/Boeke.SM.pdf http://www.nytimes.com/2016/06/03/science/human-genome-project-write-synthetic-dna.html http://diyhpl.us/wiki/transcripts/2017-01-26-george-church/ https://www.wired.com/story/live-forever-synthetic-human-genome/ https://medium.com/neodotlife/andrew-hessel-human-genome-project-write-d15580dd0885 “Is the World Ready for Syn­thetic Peo­ple?: Stan­ford bio­engi­neer Drew Endy does­n’t mind bring­ing drag­ons to life. What really scares him are humans.” https://medium.com/neodotlife/q-a-with-drew-endy-bde0950fd038 https://www.chemistryworld.com/feature/step-by-step-synthesis-of-dna/3008753.article

Church is opti­mistic: maybe even $100k/genome by 2037 http://www.wired.co.uk/article/human-genome-synthesise-dna “Humans 2.0: these geneti­cists want to cre­ate an arti­fi­cial genome by syn­the­sis­ing our DNA; Sci­en­tists intend to have fully syn­the­sised the genome in a liv­ing cell - which would make the mate­r­ial func­tional - within ten years, at a pro­jected cost of $1 bil­lion” > But these are the “byprod­ucts” of HGP-Write, in Hes­sel’s view: the pro­jec­t’s true pur­pose is to cre­ate the impe­tus for tech­no­log­i­cal advances that will lead to these long-term ben­e­fits. “Since all these [syn­the­sis] tech­nolo­gies are expo­nen­tially improv­ing, we should keep push­ing that improve­ment rather than just turn­ing the crank blindly and expen­sive­ly,” Church says. In 20 years, this could cut the cost of syn­the­sis­ing a human genome to $100,000, com­pared to the $12 bil­lion esti­mated a decade ago.

The ben­e­fit of this invest­ment would be to bypass the death by a thou­sand cuts of CRISPR edit­ing and cre­ate a genome with an arbi­trary num­ber of edits on an arbi­trary num­ber of traits for the fixed upfront cost. Unlike mul­ti­ple selec­tion, one would not need to trade off mul­ti­ple traits against each other (ex­cept for pleiotropy); unlike edit­ing, one would not be lim­ited to mak­ing only edits with a mar­ginal expected value exceed­ing the cost of 1 edit. Doing indi­vid­ual genome syn­the­ses will be out of the ques­tion for a long time to come, so genome syn­the­sis is like IES in amor­tiz­ing its cost over prospec­tive par­ents.

The “2013 Assisted Repro­duc­tive Tech­nol­ogy National Sum­mary Report” says ~10% of IVF cycles use donor eggs, and a total of 67996 infants, imply­ing >6.7k infants con­ceived with donor eggs, embryos, or sperm (sperm is not cov­ered by that report) and were only half or less related to their par­ents. What imme­di­ate 1-year return over 6.7k infants would jus­tify spend­ing $773m? Con­sid­er­ing just the low esti­mate of IQ at $3270/point and no other traits, that would trans­late to (773m/6.7k) / 3270 = 35 IQ points or at an aver­age IQ gain of 0.1 points, the equiv­a­lent of 350 causal edits. This is doable. If we allow amor­ti­za­tion at a high dis­count rate of 5% and reuse the genome indef­i­nitely for each year’s crop of 6.7k infants, then we need at least X IQ points where ((x*3270*6700) / log(1.05)) - 773000000 >= 0; x >= 1.73 or at ~0.1 points per edit, 18 edits. We could also syn­the­size only 1 chro­mo­some and pay much less upfront (but at the cost of a lower upper bound, as GCTA heritability/length regres­sions and GWAS poly­genic score results indi­cates that intel­li­gence and many other com­plex traits are spread very evenly over the genome, so each chro­mo­some will har­bor vari­ants pro­por­tional to its length).

The causal edit prob­lem remains but at 12% causal rates, 18 causal edits can eas­ily be made with 150 edits of SNP can­di­dates, which is less than already avail­able. So at first glance, whole genome syn­the­sis can be prof­itable with opti­miza­tion of only one trait using exist­ing GWAS hits, and will be extremely prof­itable if dozens of traits are opti­mized and muta­tion load min­i­mized.

How much prof­itable? …see embryo selec­tion cal­cu­la­tions… At 70 SDs and 12% causal, then the profit would be 70*15*3270*0.12*6700 - 773000000 = $1,987,534,000 the first year or NPV of $55,806,723,536. TODO: only half-re­lat­ed­ness

TODO:

  • model DNA syn­the­sis cost curve; when can we expect a whole human genome to be syn­the­siz­able with a sin­gle lab’s resources, like $1m/$5m/$10m? when does syn­the­sis begin to look bet­ter than IES?

    eye­balling http://science.sciencemag.org/content/sci/suppl/2016/06/01/science.aaf6850.DC1/Boeke.SM.pdf , 0.01/$ or 100$ in 1990, 3/$ or 0.3$ in 2015?

    R> synthesis <- data.frame(Year=c(1990,2015), Cost=c(100, 0.33))
    R> summary(l <- lm(log(Cost) ~ Year, data=synthesis))
    R> prettyNum(big.mark=",", round(exp(predict(l, data.frame(Year=c(2016:2040), Cost=NA))) * 3095693981))
                1             2             3             4             5             6             7             8             9            10            11            12            13
    "812,853,950" "646,774,781" "514,628,265" "409,481,413" "325,817,758" "259,247,936" "206,279,403" "164,133,195" "130,598,137" "103,914,832"  "82,683,356"  "65,789,813"  "52,347,894"
               14            15            16            17            18            19            20            21            22            23            24            25
     "41,652,375"  "33,142,123"  "26,370,653"  "20,982,703"  "16,695,599"  "13,284,419"  "10,570,198"   "8,410,536"   "6,692,128"   "5,324,818"   "4,236,872"   "3,371,211"

    As the cost appears to be roughly lin­ear in chro­mo­some length, it would be pos­si­ble to scale down syn­the­sis projects if an entire genome can­not be afford­ed.

    For exam­ple, IQ is highly poly­genic and the rel­e­vant SNPs & causal vari­ants are spread fairly evenly over the entire genome (as indi­cated by the orig­i­nal GCTAs show SNP her­i­tabil­ity per chro­mo­some cor­re­lates with chro­mo­some length, and loca­tion of GWAS hit­s), so one could instead syn­the­size a chro­mo­some account­ing for ~1% of base­pairs which will carry 1% of vari­ants at 1% of the total cost.

    So if a whole genome costs $1b, there are ~10,000 vari­ants, with an aver­age effect of ~0.1 IQ points and a fre­quency of 50%, then for $10m one could cre­ate a chro­mo­some which would improve over a wild genome’s chro­mo­some by 10000 * 0.01 * 0.5 * 0.1 = 5 points; then as resources allow and the syn­the­sis price keeps drop­ping, cre­ate a sec­ond small chro­mo­some for another 5 points, and so on with the big­ger chro­mo­somes for larger gains.

“Large-s­cale de novo DNA syn­the­sis: tech­nolo­gies and appli­ca­tions”, Kosuri & Church 2014 http://arep.med.harvard.edu/pdf/Kosuri_Church_2014.pdf

Cost curve:

His­tor­i­cal cost curves of genome sequenc­ing & syn­the­sis, 1980-2015 (log scale)

“Bricks and blue­prints: meth­ods and stan­dards for DNA assem­bly” http://scienseed.com/clients/tomellis/wp-content/uploads/2015/08/BricksReview.pdf Casini et al 2015

“Lep­roust says that won’t always be the case-not if her plans to improve the tech­nol­ogy work out.”In a few years it won’t be $100,000 to store that data," she says. “It will be 10 cents.”" https://www.technologyreview.com/s/610717/this-company-can-encode-your-favorite-song-in-dnafor-100000/ April 2018

http://www.synthesis.cc/synthesis/2016/03/on_dna_and_transistors

Ques­tions: what is the best way to do genome syn­the­sis? Lots of pos­si­bil­i­ties:

  • can do one or more chro­mo­somes at a time (which would fit in small bud­gets)

  • opti­mize 1 trait to max­i­mize PGS SNP-wise (but causal tagging/LD prob­lem…)

  • opti­mize 1 trait to max­i­mize hap­lo­type PGS

  • opti­mize mul­ti­ple traits with genetic cor­re­la­tions and unit-weighted

  • mul­ti­ple trait, util­i­ty-weighted

  • lim­ited opti­miza­tion:

  • par­tial fac­to­r­ial trial of hap­lo­types (eg take the max­i­mal util­i­ty-weight­ed, then flip a ran­dom half for the first genome; flip a dif­fer­ent ran­dom half for the sec­ond genome; etc)

    • this could be used for respon­se-­sur­face esti­ma­tion: to try to esti­mate where addi­tiv­ity breaks down and genetic cor­re­la­tions change sub­stan­tially
  • con­strained opti­miza­tion of hap­lo­types: max­i­mize the util­i­ty-weight sub­ject to a soft con­straint like total phe­no­type increases of >2SD on aver­age (eg if there are 10 traits, allow +20SD of total phe­no­type change); or a hard con­straint, like no trait past >5SD (so at least a few peo­ple to ever live could have had a sim­i­lar PGS value on each trait)

    • because of how many real-­world out­comes are log-nor­mally dis­trib­uted and the com­po­nent nor­mals have thin tails, it will be more effi­cient to increase 20 traits by 1SD than 1 trait by 20SD
  • modal­iza­tion: sim­ply take the modal human genome, implic­itly reap­ing gains from remov­ing much muta­tion load

  • par­tial opti­miza­tion of a pro­to­type genome: select some exem­plar genome as a base­line, like a modal genome or very accom­plished or very intel­li­gent per­son, and opti­mize only a few SD up from that

  • “dose-rang­ing study”: mul­ti­ple genomes opti­mized to var­i­ous SDs or var­i­ous hard/soft con­straints, to as quickly as pos­si­ble esti­mate the safe extreme (eg +5 vs 10 vs 15 SD)

  • exotic changes: adding very rare vari­ants like the short­-sleeper or myo­stat­in; increas­ing CNVs of genes dif­fer­ing between humans and chim­panzees; genome with all codons recorded to make viral infec­tion impos­si­ble

CRISPR

The past 5 years have seen major break­throughs in cheap, reli­able, gen­er­al-pur­pose genetic engi­neer­ing & edit­ing using , since the 2012 demon­stra­tion that it could edit cells, includ­ing human ones ().5 Com­men­tary in 2012 and 2013 regarded prospects for embryo edit­ing as highly remote6 Even as late as July 2014, cov­er­age was highly cir­cum­spect, with vague mus­ing that “Some exper­i­ments also hint that doc­tors may some­day be able to use it to treat genetic dis­or­ders”; suc­cess­ful edit­ing of zebrafish (), mon­key, and human embryos was already being demon­strated in the lab, and human tri­als would begin 2-3 years lat­er. (Sur­pris­ing­ly, Shul­man & Bostrom do not men­tion CRISPR, but that gives an idea of how shock­ingly fast CRISPR went from strange to news to stan­dard, and how low expec­ta­tions for genetic engi­neer­ing were pre-2015 after decades of ago­niz­ingly slow progress & high­-pro­file fail­ures & deaths, such that the default assump­tion was that direct cheap safe genetic engi­neer­ing of embryos would not be fea­si­ble for decades and cer­tainly not the fore­see­able future.)

The CRISPR/Cas sys­tem exploits a bac­te­r­ial anti-vi­ral immune sys­tem in which snip­pets of virus DNA are stored and an enzyme sys­tem detects the pres­ence in the bac­te­r­ial genome of fresh viral DNA and then edits it, break­ing it, and pre­sum­ably stop­ping the infec­tion in its latent phase. This requires the CRISPR enzymes to be highly pre­cise (lest it attack legit­i­mate DNA, dam­ag­ing or killing itself), repeat­able (it’s a poor immune sys­tem that can only fight off one infec­tion ever), and pro­gram­ma­ble by short RNA sequences (be­cause viruses con­stantly mutate).

This turns out to be usable in ani­mal and human cells to delete/knock-out genes: cre­ate an RNA sequence match­ing a par­tic­u­lar gene, inject the RNA sequence along with the key enzymes into a cell, and it will find the gene in ques­tion inside the nucleus and snip it; this can be aug­mented to edit rather than delete by pro­vid­ing another DNA tem­plate which the snip-re­pair mech­a­nisms will unwit­tingly copy from. Com­pared to the major ear­lier approaches using & , CRISPR is far faster and eas­ier and cheaper to use, with large (at least halv­ing) decreases in time & money cit­ed, and use of it has exploded in research labs, draw­ing com­par­isons to the inven­tion of PCR and Nobel Prize pre­dic­tions. It has been used to edit at least 36 crea­tures as of June 20157, includ­ing:

(I am con­vinced some of these were done pri­mar­ily for the lulz.)

It has appeared to be a very effec­tive and promis­ing genome edit­ing tool in mam­malian cells Cho et al., 2013 “Tar­geted genome engi­neer­ing in human cells with the Cas9 RNA-guided end” http://www.bmskorea.co.kr/bms_email/email2013/13-0802/paper.pdf human cells Cong et al., 2013 “Mul­ti­plex genome engi­neer­ing using CRISPR/Cas sys­tems” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3795411/ mouse and human cells Jinek et al., 2012 “A pro­gram­ma­ble dual-RNA-guided DNA endonu­cle­ase in adap­tive bac­te­r­ial immu­nity” zebrafish somatic cells at the organ­is­mal level Hwang et al 2013“Effi­cient genome edit­ing in zebrafish using a CRISPR-Cas sys­tem” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3686313/ genomic edit­ing in cul­tured mam­malian cells pluripo­tent stem cells, but also in zebrafish embryos with effi­cien­cies that are com­pa­ra­ble to those obtained using ZFNs and TALENs (Hwang et al., 2013).

Jenko et al 2016, “Poten­tial of pro­mo­tion of alle­les by genome edit­ing to improve quan­ti­ta­tive traits in live­stock breed­ing pro­grams” https://gsejournal.biomedcentral.com/articles/10.1186/s12711-015-0135-3

, Yang et al 2019 (—“engi­neer­ing 18 dif­fer­ent loci using mul­ti­ple genome engi­neer­ing meth­ods” in pigs; fol­lowup to )

Esti­mat­ing the profit from CRISPR edits is, in some ways, less straight­for­ward than from embryo selec­tion:

  1. tak­ing the high­est n reported betas/coefficients from a GWAS OLS regres­sions implies that they will be sys­tem­at­i­cally biased upwards due to the win­ner’s curse and sta­tis­ti­cal-sig­nif­i­cance fil­ter­ing, thereby exag­ger­at­ing the poten­tial ben­e­fit from each SNP
  2. the causal tag­ging prob­lem: GWAS esti­mates cor­re­lat­ing SNPs with phe­no­type traits, while valid for pre­dic­tion (and hence selec­tion), are not nec­es­sar­ily causal (such that an edit at that SNP will have the esti­mated effec­t), and the prob­a­bil­ity of being non-­causal
  3. each CRISPR edit has a chance of not mak­ing the cor­rect edit, and mak­ing wrong edits; an edit may not work in an embryo (the speci­fici­ty, false neg­a­tive), and there is a chance of an ‘off-­tar­get’ muta­tion (false pos­i­tive). A non-edit is a waste of mon­ey, while an off-­tar­get muta­tion could be fatal.
  4. CRISPR has advanced at such a rapid rate that num­bers on cost, speci­fici­ty, & off-­tar­get muta­tion rate are gen­er­ally either not avail­able, or are arguably out of date before they were pub­lished19

The win­ner’s curse can be dealt with sev­eral ways; dis­cusses 4 meth­ods (“invert­ing the con­di­tional expec­ta­tion of the OLS esti­ma­tor, max­i­mum like­li­hood esti­ma­tion (MLE), Bayesian esti­ma­tion, and empir­i­cal-Bayes esti­ma­tion”). The best one for our pur­poses would be a Bayesian approach, yield­ing pos­te­rior dis­tri­b­u­tions of effect sizes. Unfor­tu­nate­ly, the raw data for GWAS stud­ies like Rietveld et al 2013 is not avail­able; but for our pur­pos­es, we can, like in the Rietveld et al 2014 sup­ple­ment, sim­ply sim­u­late a dataset and work with that to get pos­te­ri­ors to find the SNPs with unbi­ased largest pos­te­rior means.

The causal tag­ging prob­lem is more dif­fi­cult. The back­ground for the causal tag­ging prob­lem is that genes are recom­bined ran­domly at con­cep­tion, but they are not recom­bined at the indi­vid­ual gene lev­el; rather, genes tend to live in ‘blocks’ of con­tigu­ous genes called , lead­ing to (LD). Not every pos­si­ble vari­ant in a hap­lo­type is detected by a SNP array chip, so if you have genes A/B/C/D, it may be the case that a vari­ant of A will increase intel­li­gence but your SNP array chip only detects vari­ants of D; when you do a GWAS, you then dis­cover D pre­dicts increased intel­li­gence. (And if your SNP array chip tags B or C, you may get hits on those as well!) This is not a prob­lem for embryo selec­tion, because if you can only see D’s vari­ants, and you see that an embryo has the ‘good’ D vari­ant, and you pick that embryo, it will indeed grow up as you hoped because that D vari­ant pulled the true causal A vari­ant along for the ride. Indeed, for selec­tion or pre­dic­tion, the causal tag­ging prob­lem can be seen as a good thing: your GWASes can pick up effects from parts of the genome you did­n’t even pay to sequence - “buy one, get one free”. (The down­side can be under­es­ti­ma­tion due to imper­fect prox­ies.) But this is a prob­lem for embryo edit­ing because if a CRISPR enzyme goes in and care­fully edits D while leav­ing every­thing untouched, A by def­i­n­i­tion remains the same and there will be no ben­e­fits. A SNP being non-­causal is not a seri­ous prob­lem for embryo edit­ing if we know which SNPs are non-­causal; as illus­trated above, the dis­tri­b­u­tion of effects is smooth enough that dis­card­ing a top SNP for the next best alter­na­tive costs lit­tle. But it is a seri­ous prob­lem if we don’t know which ones are non-­causal, because then we waste pre­cious edits (imag­ine a bud­get of 30 edits and a non-­causal rate of 50%; if we are igno­rant which are non-­causal, we effec­tively get only 15 edits, but if we know which to drop, then it’s almost as good as if all were causal). Causal­ity can be estab­lished in a few ways; for exam­ple, a hit can be reused in a mutant lab­o­ra­tory ani­mal breed to see if it also pre­dicts there (This is behind some strik­ing break­throughs like Sekar et al 2016’s proof that neural prun­ing is a cause of schiz­o­phre­ni­a), either using exist­ing strains or cre­at­ing a fresh mod­i­fi­ca­tion (us­ing, say, CRISPR). This has not been done for the top intel­li­gence hits and given the expense & dif­fi­culty of ani­mal exper­i­men­ta­tion, we can’t expect it any­time soon. One can also try to use prior infor­ma­tion to boost the pos­te­rior prob­a­bil­ity of an effect: if a gene has already been linked to the ner­vous sys­tem by pre­vi­ous stud­ies explor­ing muta­tions or gene expres­sion data etc, or other aspects of the phys­i­cal struc­ture point towards that SNP like being clos­est to a gene, then that is evi­dence for the asso­ci­a­tion being causal. Intel­li­gence hits are enriched for ner­vous sys­tem con­nec­tions, but this method is inher­ently weak. A bet­ter method is fine-map­ping or whole-genome sequenc­ing: when all the vari­ants in a hap­lo­type are sequenced, then the true causal vari­ant will tend to per­form sub­tly bet­ter and one can sin­gle it out of the whole SNP set using var­i­ous sta­tis­ti­cal cri­te­ria (eg Farh et al 2015 using their algo­rithm on autoim­mune dis­or­der esti­mate 5.5% of their 4.9k SNPs are causal). Use­ful, but whole-genomes are still expen­sive enough that they are not cre­ated nearly as much as SNPs and there do not seem to be many com­par­isons to ground-truths or meta-­analy­ses. Another approach is sim­i­lar to the lab ani­mal approach: human groups dif­fer genet­i­cal­ly, and their hap­lo­types & LD pat­terns can dif­fer great­ly; if D looks asso­ci­ated with intel­li­gence in one group, but is not asso­ci­ated in a genet­i­cally dis­tant group with dif­fer­ent hap­lo­types, that strongly sug­gests that in the first group, D was indeed just prox­y­ing for another vari­ant. We can also expect that vari­ants with high fre­quen­cies will not be pop­u­la­tion-spe­cific but be ancient & shared causal vari­ants. Some of the intel­li­gence hits have repli­cated in Euro­pean-Amer­i­can sam­ples, as expected but not help­ful­ly; more impor­tant­ly, in African-Amer­i­can (Domingue et al 2015) and East Asian sam­ples (Zhu et al 2015), and the top SNPs have some pre­dic­tive power of mean IQs across eth­nic groups (Pif­fer 2015). More gen­er­al­ly, while GWASes usu­ally are para­noid about ances­try, using as homo­ge­neous a sam­ple as pos­si­ble and con­trol­ling away any detectable dif­fer­ences in ances­try, GWASes can use cross-eth­nic and dif­fer­ing ances­tries in “admix­ture map­ping” to home in on causal vari­ants, but this has­n’t been done for intel­li­gence. We can note that some GWASes have com­pared how hits repli­cate across pop­u­la­tions (eg , , , , Chang et al 2011, , /Gong et al 2013, , Xing et al 2014, , Yin et al 2015, , He et al 2015); despite inter­pre­ta­tive dif­fi­cul­ties such as sta­tis­ti­cal pow­er, hits often repli­cate from Euro­pean-de­s­cent sam­ples to dis­tant eth­nic­i­ties, and the exam­ple of the schiz­o­phre­nia GWASes (Can­dia et al 2013, ) also offers hope in show­ing a strong cor­re­la­tion of 0.66/0.61 between African & Euro­pean schiz­o­phre­nia SNP-based s. (It also seems to me that there is a trend with the com­plex highly poly­genic traits hav­ing bet­ter cross-eth­nic replic­a­bil­ity than in sim­pler dis­eases.)

  1. Ntzani et al 2012, “Con­sis­tency of genome-wide asso­ci­a­tions across major ances­tral groups” /docs/genetics/correlation/2012-ntzani.pdf
  2. Marig­orta & Navarro 2013 “High Tran­s-eth­nic Replic­a­bil­ity of GWAS Results Implies Com­mon Causal Vari­ants” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3681663/

“Genetic effects influ­enc­ing risk for major depres­sive dis­or­der in China and Europe”, Bigdeli et al 2017 https://www.nature.com/tp/journal/v7/n3/full/tp2016292a.html

“Father Absence and Accel­er­ated Repro­duc­tive Devel­op­ment”, Gay­dosh et al 2017 https://www.biorxiv.org/content/biorxiv/early/2017/04/04/123711.full.pdf

“Transeth­nic dif­fer­ences in GWAS sig­nals: A sim­u­la­tion study”, Zanetti & Weale 2018

, Brown et al 2016

, Lencz et al 2013/2014: IQ PGS applied to schiz­o­phre­nia case sta­tus:

  • EA: 0.41%
  • Japan­ese: 0.38%
  • Ashke­nazi Jew: 0.16%
  • MGS African-Amer­i­can: 0.00%

myopia (re­frac­tive error): European/East Asian (Tedja et al 2018, “Genome-wide asso­ci­a­tion meta-­analy­sis high­lights light-in­duced sig­nal­ing as a dri­ver for refrac­tive error”): r_g = 0.90/0.80

“Con­sis­tent Asso­ci­a­tion of Type 2 Dia­betes Risk Vari­ants Found in Euro­peans in Diverse Racial and Eth­nic Groups”, Waters et al 2010 http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1001078 Ware et al 2017, “Het­ero­gene­ity in poly­genic scores for com­mon human traits” https://www.biorxiv.org/content/early/2017/02/05/106062 Fig­ure 3 - the height/education/etc poly­genic scores roughly 5x as pre­dic­tive in white Amer­i­cans as African-Amer­i­cans, ~0.05 R^2 vs ~0.01 R^2, and since African-Amer­i­cans aver­age about 25% white any­way, that’s con­sis­tent with 10% or less… “Using Genetic Dis­tance to Infer the Accu­racy of Genomic Pre­dic­tion”, Scu­tari et al 2016 http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1006288

Height PGSes don’t work cross­ra­cial­ly: “Human Demo­graphic His­tory Impacts Genetic Risk Pre­dic­tion across Diverse Pop­u­la­tions”, Mar­tin et al 2017 (note that this paper had ):

The vast major­ity of genome-wide asso­ci­a­tion stud­ies (GWASs) are per­formed in Euro­peans, and their trans­fer­abil­ity to other pop­u­la­tions is depen­dent on many fac­tors (e.g., link­age dis­e­qui­lib­ri­um, allele fre­quen­cies, genetic archi­tec­ture). As med­ical genomics stud­ies become increas­ingly large and diverse, gain­ing insights into pop­u­la­tion his­tory and con­se­quently the trans­fer­abil­ity of dis­ease risk mea­sure­ment is crit­i­cal. Here, we dis­en­tan­gle recent pop­u­la­tion his­tory in the widely used 1000 Genomes Project ref­er­ence pan­el, with an empha­sis on pop­u­la­tions under­rep­re­sented in med­ical stud­ies. To exam­ine the trans­fer­abil­ity of sin­gle-ances­try GWASs, we used pub­lished sum­mary sta­tis­tics to cal­cu­late poly­genic risk scores for eight well-s­tud­ied phe­no­types. We iden­tify direc­tional incon­sis­ten­cies in all scores; for exam­ple, height is pre­dicted to decrease with genetic dis­tance from Euro­peans, despite robust anthro­po­log­i­cal evi­dence that West Africans are as tall as Euro­peans on aver­age. To gain deeper quan­ti­ta­tive insights into GWAS trans­fer­abil­i­ty, we devel­oped a com­plex trait coa­les­cen­t-based sim­u­la­tion frame­work con­sid­er­ing effects of poly­genic­i­ty, causal allele fre­quency diver­gence, and her­i­tabil­i­ty. As expect­ed, cor­re­la­tions between true and inferred risk are typ­i­cally high­est in the pop­u­la­tion from which sum­mary sta­tis­tics were derived. We demon­strate that scores inferred from Euro­pean GWASs are biased by genetic drift in other pop­u­la­tions even when choos­ing the same causal vari­ants and that biases in any direc­tion are pos­si­ble and unpre­dictable. This work cau­tions that sum­ma­riz­ing find­ings from large-s­cale GWASs may have lim­ited porta­bil­ity to other pop­u­la­tions using stan­dard approaches and high­lights the need for gen­er­al­ized risk pre­dic­tion meth­ods and the inclu­sion of more diverse indi­vid­u­als in med­ical genomics.

“Tran­s-eth­nic genome-wide asso­ci­a­tion stud­ies: advan­tages and chal­lenges of map­ping in diverse pop­u­la­tions”, Li & Keat­ing 2014

“Genetic con­trib­u­tors to vari­a­tion in alco­hol con­sump­tion vary by race/ethnicity in a large mul­ti­-eth­nic genome-wide asso­ci­a­tion study”, Jor­gen­son et al 2017 /docs/genetics/correlation/2017-jorgenson.pdf

“High­-Res­o­lu­tion Genetic Maps Iden­tify Mul­ti­ple Type 2 Dia­betes Loci at Reg­u­la­tory Hotspots in African Amer­i­cans and Euro­peans”, Lau et al 2017 /docs/genetics/correlation/2017-lau.pdf

“The genomic land­scape of African pop­u­la­tions in health and dis­ease”, Rotimi et al 2017 /docs/genetics/selection/2017-rotimi.pdf

Wray et al (MDDWG PGC) 2017, “Genome-wide asso­ci­a­tion analy­ses iden­tify 44 risk vari­ants and refine the genetic archi­tec­ture of major depres­sion”:

  • European/Chinese depres­sion: rg = 0.31
  • European/Chinese schiz­o­phre­nia: rg = 0.34
  • European/Chinese bipo­lar dis­or­der: rg = 0.45

, Woj­cik et al 2017:

To demon­strate the ben­e­fit of study­ing under­rep­re­sented pop­u­la­tions, the Pop­u­la­tion Archi­tec­ture using Genomics and Epi­demi­ol­ogy (PAGE) study con­ducted a GWAS of 26 clin­i­cal and behav­ioral phe­no­types in 49,839 non-Eu­ro­pean indi­vid­u­als. Using novel strate­gies for mul­ti­-eth­nic analy­sis of admixed pop­u­la­tions, we con­firm 574 GWAS cat­a­log vari­ants across these traits, and find 28 novel loci and 42 resid­ual sig­nals in known loci. Our data show strong evi­dence of effec­t-­size het­ero­gene­ity across ances­tries for pub­lished GWAS asso­ci­a­tions, which sub­stan­tially restricts genet­i­cal­ly-guided pre­ci­sion med­i­cine. We advo­cate for new, large genome-wide efforts in diverse pop­u­la­tions to reduce health dis­par­i­ties.

Akiyama et al 2017, : r = 0.82 between top European/Japanese SNP hits

, Grinde et al 2018:

…we com­pare var­i­ous approaches for GRS con­struc­tion, using GWAS results from both large EA stud­ies and a smaller study in Hispanics/Latinos, the His­panic Com­mu­nity Health Study/Study of Lati­nos (HCHS/SOL, n=12,803). We con­sider mul­ti­ple ways to select SNPs from asso­ci­a­tion regions and to cal­cu­late the SNP weights. We study the per­for­mance of the result­ing GRSs in an inde­pen­dent study of Hispanics/Latinos from the Woman Health Ini­tia­tive (WHI, n=3,582). We sup­port our inves­ti­ga­tion with sim­u­la­tion stud­ies of poten­tial genetic archi­tec­tures in a sin­gle locus. We observed that select­ing vari­ants based on EA GWASs gen­er­ally per­forms well, as long as SNP weights are cal­cu­lated using Hispanics/Latinos GWASs, or using the meta-­analy­sis of EA and Hispanics/Latinos GWASs. The opti­mal approach depends on the genetic archi­tec­ture of the trait.

, Mogil et al 2018: causal vari­ants are mostly shared cross-ra­cially despite dif­fer­ent LD pat­terns, as indi­cated by sim­i­lar gene expres­sion effects?

, Liu et al 2015:

Con­sis­tent with the con­cor­dant direc­tion of effect at asso­ci­ated SNPs, there was high genetic cor­re­la­tion (rG) between the Euro­pean and East Asian cohort when con­sid­er­ing the addi­tive effects of all SNPs geno­typed on the Immunochip19 (Crohn’s dis­ease rG = 0.76, ulcer­a­tive col­i­tis rG = 0.79) (Sup­ple­men­tary Table 11). Given that rare SNPs (mi­nor allele fre­quency (MAF) < 1%) are more likely to be pop­u­la­tion-speci­fic, these high rG val­ues also sup­port the notion that the major­ity of causal vari­ants are com­mon (MAF>5%).

, Wang et al 2020:

Poly­genic scores (PGS) have been widely used to pre­dict com­plex traits and risk of dis­eases using vari­ants iden­ti­fied from genome-wide asso­ci­a­tion stud­ies (GWASs). To date, most GWASs have been con­ducted in pop­u­la­tions of Euro­pean ances­try, which lim­its the use of GWAS-derived PGS in non-Eu­ro­pean pop­u­la­tions. Here, we develop a new the­ory to pre­dict the rel­a­tive accu­racy (RA, rel­a­tive to the accu­racy in pop­u­la­tions of the same ances­try as the dis­cov­ery pop­u­la­tion) of PGS across ances­tries. We used sim­u­la­tions and real data from the UK Biobank to eval­u­ate our results. We found across var­i­ous sim­u­la­tion sce­nar­ios that the RA of PGS based on trait-as­so­ci­ated SNPs can be pre­dicted accu­rately from mod­el­ling link­age dis­e­qui­lib­rium (LD), minor allele fre­quen­cies (MAF), cross-pop­u­la­tion cor­re­la­tions of SNP effect sizes and her­i­tabil­i­ty. Alto­geth­er, we find that LD and MAF dif­fer­ences between ances­tries explain alone up to ~70% of the loss of RA using Euro­pean-based PGS in African ances­try for traits like body mass index and height. Our results sug­gest that causal vari­ants under­ly­ing com­mon genetic vari­a­tion iden­ti­fied in Euro­pean ances­try GWASs are mostly shared across con­ti­nents.

“Poly­genic pre­dic­tion of the phe­nome, across ances­try, in emerg­ing adult­hood”, Docherty et al 2017 (sup­ple­ment): large loss of PGS power in many traits, but direct com­par­i­son seems to be unavail­able for most of the PGSes other than stuff like height?

“Genet­ics of self­-re­ported risk-­tak­ing behav­iour, tran­s-eth­nic con­sis­tency and rel­e­vance to brain gene expres­sion”, Straw­bridge et al 2018:

There were strong pos­i­tive genetic cor­re­la­tions between risk-­tak­ing and atten­tion-d­eficit hyper­ac­tiv­ity dis­or­der, bipo­lar dis­or­der and schiz­o­phre­nia. Index genetic vari­ants demon­strated effects gen­er­ally con­sis­tent with the dis­cov­ery analy­sis in indi­vid­u­als of non-Bri­tish White, South Asian, African-­Caribbean or mixed eth­nic­i­ty.

, Reis­berg et al 2017:

Poly­genic risk scores are gain­ing more and more atten­tion for esti­mat­ing genetic risks for lia­bil­i­ties, espe­cially for non­com­mu­ni­ca­ble dis­eases. They are now cal­cu­lated using thou­sands of DNA mark­ers. In this paper, we com­pare the score dis­tri­b­u­tions of two pre­vi­ously pub­lished very large risk score mod­els within dif­fer­ent pop­u­la­tions. We show that the risk score model together with its risk strat­i­fi­ca­tion thresh­olds, built upon the data of one pop­u­la­tion, can­not be applied to another pop­u­la­tion with­out tak­ing into account the tar­get pop­u­la­tion’s struc­ture. We also show that if an indi­vid­ual is clas­si­fied to the wrong pop­u­la­tion, his/her dis­ease risk can be sys­tem­at­i­cally incor­rectly esti­mat­ed.

, Dun­can et al 2018:

We ana­lyzed the first decade of poly­genic scor­ing stud­ies (2008-2017, inclu­sive), and found that 67% of stud­ies included exclu­sively Euro­pean ances­try par­tic­i­pants and another 19% included only East Asian ances­try par­tic­i­pants. Only 3.8% of stud­ies were car­ried out on sam­ples of African, His­pan­ic, or Indige­nous peo­ples. We find that effect sizes for Euro­pean ances­try-derived poly­genic scores are only 36% as large in African ances­try sam­ples, as in Euro­pean ances­try sam­ples (t=-10.056, df=22, p=5.5x10-10). Poorer per­for­mance was also observed in other non-Eu­ro­pean ances­try sam­ples. Analy­sis of poly­genic scores in the 1000Genomes sam­ples revealed many strong cor­re­la­tions with global prin­ci­pal com­po­nents, and rela­tion­ships between height poly­genic scores and height phe­no­types that were highly vari­able depend­ing on method­olog­i­cal choices in poly­genic score con­struc­tion.

“Tran­sances­tral GWAS of alco­hol depen­dence reveals com­mon genetic under­pin­nings with psy­chi­atric dis­or­ders”, Wal­ters et al 2018:

PRS based on our meta-­analy­sis of AD were sig­nif­i­cantly pre­dic­tive of AD out­comes in all three tested exter­nal cohorts. PRS derived from the unre­lated EU GWAS pre­dicted up to 0.51% of the vari­ance in past month alco­hol use dis­or­der in the Avon Lon­gi­tu­di­nal Study of Par­ents and Chil­dren (ALSPAC; P=0.0195; Sup­ple­men­tary Fig. 10a) and up to 0.3% of prob­lem drink­ing in Gen­er­a­tion Scot­land (P=7.9×10-6; Sup­ple­men­tary Fig. 10b) as indexed by the CAGE (Cut­ting down, Annoy­ance by crit­i­cism, Guilty feel­ings, and Eye­-open­ers) ques­tion­naire. PRS derived from the unre­lated AA GWAS pre­dicted up to 1.7% of the vari­ance in alco­hol depen­dence in the COGA AAfGWAS cohort (P=1.92×10-7; Sup­ple­men­tary Fig. 10c). Notably, PRS derived from the unre­lated EU GWAS showed much weaker pre­dic­tion (max­i­mum r2=0.37%, P=0.01; Sup­ple­men­tary Fig. 10d) in the COGA AAfGWAS than the ances­trally matched AA GWAS-based PRS despite the much smaller dis­cov­ery sam­ple for AA. In addi­tion, the AA GWAS-based AD PRS also still yielded sig­nif­i­cant vari­ance explained after con­trol­ling for other genetic fac­tors (r2=1.16%, P=2.5×10-7). Pre­dic­tion of CAGE scores in Gen­er­a­tion Scot­land remained sig­nif­i­cant and showed min­i­mal atten­u­a­tion (r2=0.29%, P=1.0×10-5) after con­di­tion­ing on PRS for alco­hol con­sump­tion derived from UK Biobank results17. In COGA AAfGWAS, the AA PRS derived from our study con­tin­ued to pre­dict 1.6% of the vari­ance in alco­hol depen­dence after inclu­sion of rs2066702 geno­type as a covari­ate, indi­cat­ing inde­pen­dent poly­genic effects beyond the lead ADH1B vari­ant (Sup­ple­men­tary Meth­od­s).

So EU->AA PGS is 0.37/1.7=21%?

, Telkar et al 2019:

A poly­genic score based on estab­lished LDL-cholesterol-associated loci from Euro­pean dis­cov­ery sam­ples had con­sis­tent effects on serum lev­els in sam­ples from the UK, Uganda and Greek pop­u­la­tion iso­lates (cor­re­la­tion coef­fi­cient r=0.23 to 0.28 per LDL stan­dard devi­a­tion, p<1.9x10-14). Tran­s-eth­nic genetic cor­re­la­tions between Euro­pean ances­try, Chi­nese and Japan­ese cohorts did not dif­fer sig­nif­i­cantly from 1 for HDL, LDL and triglyc­erides. In each study, >60% of major lipid loci dis­played evi­dence of repli­ca­tion with one excep­tion. There was evi­dence for an effect on serum lev­els in the Ugan­dan sam­ples for only 10% of major triglyc­eride loci. The PRS was only weakly asso­ci­ated in this group (r=0.06, SE=0.013).

“Iden­ti­fi­ca­tion of 28 new sus­cep­ti­bil­ity loci for type 2 dia­betes in the Japan­ese pop­u­la­tion”, Suzuki et al 2019:

When we com­pared the effect sizes of 69 of the 88 lead vari­ants in Japan­ese and Euro­peans that were avail­able in a pub­lished Euro­pean GWAS2 (Sup­ple­men­tary Table 3 and Sup­ple­men­tary Fig. 5), we found a strong pos­i­tive cor­re­la­tion (Pear­son’s r= 0.87, P= 1.4 × 10−22) and direc­tional con­sis­tency (65 of 69 loci, 94%, sign-test P= 3.1 × 10−15). In addi­tion, when we com­pared the effect sizes of the 95 of 113 lead vari­ants reported in the Euro­pean type 2 dia­betes GWAS2 that were avail­able in both Japan­ese and Euro­pean type 2 dia­betes GWAS (Sup­ple­men­tary Table 2 and Sup­ple­men­tary Fig. 6a), we also found a strong pos­i­tive cor­re­la­tion (Pear­son’s r= 0.74, P= 5.9 × 10−18) and direc­tional con­sis­tency (83 of 95 loci, 87%, sign-test P= 3.2 × 10−14). After this man­u­script was sub­mit­ted, a larger type 2 dia­betes GWAS of Euro­pean ances­try was pub­lished17. When we repeated the com­par­i­son at the lead vari­ants reported in this larger Euro­pean GWAS, we found a more promi­nent cor­re­la­tion (Pear­son’s r= 0.83, P= 8.7 × 10−51) and direc­tional con­sis­tency (181 of 192 loci, 94%, sign-test P= 8.3 × 10−41) of the effect sizes (Sup­ple­men­tary Table 4 and Sup­ple­men­tary Fig. 6b). These results indi­cate that most of the type 2 dia­betes sus­cep­ti­bil­ity loci iden­ti­fied in the Japan­ese or Euro­pean pop­u­la­tion had com­pa­ra­ble effects on type 2 dia­betes in the other pop­u­la­tion.

, Spracklen et al 2019:

Over­all, the per-al­lele effect sizes between the two ances­tries were mod­er­ately cor­re­lated (r=0.54; Fig­ure 2A). When the com­par­i­son was restricted to the 290 vari­ants that are com­mon (MAF≥5%) in both ances­tries, the effect size cor­re­la­tion increased to r=0.71 (Fig­ure 2B; Sup­ple­men­tary Fig­ure 8). This effect size cor­re­la­tion fur­ther increased to r=0.88 for 116 vari­ants sig­nif­i­cantly asso­ci­ated with T2D (P<5x10-8) in both ances­tries. While the over­all effect sizes for all 343 vari­ants appear, on aver­age, to be stronger in East Asian indi­vid­u­als than Euro­pean, this trend is reduced when each locus is rep­re­sented only by the lead vari­ant from one pop­u­la­tion (Sup­ple­men­tary Fig­ure 9). Specif­i­cal­ly, many vari­ants iden­ti­fied with larger effect sizes in the Euro­pean meta-­analy­sis are miss­ing from the com­par­i­son because they were rare/monomorphic or poorly imputed in the East Asian meta-­analy­sis, for which impu­ta­tion ref­er­ence pan­els are less com­pre­hen­sive com­pared to the Euro­pean-­cen­tric Hap­lo­type Ref­er­ence Con­sor­tium pan­el.

“Genetic analy­ses of diverse pop­u­la­tions improves dis­cov­ery for com­plex traits”, Woj­cik

When strat­i­fied by self­-i­den­ti­fied race/ethnicity, the effect sizes for the Hispanic/Latino pop­u­la­tion remained sig­nif­i­cantly atten­u­ated com­pared to the pre­vi­ously reported effect sizes (β= 0.86; 95% con­fi­dence inter­val = 0.83–0.90; Fig. 2a). Effect sizes for the African Amer­i­can pop­u­la­tion were even fur­ther dimin­ished at nearly half the strength (β= 0.54; 95% con­fi­dence inter­val = 0.50–0.58; Fig. 2a). This is sug­ges­tive of truly dif­fer­en­tial effect sizes between ances­tries at pre­vi­ously reported vari­ants, rather than these effect sizes being upwardly biased in gen­eral (that is, exhibit­ing ‘win­ner’s curse’), which should affect all groups equal­ly.

“Con­tri­bu­tions of com­mon genetic vari­ants to risk of schiz­o­phre­nia among indi­vid­u­als of African and Latino ances­try”, Bigdeli et al 2019:

Con­sis­tent with pre­vi­ous reports demon­strat­ing the gen­er­al­iz­abil­ity of poly­genic find­ings for schiz­o­phre­nia across diverse pop­u­la­tions [14, 43, 44], indi­vid­u­al-level scores con­structed from PGC-SCZ2 sum­mary sta­tis­tics were sig­nif­i­cantly asso­ci­ated with case−­con­trol sta­tus in admixed African, Lati­no, and Euro­pean cohorts in the cur­rent study (Fig. 2a). When con­sid­er­ing scores con­structed from approx­i­mately inde­pen­dent com­mon vari­ants (pair­wise r2 < 0.1), we observed the best over­all pre­dic­tion at a P value thresh­old (PT) of 0.05; these scores explained ~3.5% of the vari­ance in schiz­o­phre­nia lia­bil­ity among Euro­peans (P = 4.03 × 10−110), ~1.7% among Latino indi­vid­u­als (P = 9.02 × 10−52), and ~0.5% among admixed African indi­vid­u­als (P = 8.25 × 10−19) (Fig. 2a; Sup­ple­men­tal Table 6). Con­sis­tent with expec­ta­tion, when com­par­ing results for scores con­structed from larger num­bers of non­in­de­pen­dent SNPs, we gen­er­ally observed an improve­ment in pre­dic­tive value (Fig. 2b; Sup­ple­men­tal Table 7).

Poly­genic scores based on African ances­try GWAS results were sig­nif­i­cantly asso­ci­ated with schiz­o­phre­nia among admixed African indi­vid­u­als, attain­ing the best over­all pre­dic­tive value when con­structed from approx­i­mately inde­pen­dent com­mon vari­ants (pair­wise r2 < 0.1) with PT ≤ 0.5 in the dis­cov­ery analy­sis (Fig. 2a and Sup­ple­men­tal Table 6); this score explained ~1.3% of the vari­ance in schiz­o­phre­nia lia­bil­ity (P = 3.47 × 10−41). Scores trained on African ances­try GWAS results also sig­nif­i­cantly pre­dicted case−­con­trol sta­tus across pop­u­la­tions; scores based on a PT ≤ 0.5 and pair­wise r2 < 0.8 explained ~0.2% of the vari­abil­ity in lia­bil­ity in Euro­peans (P = 2.35 × 10−7) and ~0.1% among Latino indi­vid­u­als (P = 0.000184) (Fig. 2b and Sup­ple­men­tal Table 7). Sim­i­lar­ly, scores con­structed from Latino GWAS results (PT ≤ 0.5) were of great­est pre­dic­tive value among Lati­nos (li­a­bil­ity R2 = 2%; P = 3.11 × 10−19) and Euro­peans (li­a­bil­ity R2 = 0.8%; P = 1.60 × 10−9); with scores based on PT ≤ 0.05 and pair­wise r2 < 0.1 show­ing nom­i­nally sig­nif­i­cant asso­ci­a­tion with case-­con­trol sta­tus among African ances­try indi­vid­u­als (li­a­bil­ity R2 = 0.2%; P = 0.00513).

We next con­sid­ered poly­genic scores con­structed from tran­s-ances­try meta-­analy­sis of PGC-SCZ2 sum­mary sta­tis­tics and our African and Latino GWAS, which revealed increased sig­nif­i­cance and improved pre­dic­tive value in all three ances­tries. Among African ances­try indi­vid­u­als, meta-­an­a­lytic scores based on PT ≤ 0.5 explained ~1.7% of the vari­ance (P = 4.37 × 10−53); while scores based on PT ≤ 0.05 accounted for ~2.1% and ~3.7% of the vari­abil­ity in lia­bil­ity among Latino (P = 1.10 × 10−59) and Euro­pean indi­vid­u­als (P = 1.73 × 10−114), respec­tive­ly.

, Guo et al 2019:

Genome-wide asso­ci­a­tion stud­ies (GWAS) in sam­ples of Euro­pean ances­try have iden­ti­fied thou­sands of genetic vari­ants asso­ci­ated with com­plex traits in humans. How­ev­er, it remains largely unclear whether these asso­ci­a­tions can be used in non-Eu­ro­pean pop­u­la­tions. Here, we seek to quan­tify the pro­por­tion of genetic vari­a­tion for a com­plex trait shared between con­ti­nen­tal pop­u­la­tions. We esti­mated the between-pop­u­la­tion cor­re­la­tion of genetic effects at all SNPs (rg) or genome-wide sig­nif­i­cant SNPs (rg(GWS)) for height and body mass index (BMI) in sam­ples of Euro­pean (EUR; n = 49,839) and African (AFR; n = 17,426) ances­try. The rg between EUR and AFR was 0.75 (s. e. = 0.035) for height and 0.68 (s. e. = 0.062) for BMI, and the cor­re­spond­ing rg(g­was) was 0.82 (s. e. = 0.030) for height and 0.87 (s. e. = 0.064) for BMI, sug­gest­ing that a large pro­por­tion of GWAS find­ings dis­cov­ered in Euro­peans are likely applic­a­ble to non-Eu­ro­peans for height and BMI. There was no evi­dence that rg dif­fers in SNP groups with dif­fer­ent lev­els of between-pop­u­la­tion dif­fer­ence in allele fre­quency or link­age dis­e­qui­lib­ri­um, which, how­ev­er, can be due to the lack of pow­er.

, Koyama et al 2019:

To elu­ci­date the genet­ics of coro­nary artery dis­ease (CAD) in the Japan­ese pop­u­la­tion, we con­ducted a large-s­cale genome-wide asso­ci­a­tion study (GWAS) of 168,228 Japan­ese (25,892 cases and 142,336 con­trols) with geno­type impu­ta­tion using a newly devel­oped ref­er­ence panel of Japan­ese hap­lo­types includ­ing 1,782 CAD cases and 3,148 con­trols. We detected 9 novel dis­ease-­sus­cep­ti­bil­ity loci and Japan­ese-spe­cific rare vari­ants con­tribut­ing to dis­ease sever­ity and increased car­dio­vas­cu­lar mor­tal­i­ty. We then con­ducted a transeth­nic meta-­analy­sis and dis­cov­ered 37 addi­tional novel loci. Using the result of the meta-­analy­sis, we derived a poly­genic risk score (PRS) for CAD, which out­per­formed those derived from either Japan­ese or Euro­pean GWAS. The PRS pri­or­i­tized risk fac­tors among var­i­ous clin­i­cal para­me­ters and seg­re­gated indi­vid­u­als with increased risk of long-term car­dio­vas­cu­lar mor­tal­i­ty. Our data improves clin­i­cal char­ac­ter­i­za­tion of CAD genet­ics and sug­gests the util­ity of transeth­nic meta-­analy­sis for PRS deriva­tion in non-Eu­ro­pean pop­u­la­tions.

, Ekoru et al 2020:

There is grow­ing sup­port for the use of genetic risk scores (GRS) in rou­tine clin­i­cal set­tings. Due to the lim­ited diver­sity of cur­rent genomic dis­cov­ery sam­ples, there are con­cerns that the pre­dic­tive power of GRS will be lim­ited in non-Eu­ro­pean ances­try pop­u­la­tions. Here, we eval­u­ated the pre­dic­tive util­ity of GRS for 12 car­diometa­bolic traits in sub­-Sa­ha­ran Africans (AF; n=5200), African Amer­i­cans (AA; n=9139), and Euro­pean Amer­i­cans (EA; n=9594). GRS were con­structed as weighted sums of the num­ber of risk alle­les. Pre­dic­tive util­ity was assessed using the addi­tional phe­no­typic vari­ance explained and increase in dis­crim­i­na­tory abil­ity over tra­di­tional risk fac­tors (age, sex and BMI), with adjust­ment for ances­try-derived prin­ci­pal com­po­nents. Across all traits, GRS showed upto a 5-fold and 20-­fold greater pre­dic­tive util­ity in EA rel­a­tive to AA and AF, respec­tive­ly. Pre­dic­tive util­ity was most con­sis­tent for lipid traits, with per­cent increase in explained vari­a­tion attrib­ut­able to GRS rang­ing from 10.6% to 127.1% among EA, 26.6% to 65.8% among AA, and 2.4% to 37.5% among AF. These dif­fer­ences were reca­pit­u­lated in the dis­crim­i­na­tory pow­er, whereby the pre­dic­tive util­ity of GRS was 4-fold greater in EA rel­a­tive to AA and up to 44-­fold greater in EA rel­a­tive to AF. Obe­sity and blood pres­sure traits showed a sim­i­lar pat­tern of greater pre­dic­tive util­ity among EA.


Given the prac­tice of embryo edit­ing, the causal tag­ging prob­lem can grad­u­ally solve itself: as edits are made, forcibly break­ing the poten­tial con­founds, the causal nature of an SNP becomes clear. But how to allo­cate edits across the top SNPs to deter­mine each’s causal nature as effi­ciently as pos­si­ble with­out spend­ing too many edits inves­ti­gat­ing? A naive answer might be some­thing along the lines of a power analy­sis: in a two-­group t-test try­ing to detect a dif­fer­ence of ~0.03 SD for each vari­ant (the rough size of the top few vari­ants), with vari­ance reduced by the known poly­genic score, and desired power is the stan­dard 80%; it fol­lows that one would need to ran­dom­ize a total sam­ple of n = 34842 to reject the null hypoth­e­sis of 0 effect20. Set­ting up a & ran­dom­iz­ing sev­eral vari­ants simul­ta­ne­ously may allow infer­ences on them as well, but clearly this is going to be a tough row to hoe. This is unduly pes­simistic, since we nei­ther need nor desire 80% pow­er, nor are we com­par­ing to a null hypoth­e­sis, as our goal is more mod­est: since only a cer­tain num­ber of edits will be doable for any embryo, say 30, we merely want to accu­mu­late enough evi­dence about the top 30 vari­ants to either demote it to #31 (and so we no longer spend any edits on it) or con­firm it belongs in the top 30 and we should always be edit­ing it. This is imme­di­ately rec­og­niz­able as : the (each pos­si­ble edit being an inde­pen­dent arm which can pulled or not); or more pre­cise­ly, since early child­hood (5yo) IQ scores are rel­a­tively poorly cor­re­lated with adult scores (r = 0.55) and many embryos may be edited before data on the first edits starts com­ing in, a mul­ti­-armed ban­dit with mul­ti­ple plays and delayed feed­back. (There is no way imme­di­ately upon birth to receive mean­ing­ful feed­back about the effect of an edit, although there might be ways to get feed­back faster, such as using short­-sleeper gene edits to enhance edu­ca­tion.) is a ran­dom­ized Bayesian approach which is sim­ple and the­o­ret­i­cally opti­mal, with excel­lent per­for­mance in prac­tice as well; an is also opti­mal. Deal­ing with the delayed feed­back is known to be dif­fi­cult and mul­ti­ple-­play Thomp­son sam­pling may not be opti­mal, but in sim­u­la­tions it per­forms bet­ter with delayed feed­back than other stan­dard MABs. We can con­sider a sim­u­la­tion of the sce­nario in which every time-step is a day and 1 or more embryos must be edited that day; a noisy mea­sure of IQ is then made avail­able 9*31+5*365=2104 days lat­er, which is fed into a GWAS in which the GWAS cor­re­la­tion for each SNP is con­sid­ered as drawn with an unknown prob­a­bil­ity from a causal dis­tri­b­u­tion and from a nui­sance dis­tri­b­u­tion, so with addi­tional data, the effect esti­mates of the SNPs are refined, the prob­a­bil­ity of being drawn from the causal dis­tri­b­u­tion is refined, and the over­all mix­ture prob­a­bil­ity is like­wise refined, sim­i­lar to the . (So for the first 2104 time-steps, a Thomp­son sam­ple would be per­formed to yield a new set of edits, then each sub­se­quent time-step a dat­a­point would mature, the pos­te­ri­ors updat­ed, and another set of edits cre­at­ed.) The rel­e­vant ques­tion is how much regret will fall and how many causal SNPs become the top picks after how many edits & days: hope­fully high per­for­mance & low regret will be achieved within a few years after the ini­tial 5-year delay.

a more con­crete exam­ple: imag­ine we have a bud­get of 60 edits (based on the mul­ti­plex pig edit­ing), a causal prob­a­bil­ity of 10%, an expo­nen­tial dis­tri­b­u­tion (rate 70.87) over 500000 can­di­date alle­les of which we con­sider the top 1000, each of which has a fre­quency of 50% and we sequence before edit­ing to avoid wast­ing edits. What is our best case and worst-­case IQ increase? In the worst case, the top 60 are all non-­causal, so our improve­ment is 0 IQ points; in the best case where all hits are causal, half of the hits are dis­carded after sequenc­ing, and then the remain­ing top 60 get us ~6.1 IQ points; the inter­me­di­ate case of 10% causal gets us to ~0.61 IQ points, and so our regret is 5.49 IQ points per embryo. Unsur­pris­ing­ly, a 10% causal rate is hor­ri­bly inef­fi­cient. In the 10% case, if we can infer the true causal SNPs, we only need to start with ~600 SNPs to sat­u­rate our edit­ing bud­get on aver­age, or ~900 to have <1% chance of wind­ing up with <60 causal SNPs, so 1000 SNPs seems like a good start­ing point. (Of course, we also want a larger win­dow so as our edit bud­get increases with future income growth & tech­no­log­i­cal improve­ment, we can smoothly incor­po­rate the addi­tional SNPs.) So what order of sam­ples do we need here to reduce our regret of 5.49 to some­thing more rea­son­able like <0.25 IQ points?

SNPs <- 500000
SNPlimit <- 1000
rate <- 70.87
editBudget <- 60
frequency <- 0.5
mean(replicate(1000, {
    hits <- sort(rexp(SNPs, rate=rate), decreasing=TRUE)[1:SNPlimit]
    sum(sample(hits, length(hits) * 0.5)[1:editBudget])
    }))

http://jmlr.csail.mit.edu/proceedings/papers/v31/agrawal13a.pdf Regret of Thomp­son sam­pling with Gauss­ian pri­ors & like­li­hood is O(sqrt(N * T * ln(N))), where N = num­ber of dif­fer­ent arms/actions and T = cur­rent timestep hence, if we have 1000 actions and we sam­ple 1 time, our expected total regret is on the order of sqrt(1000 * 1 * ln(1000)) = 83; with 100 sam­ples, our expected total regret has increased by two orders to 831 but we are only incur­ring an addi­tional expected regret of ~4 or 5% of the first timestep’s regret dif­f(s­ap­ply((1:10000, func­tion(t) { sqrt(1000 * t * log(1000)) } )))

Thomp­son sam­pling also achieves the lower bound in mul­ti­ple-­play but the asymp­totic is more com­plex, and does not take into account the long delay & noise in mea­sur­ing IQ. TS empir­i­cally per­forms well but hard to know what sort of sam­ple size is required. But at least we can say that the asymp­tot­ics don’t imply dozens of thou­sands of embryos.

prob­lem: what’s the prob­a­bil­ity of non-­causal tag­ging due to LD? prob­a­bly low since they work cross-eth­ni­cally don’t they? on the other hand: http://emilkirkegaard.dk/en/?p=5415 "If the GWAS SNPs owe their pre­dic­tive power to being actual causal vari­ants, then LD is irrel­e­vant and they should pre­dict the rel­e­vant out­come in any racial group. If how­ever they owe wholly or partly their pre­dic­tive power to just being sta­tis­ti­cally related to causal vari­ants, they should be rel­a­tively worse pre­dic­tors in racial groups that are most dis­tantly relat­ed. One can inves­ti­gate this by com­par­ing the pre­dic­tive power of GWAS betas derived from one pop­u­la­tion on another pop­u­la­tion. Since there are by now 1000s of GWAS, meta-­analy­ses have in fact made such com­par­isons, mostly for dis­ease traits. Two reviews found sub­stan­tial cross-­va­lid­ity for the Eurasian pop­u­la­tion (Eu­ro­peans and East Asian­s), and less for Africans (usu­ally African Amer­i­cans) (23,24). The first review only relied on SNPs with p<α and found weaker results. This is expected because using only these is a thresh­old effect, as dis­cussed ear­li­er.

The sec­ond review (from 2013; 299 included GWAS) found much stronger results, prob­a­bly because it included more SNPs and because they also adjusted for sta­tis­ti­cal pow­er. Doing so, they found that: ~100% of SNPs repli­cate in other Euro­pean sam­ples when account­ing for sta­tis­ti­cal pow­er, ~80% in East Asian sam­ples but only ~10% in the African Amer­i­can sam­ple (not adjusted for sta­tis­ti­cal pow­er, which was ~60% on aver­age). There were fairly few GWAS for AAs how­ev­er, so some cau­tion is needed in inter­pret­ing the num­ber. Still, this throws some doubt on the use­ful­ness of GWAS results from Euro­peans or Asians used on African sam­ples (or reverse­ly)." and http://emilkirkegaard.dk/en/?p=6415

“Iden­ti­fy­ing Causal Vari­ants at Loci with Mul­ti­ple Sig­nals of Asso­ci­a­tion”, Hor­moz­di­ari et al 2014 http://genetics.org/content/198/2/497.full “Where is the causal vari­ant? On the advan­tage of the fam­ily design over the case-­con­trol design in genetic asso­ci­a­tion stud­ies”, Dandine-Roul­land & Perdry 2015 http://www.nature.com/ejhg/journal/v23/n10/abs/ejhg2014284a.html worst-­case, ~10% of SNPs are causal?


https://www.addgene.org/crispr/reference/ http://www.genome.gov/sequencingcosts/ https://crispr.bme.gatech.edu/ http://crispr.mit.edu/ low, near zero muta­tion rates: “High­-­fi­delity CRISPR-Cas9 nucle­ases with no detectable genome-wide off-­tar­get effects” Kle­in­stiver et al 2016, /docs/genetics/editing/2016-kleinstiver.pdf ; “Ratio­nally engi­neered Cas9 nucle­ases with improved speci­ficity”, Slay­maker et al 2016 /docs/genetics/editing/2016-slaymaker.pdf Church, April 2016: “Indeed, the lat­est ver­sions of gene-edit­ing enzymes have zero detectable off-­tar­get activ­i­ties.” http://www.wsj.com/articles/should-heritable-gene-editing-be-used-on-humans-1460340173 Church, June 2016 “Church: In prac­tice, when we intro­duced our first CRISPR in 2013,19 it was about 5% off tar­get. In other words, CRISPR would edit five treated cells out of 100 in the wrong place in the genome. Now, we can get down to about one error per 6 tril­lion cell­s…­Fahy: Just how effi­cient is CRISPR at edit­ing tar­geted genes? Church: With­out any par­tic­u­lar tricks, you can get any­where up to, on the high end, into the range of 50% to 80% or more of tar­geted genes actu­ally get­ting edited in the intended way. Fahy: Why not 100%? Church: We don’t really know, but over time, we’re get­ting closer and closer to 100%, and I sus­pect that some­day we will get to 100%. Fahy: Can you get a higher per­cent­age of suc­cess­ful gene edits by dos­ing with CRISPR more than once? Church: Yes, but there are lim­its.” http://www.lifeextension.com/Lpages/2016/CRISPR/index “A per­son famil­iar with the research says ‘many tens’ of human IVF embryos were cre­ated for the exper­i­ment using the donated sperm of men car­ry­ing inher­ited dis­ease muta­tions. Embryos at this stages are tiny clumps of cells invis­i­ble to the naked eye. ‘It is proof of prin­ci­ple that it can work. They sig­nif­i­cantly reduced mosaicism. I don’t think it’s the start of clin­i­cal tri­als yet, but it does take it fur­ther than any­one has before’, said a sci­en­tist famil­iar with the pro­ject. Mital­ipov’s group appears to have over­come ear­lier dif­fi­cul­ties by ‘get­ting in early’ and inject­ing CRISPR into the eggs at the same time they were fer­til­ized with sperm.” https://www.technologyreview.com/s/608350/first-human-embryos-edited-in-us/ cost of the top vari­ants? want to edit all vari­ants such that: sequenc­ing-based edit: pos­te­rior mean * value of IQ point > cost of 1 edit for blind edits: prob­a­bil­ity of the bad vari­ant * pos­te­rior mean * value of IQ point > cost of 1 edit

how to sim­u­late pos­te­rior prob­a­bil­i­ties? https://cran.r-project.org/web/packages/BGLR/BGLR.pdf https://cran.r-project.org/web/packages/BGLR/vignettes/BGLR-extdoc.pdf looks use­ful but won’t han­dle the mix­ture mod­el­ing

pre­vi­ous: Liang et al 2015 “CRISPR/Cas9-mediated gene edit­ing in human tripronu­clear zygotes” http://link.springer.com/article/10.1007/s13238-015-0153-5%20/fulltext.html http://www.nature.com/news/chinese-scientists-genetically-modify-human-embryos-1.17378 Kang et al 2016, “Intro­duc­ing pre­cise genetic mod­i­fi­ca­tions into human 3PN embryos by CRISPR/Cas-mediated genome edit­ing” /docs/genetics/editing/2016-kang.pdf http://www.nature.com/news/second-chinese-team-reports-gene-editing-in-human-embryos-1.19718 Komor et al 2016, “Pro­gram­ma­ble edit­ing of a tar­get base in genomic DNA with­out dou­ble-s­tranded DNA cleav­age” https://ase.tufts.edu/chemistry/kumar/jc/pdf/Liu_2016.pdf http://www.nature.com/news/chinese-scientists-to-pioneer-first-human-crispr-trial-1.20302 “CRISPR/Cas9-mediated gene edit­ing in human zygotes using Cas9 pro­tein” Tang et al 2017 /docs/genetics/editing/2017-tang.pdf : no observed off-­tar­get muta­tions; effi­ciency of 20%, 50%, and 100% “Cor­rec­tion of a path­o­genic gene muta­tion in human embryos”, Ma et al 2017 https://www.nature.com/articles/nature23305 no observed off-­tar­gets, 27.9% effi­ciency

legal in USA (no leg­is­la­tion but some inter­est­ing reg­u­la­tory wrin­kles: see ch7 of Human Genome Edit­ing: Sci­ence, Ethics, and Gov­er­nance 2017 ), legal in China (only ‘unen­force­able guide­lines’) as of 2014, accord­ing to “Inter­na­tional reg­u­la­tory land­scape and inte­gra­tion of cor­rec­tive genome edit­ing into in vitro fer­til­iza­tion”, Araki & Ishii 2014 http://rbej.biomedcentral.com/articles/10.1186/1477-7827-12-108 as of 2015 too accord­ing to http://www.nature.com/news/where-in-the-world-could-the-first-crispr-baby-be-born-1.18542 ille­gal in the UK but they have given per­mis­sion to mod­ify human embryos for research http://www.popsci.com/scientists-get-government-approval-to-edit-human-embryos? http://www.nytimes.com/2016/02/02/health/crispr-gene-editing-human-embryos-kathy-niakan-britain.html legal in Japan for research, but maybe not appli­ca­tion? http://mainichi.jp/english/articles/20160423/p2g/00m/0dm/002000c legal in Swe­den for edit­ing, which has been done as of Sep­tem­ber 2016 by Fredrik Lan­ner http://www.npr.org/sections/health-shots/2016/09/22/494591738/breaking-taboo-swedish-scientist-seeks-to-edit-dna-of-healthy-human-embryos

Also, what about mosaicism? When the CRISPR RNA is injected into an even sin­gle-­celled zygote, it may already have cre­ated some of the DNA for a split and so the edit cov­ers only a frac­tion of the cells of the future ful­l-­grown organ­ism. “Addi­tion­al­ly, edit­ing may hap­pen after first embry­onic divi­sion, due to per­sis­tence of Cas9:gRNA com­plex­es, also caus­ing mosaicism. We (un­pub­lished results) and oth­ers (Yang et al. 2013a; Ma et al. 2014; Yen et al. 2014) have observed mosaic ani­mals car­ry­ing three or more alle­les. A recent study reported sur­pris­ingly high per­cent­age of mosaic mice (up to 80%) gen­er­ated by CRISPR tar­get­ing of the tyrosi­nase gene (Tyr) (Yen et al. 2014). We have observed a vary­ing fre­quency of mosaicism, 11-35%, depend­ing on the gene/locus (our unpub­lished data)… The pronu­clear microin­jec­tion of gRNA and Cas9, in a man­ner essen­tially iden­ti­cal to what is used for gen­er­at­ing trans­genic mice, can be eas­ily adapted by most trans­genic facil­i­ties. Facil­i­ties equipped with a Piezo-­elec­tric micro­ma­nip­u­la­tor can opt for cyto­plas­mic injec­tions as reported (Wang et al. 2013; Yang et al. 2013a). Horii et al. (2014) per­formed an exten­sive com­par­i­son study sug­gest­ing that cyto­plas­mic injec­tion of a gRNA and Cas9 mRNA mix­ture as the best deliv­ery method. Although the over­all edit­ing effi­ciency in born pups yielded by pronu­clear vs. cyto­plas­mic RNA injec­tion seems to be com­pa­ra­ble (Table 1), the lat­ter method gen­er­ated two- to four­fold more live born pups. Injec­tion of plas­mid DNA car­ry­ing Cas9 and gRNA to the pronu­cleus was the least effi­cient method in terms of sur­vival and tar­get­ing effi­ciency (Mashiko et al. 2013; Horii et al. 2014). Injec­tion into pronu­clei seems to be more dam­ag­ing to embryos than injec­tion of the same vol­ume or con­cen­tra­tion of edit­ing reagents to the cyto­plasm. It has been shown that cyto­plas­mic injec­tion of Cas9 mRNA at con­cen­tra­tions up to 200 ng/μl is not toxic to embryos (Wang et al. 2013) and effi­cient edit­ing was achieved at con­cen­tra­tions as low as 1.5 ng/μl (Ran et al. 2013a). In our hands, inject­ing Cas9 mRNA at 50-150 ng/μl and gRNA at 50-75 ng/μl first into the pronu­cleus and also into the cyto­plasm as the nee­dle is being with­drawn, yields good sur­vival of embryos and effi­cient edit­ing by NHEJ in live born pups (our unpub­lished obser­va­tion­s).” http://genetics.org/content/199/1/1.full

dnorm((150-100)/15) * 320000000 [1] 493,529.2788 dnorm((170-100)/15) * 320000000 [1] 2382.734679

if you’re curi­ous how I cal­cu­lated that, (10*1000 + 10 * 98 * 500) > 500000 → [1] FALSE sum(sort((rexp(10000)/1)/18, decreasing=TRUE)[1:98] * 0.5) → [1] 15.07656556

hm. there are ~50k IVF babies each year in the USA. my quick CRISPR sketch sug­gested that for a few mill you could get up to 150-170. dnorm((150-100)/15) * 320000000 → [1] 493,529.2788; dnorm((170-100)/15) * 320000000 → [1] 2382.734679. so depend­ing on how many IVFers used it, you could boost the total genius pop­u­la­tion by any­where from 1/10th to 9x

but if only 10% causal rate and so only 100 effec­tive edits from 1000, and a net gain of 15 IQ points (1SD) then increas­es: IVF <- (dnorm((115-100)/15) * 50000); gen­pop <- (dnorm((150-100)/15) * 320000000); (IVF+genpop)/genpop [1] 1.024514323 IVF <- (dnorm((115-100)/15) * 50000); gen­pop <- (dnorm((170-100)/15) * 320000000); (IVF+genpop)/genpop [1] 6.077584313 an increase of 1.02x (150) and 6x (170) respec­tively

“To con­firm these GUIDE-seq find­ings, we used tar­geted ampli­con sequenc­ing to more directly mea­sure the fre­quen­cies of indel muta­tions induced by wild-­type SpCas9 and SpCas9-H­F1. For these exper­i­ments, we trans­fected human cells only with sgRNA- and Cas9en­cod­ing plas­mids (with­out the GUIDE-seq tag). We used nex­t-­gen­er­a­tion sequenc­ing to exam­ine the on-­tar­get sites and 36 of the 40 off-­tar­get sites that had been iden­ti­fied for six sgRNAs with wild-­type SpCas9 in our GUIDE-seq exper­i­ments (four of the 40 sites could not be specif­i­cally ampli­fied from genomic DNA). These deep sequenc­ing exper­i­ments showed that: (1) wild-­type SpCas9 and SpCas9-HF1 induced com­pa­ra­ble fre­quen­cies of indels at each of the six sgRNA on-­tar­get sites, indi­cat­ing that the nucle­ases and sgRNAs were func­tional in all exper­i­men­tal repli­cates (Fig. 3a, b); (2) as expect­ed, wild-­type SpCas9 showed sta­tis­ti­cally sig­nif­i­cant evi­dence of indel muta­tions at 35 of the 36 off-­tar­get sites (Fig. 3b) at fre­quen­cies that cor­re­lated well with GUIDE-seq read counts for these same sites (Fig. 3c); and (3) the fre­quen­cies of indels induced by SpCas9-HF1 at 34 of the 36 off-­tar­get sites were sta­tis­ti­cally indis­tin­guish­able from the back­ground level of indels observed in sam­ples from con­trol trans­fec­tions (Fig. 3b). For the two off-­tar­get sites that appeared to have sta­tis­ti­cally sig­nif­i­cant muta­tion fre­quen­cies with SpCas9-HF1 rel­a­tive to the neg­a­tive con­trol, the mean fre­quen­cies of indels were 0.049% and 0.037%, lev­els at which it is dif­fi­cult to deter­mine whether these are due to sequenc­ing or PCR error or are bona fide nucle­ase-in­duced indels. Based on these results, we con­clude that SpCas9-HF1 can com­pletely or nearly com­pletely reduce off-­tar­get muta­tions that occur across a range of dif­fer­ent fre­quen­cies with wild-­type SpCas9 to lev­els gen­er­ally unde­tectable by GUIDE-seq and tar­geted deep sequenc­ing.”

So no detected off-­tar­get muta­tions down to the level of lab error rate detectabil­i­ty. Amaz­ing. So you can do a CRISPR on a cell with a >75% chance of mak­ing the edit to a desired gene cor­rect­ly, and a <0.05% chance of a mis­taken (po­ten­tially harm­less) edit/mutation on a sim­i­lar gene. With an error rate that low, you could do hun­dreds of CRISPR edits to a set of embryos with a low net risk of error… The median num­ber of eggs extracted from a woman dur­ing IVF in Amer­ica is ~9; assume the worst case of 0.05% risk of off-­tar­get muta­tion and that one scraps any embryo found to have any muta­tion at all even if it looks harm­less; then the prob­a­bil­ity of mak­ing 1000 edits with­out an off-­tar­get muta­tion could be (1-(0.05/100)) ^ 1000 = 60%, so you’re left with 5.4 good embryos, which is a decent yield. Mak­ing an edit of the top 1000 betas from the Rietveld 2013 poly­genic score and fig­ur­ing that it’s weak­ened by maybe 25% due to par­tic­u­lar cells not get­ting par­tic­u­lar edits and that is… a very large num­ber.

When I was doing my dys­gen­ics analy­sis, I found that the Rietveld betas could be rea­son­ably approx­i­mated by rexp, and we can anchor it by assum­ing the biggest effect is 0.5 IQ points, so we divide by 18, in which case we might esti­mate the top 750 edits at a cumu­la­tive value of sum(sort((rexp(10000)/1)/18, decreasing=TRUE)[1:750] * 0.5) → [1] 73.97740467. (Caveats: assumes knowl­edge of true betas, needs to be weak­ened for actual pos­te­rior prob­a­bil­i­ties, etc etc.)

How much did that <74 IQ points cost? Well, I hear that TALENS in bulk costs $500 so you could ball­park mar­ginal costs of par­tic­u­lar CRISPR edits at that much too (and hope­fully much less), and whole-genomes still cost $1k, and you need to do 1000 edits on each embryo and whole-genomes at the end to check for off-­tar­get muta­tions, so you could ball­park a full suite of edits to 10 embryos at ~$5m: 10*1000 + 10 * 1000 * 500 → [1] 5010000. Of them 40% will have an off-­tar­get muta­tion, so you get 6 embryos to implant at a suc­cess rate of ~20% each which gives you about even odds for a healthy live birth, so you need to dou­ble the $5m.

CRISPR: $30? vs $5k for TALENs http://www.nature.com/news/crispr-the-disruptor-1.17673 “Zayner says the kits will con­tain every­thing a bud­ding sci­en­tist needs to carry out CRISPR exper­i­ments on yeast or bac­te­ria. For US$130, you can have a crack at re-engi­neer­ing bac­te­ria so that it can sur­vive on a food it nor­mally would­n’t be able to han­dle, or for $160, you can get your eukary­ote on and edit the ADE2 gene of yeast to give it a red pig­ment.” https://www.indiegogo.com/projects/diy-crispr-kits-learn-modern-science-by-doing#/ https://www.thermofisher.com/us/en/home/life-science/genome-editing/geneart-crispr/crispr-cas9-based-genome-editing.html http://www.sigmaaldrich.com/technical-documents/articles/biology/crispr-cas9-genome-editing.html http://www.genscript.com/CRISPR-genome-edited-mammalian-cell-lines.html http://ipscore.hsci.harvard.edu/genome-editing-services http://www.blueheronbio.com/Services/CRISPR-Cas9.aspx http://www.addgene.org/crispr/ ‘Jen­nifer Doud­na, one of the co-dis­cov­er­ers of CRISPR, told MIT Tech Review’s Anto­nio Regal­ado just how easy it was to work with the tool: “Any sci­en­tist with mol­e­c­u­lar biol­ogy skills and knowl­edge of how to work with [em­bryos] is going to be able to do this.” Har­vard geneti­cist George Church, whose lab is doing some of the pre­mier research on CRISPR, says: “You could con­ceiv­ably set up a CRISPR lab for $2000.”’ http://www.businessinsider.com/how-to-genetically-modify-human-embryos-2015-4 “Democ­ra­tiz­ing genetic engi­neer­ing: This one should keep you up at night. CRISPR is so acces­si­ble-you can order the com­po­nents online for $60-that it is putting the power of genetic engi­neer­ing into the hands of many more sci­en­tists. But the next wave of users could be at-home hob­by­ists. This year, devel­op­ers of a do-it-y­our­self genetic engi­neer­ing kit began offer­ing it for $700, less than the price of some com­put­ers. The trend might lead to an explo­sion of inno­va­tion-or to dan­ger­ous, uncon­trolled exper­i­ments by new­bies. Watch out, world.” https://www.technologyreview.com/s/543941/everything-you-need-to-know-about-crispr-gene-editings-monster-year/ “Indi­vid­ual plas­mids can be ordered at $65 per plas­mid, and will be shipped as bac­te­r­ial stabs” https://www.addgene.org/crispr/yamamoto/multiplex-crispr-kit/ “At least since 1953, when James Wat­son and Fran­cis Crick char­ac­ter­ized the heli­cal struc­ture of DNA, the cen­tral project of biol­ogy has been the effort to under­stand how the shift­ing arrange­ment of four com­pound­s-adenine, gua­nine, cytosine, and thymine-de­ter­mines the ways in which humans dif­fer from each other and from every­thing else alive. CRISPR is not the first sys­tem to help sci­en­tists pur­sue that goal, but it is the first that any­one with basic skills and a few hun­dred dol­lars’ worth of equip­ment can use.”CRISPR is the Model T of genet­ic­s," Hank Greely told me when I vis­ited him recent­ly, at Stan­ford Law School, where he is a pro­fes­sor and the direc­tor of the Cen­ter for Law and the Bio­sciences. “The Model T was­n’t the first car, but it changed the way we dri­ve, work, and live. CRISPR has made a dif­fi­cult process cheap and reli­able. It’s incred­i­bly pre­cise. But an impor­tant part of the his­tory of mol­e­c­u­lar biol­ogy is the his­tory of edit­ing genes.”…“In the past, this would have taken the field a decade, and would have required a con­sor­tium,” Platt said. “With CRISPR, it took me four months to do it by myself.” In Sep­tem­ber, Zhang pub­lished a report, in the jour­nal Cell, describ­ing yet another CRISPR pro­tein, called Cpf1, that is smaller and eas­ier to pro­gram than Cas9." http://www.newyorker.com/magazine/2015/11/16/the-gene-hackers?mbid=rss

2017 7% http://predictionbook.com/predictions/177110 2018 30% http://predictionbook.com/predictions/177114 2019 55% http://predictionbook.com/predictions/177115 by 2020, 75% http://predictionbook.com/predictions/177111

Whither embryo edit­ing? The prob­lem with IVF is that it is expen­sive, painful, and requires patience & plan­ning. Even with large gains from edit­ing, can we expect more than the cur­rent 1% or so of par­ents to ever be will­ing to con­ceive via IVF for those gains? If not, then the ben­e­fits may take gen­er­a­tions to mix into the gen­eral pop­u­la­tion as off­spring repro­duce nor­mally with unedited peo­ple and peo­ple hap­pen to need to use IVF for reg­u­lar fer­til­ity rea­sons. A solu­tion is sug­gested by the adult CRISPR tri­als: make the germline edits in advance. In females, it seems like it might be hard to reach all the eggs which could poten­tially result in con­cep­tion, but in males, sperm turnover is con­stant https://en.wikipedia.org/wiki/Spermatogenesis and sperm are replen­ished by stem cells in https://en.wikipedia.org/wiki/Seminiferous_tubule already demon­strated CRISPR edits to sper­mato­go­nia and sub­se­quent inher­i­tance by off­spring: “Tar­geted Germline Mod­i­fi­ca­tions in Rats Using CRISPR/Cas9 and Sper­mato­go­nial Stem Cells”, Chap­man et al 2014 http://www.sciencedirect.com/science/article/pii/S2211124715001989 “Genome Edit­ing in Mouse Sper­mato­go­nial Stem Cell Lines Using TALENS and Dou­ble-Nick­ing CRISPR/Cas9”, Sato et al 2015 http://www.sciencedirect.com/science/article/pii/S221367111500154X extrac­tion, mod­i­fi­ca­tion, and re-­trans­plant­ing is likely also a no-fly, but the edits demon­strate that CRISPR will not inter­fere with repro­duc­tion, and so bet­ter deliv­ery meth­ods can be devel­oped edit­ing via two intra­venous injec­tions of a virus (car­ry­ing the edit­ing tem­plate) and lipid-en­cap­su­lated Cas9-en­zyme into the mice’ tail vein: Yin et al 2016, yield­ing 6% of cells edited in the liver

https://en.wikipedia.org/wiki/Status_quo_bias “The Rever­sal Test: Elim­i­nat­ing Sta­tus Quo Bias in Applied Ethics”, Bostrom & Ord 2006 https://ethicslab.georgetown.edu/phil553/wordpress/wp-content/uploads/2015/01/Ord-and-Bostrom-Eliminating-Status-Quo-Bias-in-Applied-Ethics-.pdf A muta­tion load review leads me to some hard fig­ures from Simons et al 2014 (sup­ple­ment) using data from Fu et al 2012/; par­tic­u­larly rel­e­vant is fig­ure 3, the num­ber of sin­gle-nu­cleotide vari­ants per per­son over the Euro­pean-Amer­i­can sam­ple, split by esti­mates of harm from least to most like­ly: 21345 + 15231 + 5338 + 1682 + 1969 = 45565. The sup­ple­men­tary tables gives a count of all observed SNVs by cat­e­go­ry, which sum to 300209 + 8355 + 220391 + 7001 + 351265 + 10293 = 897514, so the aver­age fre­quency must be 45565/897514=0.05, and then the bino­mial SD will be sqrt(897514*0.05*(1-0.05))=206.47. https://en.wikipedia.org/wiki/Paternal_age_effect https://www.biorxiv.org/content/biorxiv/early/2016/03/08/042788.full.pdf “Older fathers’ chil­dren have lower evo­lu­tion­ary fit­ness across four cen­turies and in four pop­u­la­tions” “Rate of de novo muta­tions and the impor­tance of father’s age to dis­ease risk” https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3548427/ “Novel vari­a­tion and de novo muta­tion rates in pop­u­la­tion-wide de novo assem­bled Dan­ish trios” http://www.nature.com/ncomms/2015/150119/ncomms6969/full/ncomms6969.html http://www.genetics.org/content/202/3/869 “Thus, keep­ing in mind that some muta­tions in repet­i­tive DNA likely go unde­tected owing to map­ping dif­fi­cul­ties in genome-se­quenc­ing pro­jects, with a diploid genome size of ~6 bil­lion bases, an aver­age new­born con­tains ~100 de novo muta­tion­s….Nu­mer­ous stud­ies with model organ­isms indi­cate that such effects have a broad dis­tri­b­u­tion (Lynch et al. 1999; Hal­li­gan and Keight­ley 2009)-­most muta­tions have minor effects, very few have lethal con­se­quences, and even fewer are ben­e­fi­cial. In all organ­isms, the major­ity of muta­tions with effects on fit­ness reduce viability/fecundity by some­thing on the order of 1% per muta­tion (Lynch et al. 1999; Yam­pol­sky et al. 2005; Eyre-Walker and Keight­ley 2007), and this class is thought to con­sti­tute 1-10% of all human muta­tions, the remain­der being essen­tially neu­tral (Lind­blad-­Toh et al. 2011; Keight­ley 2012; Rands et al. 2014). Tak­ing the lower end of the lat­ter range sug­gests that the recur­rent load of muta­tions imposed on the human pop­u­la­tion drags fit­ness down by 1% per gen­er­a­tion, more so if the frac­tion of dele­te­ri­ous muta­tions exceeds 0.01 or if the envi­ron­ment is muta­genic, and less so if the aver­age fit­ness effect of a muta­tion were to be <1%”

“Parental influ­ence on human germline de novo muta­tions in 1,548 trios from Ice­land”, Jóns­son et al 2017:

To under­stand how the age and sex of trans­mit­ting par­ents affect de novo muta­tions, here we sequence 1,548 Ice­landers, their par­ents, and, for a sub­set of 225, at least one child, to 35× genome-wide cov­er­age. We find 108,778 de novo muta­tions, both sin­gle nucleotide poly­mor­phisms and indels, and deter­mine the par­ent of ori­gin of 42,961. The num­ber of de novo muta­tions from moth­ers increases by 0.37 per year of age (95% CI 0.32-0.43), a quar­ter of the 1.51 per year from fathers (95% CI 1.45-1.57). The num­ber of clus­tered muta­tions increases faster with the moth­er’s age than with the father’s, and the genomic span of mater­nal de novo muta­tion clus­ters is greater than that of pater­nal ones.

…To assess dif­fer­ences in the rate and class of DNMs trans­mit­ted by moth­ers and fathers, we analysed whole-genome sequenc­ing (WGS) data from 14,688 Ice­landers with an aver­age of 35x cov­er­age (Data Descrip­tor^19). This set con­tained 1,548 trios, used to iden­tify 108,778 high­-qual­ity DNMs (101,377 sin­gle nucleotide poly­mor­phisms (SNPs); Meth­ods and Fig. 1), result­ing in an aver­age of 70.3 DNMs per proband. The DNM call qual­ity was also assessed using 91 monozy­gotic twins of probands (Meth­od­s). Of 6,034 DNMs observed in these probands, 97.1% were found in their twins. Sanger sequenc­ing was used to val­i­date 38 dis­cor­dant calls in monozy­gotic twins, of which 57.9% were con­firmed to be present only in the proband, and there­fore postzy­gotic, with the rest deemed geno­typ­ing errors.

…Mu­ta­tion rates are key para­me­ters for cal­i­brat­ing the timescale of sequence diver­gence. We esti­mate the muta­tion rate as 1.29 × 10-8 per base pair per gen­er­a­tion and 4.27 × 10-10 per base pair per year (Meth­od­s). Our find­ings have a direct bear­ing on the dis­par­ity that has emerged between muta­tion rates esti­mated directly from pedi­grees (~4 × 10-10 per base pair per year) and phy­lo­ge­netic rates (~10-9 per base pair per year)3, as they indi­cate that the mol­e­c­u­lar clock is affected by life-his­tory traits in a sex-spe­cific man­ner23-25 and varies by genomic region within and across species. This allows us to pre­dict the long-term con­se­quences of a shift in gen­er­a­tion times (Meth­od­s)24. Thus, a 10 year increase in the aver­age age of fathers would increase the muta­tion rate by 4.7% per year. The same change for moth­ers would decrease the muta­tion rate by 9.6%, because extra muta­tions attrib­ut­able to older moth­ers are off­set by fewer gen­er­a­tions

, Paten et al 2017:

From short­-read based assays, it is esti­mated that the aver­age diploid human has between 4.1 and 5 mil­lion point muta­tions, either sin­gle nucleotide vari­ants (SNVs), mul­ti­-nu­cleotide vari­ants (MNVs), or short indels, which is only around 1 point vari­ant every 1450 to 1200 bases of hap­loid sequence (Au­ton et al. 2015). Such an aver­age human would also have about 20 mil­lion bases-about 0.3% of the genome-af­fected by around 2,100-2,500 larger struc­tural vari­ants (Au­ton et al. 2015). It should be noted that both these esti­mates are likely some­what con­ser­v­a­tive as some regions of the genome are not accu­rately sur­veyed by the short read tech­nol­ogy used. Indeed, long read sequenc­ing demon­strates an excess of struc­tural vari­a­tion not found by ear­lier short read tech­nol­ogy (Chais­son et al. 2015; Seo et al. 2016).

http://gnxp.com/2017/04/15/genetic-variation-in-human-populations-and-individuals/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3155974/ “Genetic costs of domes­ti­ca­tion and improve­ment” Moy­ers et al 2017 https://www.biorxiv.org/content/early/2017/03/29/122093

“The demo­graphic his­tory and muta­tional load of African hunter-­gath­er­ers and farm­ers”, Lopez et al 2017 https://www.biorxiv.org/content/early/2017/04/26/131219

“(This dataset includes 463 mil­lion vari­ants on 62784 indi­vid­u­als. Click here to switch to Freeze3a on GRCh37/hg19.)” https://bravo.sph.umich.edu/freeze5/hg38/

, Gazal et al 2017:

Recent work has hinted at the link­age dis­e­qui­lib­rium (LD)-de­pen­dent archi­tec­ture of human com­plex traits, where SNPs with low lev­els of LD (LLD) have larger per-SNP her­i­tabil­i­ty. Here we ana­lyzed sum­mary sta­tis­tics from 56 com­plex traits (av­er­age N = 101,401) by extend­ing strat­i­fied LD score regres­sion to con­tin­u­ous anno­ta­tions. We deter­mined that SNPs with low LLD have sig­nif­i­cantly larger per-SNP her­i­tabil­ity and that roughly half of this effect can be explained by func­tional anno­ta­tions neg­a­tively cor­re­lated with LLD, such as DNase I hyper­sen­si­tiv­ity sites (DHSs). The remain­ing sig­nal is largely dri­ven by our find­ing that more recent com­mon vari­ants tend to have lower LLD and to explain more her­i­tabil­ity (P = 2.38 × 10−104); the youngest 20% of com­mon SNPs explain 3.9 times more her­i­tabil­ity than the old­est 20%, con­sis­tent with the action of neg­a­tive selec­tion. We also inferred jointly sig­nif­i­cant effects of other LD-re­lated anno­ta­tions and con­firmed via for­ward sim­u­la­tions that they jointly pre­dict dele­te­ri­ous effects.

, Schoech et al 2017:

Under­stand­ing the role of rare vari­ants is impor­tant in elu­ci­dat­ing the genetic basis of human dis­eases and com­plex traits. It is widely believed that neg­a­tive selec­tion can cause rare vari­ants to have larger per-al­lele effect sizes than com­mon vari­ants. Here, we develop a method to esti­mate the minor allele fre­quency (MAF) depen­dence of SNP effect sizes. We use a model in which per-al­lele effect sizes have vari­ance pro­por­tional to [p(1-p)]α, where p is the MAF and neg­a­tive val­ues of α imply larger effect sizes for rare vari­ants. We esti­mate α by max­i­miz­ing its pro­file like­li­hood in a lin­ear mixed model frame­work using imputed geno­types, includ­ing rare vari­ants (MAF >0.07%). We applied this method to 25 UK Biobank dis­eases and com­plex traits (N=113,851). All traits pro­duced neg­a­tive α esti­mates with 20 sig­nif­i­cantly neg­a­tive, imply­ing larger rare vari­ant effect sizes. The inferred best-­fit dis­tri­b­u­tion of true α val­ues across traits had mean -0.38 (s.e. 0.02) and stan­dard devi­a­tion 0.08 (s.e. 0.03), with sta­tis­ti­cally sig­nif­i­cant het­ero­gene­ity across traits (P=0.0014). Despite larger rare vari­ant effect sizes, we show that for most traits ana­lyzed, rare vari­ants (MAF <1%) explain less than 10% of total SNP-heritability. Using evo­lu­tion­ary mod­el­ing and for­ward sim­u­la­tions, we val­i­dated the α model of MAF-dependent trait effects and esti­mated the level of cou­pling between fit­ness effects and trait effects. Based on this analy­sis an aver­age genome-wide neg­a­tive selec­tion coef­fi­cient on the order of 10-4 or stronger is nec­es­sary to explain the α val­ues that we inferred.

SNPs have two rel­e­vant prop­er­ties: a fre­quency of being zero, and an effect size

Benyamin poly­genic score dis­tri­b­u­tion: looks either expo­nen­tial or log-nor­mal and a Cullen & Frey graph indi­cates it is closes to expo­nen­tial & log-nor­mal dis­tri­b­u­tions.

library(fitdistrplus)
with(benyamin[benyamin$EFFECT_A1>0,], descdist(abs(EFFECT_A1)/15, discrete=FALSE))
fit.exp <- with(benyamin[benyamin$EFFECT_A1>0,], fitdist(abs(EFFECT_A1)/15, "exp")); fit.exp
# Fitting of the distribution ' exp ' by maximum likelihood
# Parameters:
#        estimate  Std. Error
# rate 1063.15695 1.281452665
fit.ln <- with(benyamin[benyamin$EFFECT_A1>0,], fitdist(abs(EFFECT_A1)/15, "lnorm")); fit.ln
# Fitting of the distribution ' lnorm ' by maximum likelihood
# Parameters:
#             estimate      Std. Error
# meanlog -7.402017853 0.0013198365617
# sdlog    1.095050030 0.0009332618808

Plot­ting resid­u­als & diag­nos­tics, the log-nor­mal per­forms much worse due to over­es­ti­mat­ing the num­ber of near-zero effects (the Q-Q plot is par­tic­u­larly bad), so we’ll use the expo­nen­tial for effect sizes

As pro­por­tions, the fre­quen­cies are prob­a­bly close to either uni­form or beta dis­tri­b­u­tions; in this case, they are very nearly uni­formly dis­trib­uted 0-1:

R> fitdist(benyamin$FREQ_A1, "beta", method="mme")
Fitting of the distribution ' beta ' by matching moments
Parameters:
          estimate
shape1 1.065412339
shape2 1.126576711

Set up: 50k SNPs, true effect sizes are expo­nen­tially dis­trib­uted with expo­nen­tial(rate=1063.15695), fre­quen­cies dis­trib­uted beta(1.065412339, 1.126576711) can’t do full sim­u­la­tion of 500k SNPs with 100k dat­a­points, not enough RAM given inef­fi­cient R for­mat for booleans: (100000 * 100000 * 48 bytes) / 1000000000 ; 4.8e+11 bytes or 480GB can JAGS even han­dle that much data?

SNPs <- 500000
SNPlimit <- 50000
N <- 10000
genes <- data.frame(Effects = sort(rexp(SNPs, rate=1063.15695), decreasing=TRUE)[1:SNPlimit], Frequencies = rbeta(SNPlimit, shape1=1.065412339, shape2=1.126576711))
person <- function() { rbinom(SNPlimit, 1, prob=genes$Frequencies) }
test <- as.data.frame(t(replicate(N, person())))
format(object.size(test), units="GB")
# [1] "1.9 Gb"
test$Polygenic.score <- sapply(1:nrow(test), function(i) { sum(ifelse(test[i,], genes$Effects, 0)) })
test$IQ <- 100 + 15 * rnorm(N, mean=scale(test$Polygenic.score), sd=sqrt(1-0.33))

library(BGLR)
b <- BGLR(test$IQ, ETA=list(list(X=test[,1:SNPlimit], model="BL", lambda=202, shape=1.1, rate=2.8e-06)), R2=0.33)
gc()

BGLR prob­lem: I can’t scale it to n=100k/SNP=500k, BGLR RAM con­sump­tion maxes out at n=10k/SNP=50k. This would­n’t be a prob­lem for the Thomp­son sam­pling, but I need to use JAGS any­way for that. So BGLR can’t give me pos­te­ri­ors for Rietveld et al 2013 or Benyamin 2014 data.

can do Bayesian GWAS from pub­lic sum­mary sta­tis­tics using RSS “Bayesian large-s­cale mul­ti­ple regres­sion with sum­mary sta­tis­tics from genome-wide asso­ci­a­tion stud­ies” https://www.biorxiv.org/content/biorxiv/early/2016/03/04/042457.full.pdf Mat­lab library https://github.com/stephenslab/rss instal­la­tion: https://github.com/stephenslab/rss/wiki/RSS-via-MCMC RSS exam­ple 1 https://github.com/stephenslab/rss/wiki/Example-1 code: https://github.com/stephenslab/rss/blob/master/examples/example1.m data https://uchicago.app.box.com/example1 does­n’t run under Octave at the moment although I got it close: https://github.com/stephenslab/rss/issues/1 what are my alter­na­tives? RSS is the best look­ing Bayesian one so far. I can try pirat­ing Mat­lab, or appar­ently the Machine Learn­ing Cours­era gives one a tem­po­rary 120-­day sub­scrip­tion

groundTruth <- function(alleles, causal, genotype) {
    score <- rnorm(1, mean=100, sd=15)
    for (i in 1:length(genotype)) {
      if(causal[i] && genotype[i]) { print(alleles[i]); score <- score + alleles[i]; } }
      return(score);}

alleles <- sort(rexp(10000, rate=70), decreasing=TRUE)[1:10]
causal <- c(TRUE, rep(FALSE, 8), TRUE)

df <- data.frame()
for(i in 1:50) {
 genotype <- rbinom(n=10,1,prob=0.50)
 IQ <- groundTruth(alleles, causal, genotype)
 df <- rbind(df, c(IQ, genotype))
 }
names(df) <- c("IQ", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J")
library(reshape2)
df2 <- melt(df, "IQ")

model1 <- function() {
  for (i in 1:N) {
   for (j in 1:K) {
     b[j] ~ dexp(70)
     y[i] ~ dnorm(100, 0.06) + b[j]
    }
    }
    }
data1 <- list(N=nrow(df2), K=10, y=df2$IQ, b=1:length(unique(df2$variable)))
jags(data=data1, parameters.to.save="b", model.file=model1)




# eg groundTruth(c(TRUE, FALSE, TRUE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE))
simulate <- function(a, c) {
   }

library(runjags)
model1 <- "model {
  for (i in 1:N) {
   y[i] ~ dnorm(mu[i], tau[i])
   mu[i] <- muOfClust[ clust[i] ]
   clust[i] ~ dcat(pi[])
  }

  for (i in 1:K) {
    pi[i] <- 0.05
    muOfClust[i] ~ dexp(70)
    tau[i] ~ dgamma(1.0E-3, 1.0E-3)
  }
 }"
j1 <- autorun.jags(model1, monitor=c("theta"), data = list(N=nrow(oldData2), y=oldData2$Yes, n=oldData2$N, switch=c(0.5, 0.5), clust=c(1,NA))); j1
# ...      Lower95  Median Upper95    Mean       SD Mode      MCerr MC%ofSD SSeff    AC.10   psrf
# theta[1] 0.70582 0.75651 0.97263 0.77926  0.07178   --   0.001442       2  2478  0.12978 1.0011
# theta[2] 0.72446 0.75078 0.77814 0.75054 0.013646   -- 0.00009649     0.7 20000 0.009458      1

https://github.com/jeromyanglim/JAGS_by_Example/blob/master/03-multilevel/varying-intercept-long/varying-intercept-long.rmd http://doingbayesiandataanalysis.blogspot.com/2012/06/mixture-of-normal-distributions.html http://www.stats.ox.ac.uk/~bardenet/Material/mixture_with_jags_only_mu.html


“Genome-wide asso­ci­a­tion study iden­ti­fies 74 [162] loci asso­ci­ated with edu­ca­tional attain­ment”, Okbay et al 2016 https://www.dropbox.com/s/my9719yd8s5hplf/2016-okbay-2.pdf sup­ple­men­tary info: http://www.nature.com/nature/journal/vaop/ncurrent/extref/nature17671-s1.pdf http://www.nature.com/nature/journal/vaop/ncurrent/extref/nature17671-s2.xlsx http://www.thessgac.org/#!data/kuzq8 http://ssgac.org/documents/FAQ_74_loci_educational_attainment.pdf

Edu­ca­tional attain­ment is strongly influ­enced by social and other envi­ron­men­tal fac­tors, but genetic fac­tors are esti­mated to account for at least 20% of the vari­a­tion across indi­vid­u­al­s1. Here we report the results of a genome-wide asso­ci­a­tion study (GWAS) for edu­ca­tional attain­ment that extends our ear­lier dis­cov­ery sam­ple1, 2 of 101,069 indi­vid­u­als to 293,723 indi­vid­u­als, and a repli­ca­tion study in an inde­pen­dent sam­ple of 111,349 indi­vid­u­als from the UK Biobank. We iden­tify 74 [162 total] genome-wide sig­nif­i­cant loci asso­ci­ated with the num­ber of years of school­ing com­plet­ed. Sin­gle-nu­cleotide poly­mor­phisms asso­ci­ated with edu­ca­tional attain­ment are dis­pro­por­tion­ately found in genomic regions reg­u­lat­ing gene expres­sion in the fetal brain. Can­di­date genes are pref­er­en­tially expressed in neural tis­sue, espe­cially dur­ing the pre­na­tal peri­od, and enriched for bio­log­i­cal path­ways involved in neural devel­op­ment. Our find­ings demon­strate that, even for a behav­ioural phe­no­type that is mostly envi­ron­men­tally deter­mined, a well-pow­ered GWAS iden­ti­fies replic­a­ble asso­ci­ated genetic vari­ants that sug­gest bio­log­i­cally rel­e­vant path­ways. Because edu­ca­tional attain­ment is mea­sured in large num­bers of indi­vid­u­als, it will con­tinue to be use­ful as a proxy phe­no­type in efforts to char­ac­ter­ize the genetic influ­ences of related phe­no­types, includ­ing cog­ni­tion and neu­ropsy­chi­atric dis­eases.

Using pro­ce­dures iden­ti­cal to those described in SI Sec­tion 1.6, we con­ducted a meta-­analy­sis of the EduYears phe­no­type, com­bin­ing the results from our dis­cov­ery cohorts (N = 293,723) and the results from the UKB repli­ca­tion cohort (N = 111,349). Expand­ing the over­all sam­ple size to N = 405,072 increases the num­ber of approx­i­mately inde­pen­dent genome-wide sig­nif­i­cant loci from 74 to 162.

…This back­ground suf­fices to moti­vate the bio­log­i­cal ques­tions that arise in the inter­pre­ta­tion of GWAS results and the means by which these ques­tions might be ten­ta­tively addressed. For starters, since a GWAS locus typ­i­cally con­tains many other SNPs in LD with the defin­ing lead SNP and with each oth­er, it is nat­ural to ask: which of these SNPs is the actual causal site respon­si­ble for the down­stream phe­no­typic vari­a­tion? Many SNPs in the genome appear to be bio­log­i­cally inert-nei­ther encod­ing dif­fer­ences in pro­tein com­po­si­tion nor affect­ing gene reg­u­la­tion-and a lead GWAS SNP may fall into this cat­e­gory and nonethe­less show the strongest asso­ci­a­tion sig­nal as a result of sta­tis­ti­cal noise or hap­pen­stance LD with mul­ti­ple causal sites. For­tu­nate­ly, much is known from exter­nal sources of data about whether vari­a­tion at a par­tic­u­lar site is likely to have bio­log­i­cal con­se­quences, and exploit­ing these resources is our gen­eral strat­egy for fine-map­ping loci: nom­i­nat­ing indi­vid­ual sites that may be causally respon­si­ble for the GWAS sig­nals. Descrip­tions of genomic sites or regions based on exter­nal sources of data are known as anno­ta­tions, and read­ers will not go far astray if they inter­pret this term rather lit­er­ally (as refer­ring to a note of expla­na­tion or com­ment added to a text in one of the mar­gin­s). If we regard the type genome as the basic text, then anno­ta­tions are addi­tional com­ments describ­ing the struc­tural or func­tional prop­er­ties of par­tic­u­lar sites or the regions in which they reside. For exam­ple, all non­syn­ony­mous sites that influ­ence pro­tein struc­tures might be anno­tated as such. An anno­ta­tion can be far more spe­cific than this; for instance, all sites that fall in a reg­u­la­tory region active in the fetal liver might bear an anno­ta­tion to this effect. A given causal site will exert its phe­no­typic effect through alter­ing the com­po­si­tion of a gene prod­uct or reg­u­lat­ing its expres­sion. Con­cep­tu­al­ly, once a causal site has been iden­ti­fied or at least nom­i­nat­ed, the next ques­tion to pur­sue is the iden­tity of the medi­at­ing gene. In prac­tice, because only a hand­ful of genes at most will typ­i­cally over­lap a GWAS locus, we can make some progress toward answer­ing this ques­tion with­out pre­cise knowl­edge of the causal site. The dif­fi­culty of the prob­lem, how­ev­er, should still not be under­es­ti­mat­ed. It is nat­ural to assume that a lead GWAS SNP lying inside the bound­aries of a par­tic­u­lar gene must reflect a causal mech­a­nism involv­ing that gene itself, but in cer­tain cases such a con­clu­sion would be pre­ma­ture. It is pos­si­ble for a causal SNP lying inside a cer­tain gene to exert its phe­no­typic effect by reg­u­lat­ing the expres­sion of a nearby gene or for sev­eral genes to inter­vene between the SNP and its reg­u­la­tory tar­get. Sup­ple­men­tary Table 4.1 ranks each gene over­lap­ping a DEPICT-defined locus by the num­ber of dis­crete evi­den­tiary items favor­ing that gene (see Sup­ple­men­tary Infor­ma­tion sec­tion 4.5 for details regard­ing DEPICT). These lines of evi­dence are taken from a num­ber of our analy­ses to be detailed in the fol­low­ing sub­sec­tions. Our pri­mary tool for gene pri­or­i­ti­za­tion is DEPICT, which can be used to cal­cu­late a P-value and asso­ci­ated FDR for each gene. It is impor­tant to keep in mind, how­ev­er, that a gene-level P-value returned by DEPICT refers to the tail prob­a­bil­ity under the null hypoth­e­sis that ran­dom sam­pling of loci can account for anno­ta­tions and pat­terns of co-­ex­pres­sion shared by the focal gene with genes in all other GWAS-identified loci. Although it is very rea­son­able to expect that genes involved in the same phe­no­type do indeed share anno­ta­tions and pat­terns of co-­ex­pres­sion, it may be the case that cer­tain causal genes do not con­form to this expec­ta­tion and thus fail to yield low DEPICT P-val­ues. This is why we do not rely on DEPICT alone but also the other lines of evi­dence described in the cap­tion of Sup­ple­men­tary Table 4.1.

How­ev­er, a pri­ori we know that some SNPs are more likely to be asso­ci­ated with the phe­no­type than oth­ers; for exam­ple, it is often assumed that non­syn­ony­mous SNPs are more likely to influ­ence phe­no­types than sites that fall far from all known genes. So a P-value of 5×10 −7 , say, though not typ­i­cally con­sid­ered sig­nif­i­cant at the genome-wide lev­el, might merit a sec­ond look if the SNP in ques­tion is non­syn­ony­mous. For­mal­iz­ing this intu­ition can be done with Bayesian sta­tis­tics, which com­bines the strength of evi­dence in favor of a hypoth­e­sis (in our case, that a genomic site is asso­ci­ated with a phe­no­type) with the prior prob­a­bil­ity of the hypoth­e­sis. Decid­ing how to set this prior is often sub­jec­tive. How­ev­er, if many hypothe­ses are being tested (for exam­ple, if there are thou­sands of non­syn­ony­mous poly­mor­phisms in the genome), then the prior can be esti­mated from the data them­selves using what is called “empir­i­cal Bayes” method­ol­o­gy. For exam­ple, if it turns out that SNPs with low P-val­ues tend to be non­syn­ony­mous sites rather than other types of sites, then the prior prob­a­bil­ity of true asso­ci­a­tion is increased at all non­syn­ony­mous sites. In this way a non­syn­ony­mous site that oth­er­wise falls short of the con­ven­tional sig­nif­i­cance thresh­old can become pri­or­i­tized once the empir­i­cally esti­mated prior prob­a­bil­ity of asso­ci­a­tion is taken into account. Note that such favor­able reweight­ing of sites within a par­tic­u­lar class is not set a pri­ori, but is learned from the GWAS results them­selves. In our case, we split the genome into approx­i­mately inde­pen­dent blocks and esti­mate the prior prob­a­bil­ity that each block con­tains a causal SNP that influ­ences the phe­no­type and (within each block) the con­di­tional prior prob­a­bil­ity that each indi­vid­ual SNP is the causal one. Each such prob­a­bil­ity is allowed to depend on anno­ta­tions describ­ing struc­tural or func­tional prop­er­ties of the genomic region or the SNPs within it. We can then empir­i­cally esti­mate to extent to each anno­ta­tion pre­dicts asso­ci­a­tion with the focal phe­no­type. For a com­plete descrip­tion of the fgwas method, see ref. 1. 4.2.3 Meth­ods For appli­ca­tion to the GWAS of EduYears, we used the same set of 450 anno­ta­tions as ref. 1; these are avail­able at https://github.com/joepickrell/1000-genomes. …4.2.6 Reweighted GWAS and Fine Map­ping We reweighted the GWAS results using the func­tion­al-ge­nomic results described above. Using a regional pos­te­rior prob­a­bil­ity of asso­ci­a­tion (PPA) greater than 0.90 as the cut­off, we iden­ti­fied 102 regions likely to har­bor a causal SNP with respect to EduYears (Ex­tended Data Fig. 7c and Sup­ple­men­tary Table 4.2.1). All but two of our 74 lead EduYears-as­so­ci­ated SNPs fall within one of these 102 regions. The excep­tions are rs3101246 and rs2837992, which attained PPA > 0.80 (Ex­tended Data Fig. 7c). In pre­vi­ous appli­ca­tions of fgwas, the major­ity of novel loci that attained the equiv­a­lent of genome-wide sig­nif­i­cance only upon reweight­ing later attained the con­ven­tional P < 5×10 −8 in larger cohorts 1 . Within each region attain­ing PPA > 0.90, each SNP received a con­di­tional pos­te­rior prob­a­bil­ity of being the causal SNP (un­der the assump­tion that there is just one causal SNP in the region). The method of assign­ing this lat­ter pos­te­rior prob­a­bil­ity is sim­i­lar to that of ref. 6, except that the input Bayes fac­tors are reweighted by anno­ta­tion-de­pen­dent and hence SNP-varying prior prob­a­bil­i­ties. In essence, the like­li­hood of causal­ity at an indi­vid­ual SNP derives from its Bayes fac­tor with respect to phe­no­typic asso­ci­a­tion (which is monot­o­n­i­cally related to the P-value under rea­son­able assump­tion­s), whereas the prior prob­a­bil­ity is derived from any empir­i­cal genome-wide ten­dency for the anno­ta­tions borne by the SNP to pre­dict evi­dence of asso­ci­a­tion. Thus, the SNP with the largest pos­te­rior prob­a­bil­i­ties of causal­ity tend to exhibit among the strongest P-val­ues within their loci and func­tional anno­ta­tions that pre­dict asso­ci­a­tion through­out the genome. Note that proper cal­i­bra­tion of this pos­te­rior prob­a­bil­ity requires that all poten­tial causal sites have been either geno­typed or imput­ed, which may not be the case in our appli­ca­tion; we did not include dif­fi­cult-­to-im­pute non-SNP sites such as insertions/deletions in the GWAS meta-­analy­sis. With this caveat in mind, we iden­ti­fied 17 regions where fine map­ping amassed over 50 per­cent of the pos­te­rior prob­a­bil­ity on a sin­gle SNP (Sup­ple­men­tary Table 4.2.2). Of our 74 lead EduYears SNPs, 9 are good can­di­dates for being the causal sites dri­ving their asso­ci­a­tion sig­nals [12%]. One of our top SNPs, rs4500960, is in nearly per­fect LD with the causal can­di­date rs2268894 (and is indeed the sec­ond most likely causal SNP in this region accord­ing to fgwas). The causal can­di­date rs6882046 is within 75kb of two lead SNPs on chro­mo­some 5 (rs324886 and rs10061788), but no two of these three SNPs show strong LD. Inter­est­ing­ly, the remain­ing 6 causal can­di­dates lie in genomic regions that only attain the equiv­a­lent of genome-wide sig­nif­i­cance upon Bayesian reweight­ing. Of the 17 causal can­di­dates, 9 lie in regions that are DNase I hyper­sen­si­tive in the fetal brain.

Table 4.2.2:

Pos­te­rior prob­a­bil­ity of causal­ity

0.992035 0.766500 0.842271 0.567184 0.697862 0.524760 0.632536 0.885280 0.968627 0.781563 0.629610 0.837746 0.725158 0.755457 0.784373 0.682947 0.832675

[mean(c(0.524760, 0.567184, 0.629610, 0.632536, 0.682947, 0.697862, 0.725158, 0.755457, 0.766500, 0.781563, 0.784373, 0.832675, 0.837746, 0.842271, 0.885280, 0.968627, 0.992035)) = 0.76, 0.76*19=14.4]

The results from both approaches show that pre­dic­tion accu­racy increases as more SNPs are used to con­struct the score, with the max­i­mum pre­dic­tive power achieved when using all the geno­typed SNPs (with Approach 1). In that case, the weighted aver­age across the two cohorts of the incre­men­tal R 2 is ~3.85%.

[Ver­sus 2% from Rietveld’s n=100k; this is in line with the rough dou­bling of the main SSGAC sam­ple size. The addi­tional UK Biobank sam­ple of n=111k does not seem to have been used but if it was used, should boost the poly­genic score to ~5.3%?]

…The mag­ni­tude of pre­dic­tive power that we observe is less than one might have expected on the basis of sta­tis­ti­cal genet­ics cal­cu­la­tions 6 and GCTA-GREML esti­mates of “SNP her­i­tabil­ity” from indi­vid­ual cohorts. Indeed, Rietveld et al. (2013) 7 reported GCTA-GREML esti­mates of SNP her­i­tabil­ity for each of two cohorts (STR and QIMR), and the mean esti­mate was 22.4%. Assum­ing that 22.4% is in fact the true SNP her­i­tabil­i­ty, the cal­cu­la­tions out­lined in the SOM of Rietveld et al. (pp. 22-23) gen­er­ate a pre­dic­tion of R 2 = 11.0% for a score con­structed from the GWAS esti­mates of this paper and of R 2 = 6.1% for a score con­structed from the com­bined (dis­cov­ery + repli­ca­tion cohorts, but exclud­ing the val­i­da­tion cohorts) GWAS sam­ple of N = ~117,000-119,000 in Rietveld et al.-­sub­stan­tially higher than the 3.85% that we achieve here (with the score based on all geno­typed SNPs) and the 2.2% Rietveld et al. achieved, respec­tive­ly. These dis­crep­an­cies between the scores’ pre­dicted and esti­mated R 2 may be due to the fail­ure of some of the assump­tions under­ly­ing the cal­cu­la­tion of the pre­dicted R 2 . An alter­na­tive (or addi­tion­al) expla­na­tion is that the true SNP her­i­tabil­ity for the GWAS sam­ple pooled across cohorts is lower than 22.4%. That would be the case if the true GWAS coef­fi­cients dif­fer across cohorts, per­haps due to het­ero­gene­ity in phe­no­type mea­sure­ment or gene-by-en­vi­ron­ment inter­ac­tions. If so, then a poly­genic score con­structed from the pooled GWAS sam­ple would be expected to have lower pre­dic­tive power in an indi­vid­ual cohort than implied by the cal­cu­la­tions above. Based on that rea­son­ing, the R 2 of 2.2% observed by Rietveld et al. (2013) could be ratio­nal­ized by assum­ing that the pro­por­tion of vari­ance accounted for by com­mon vari­ants across the pooled Rietveld cohorts is only 12.7% 6 . (We obtain a sim­i­lar esti­mate, 11.5% with a stan­dard error of 0.45%, when we use LD Score regres­sion 5 to esti­mate the SNP her­i­tabil­ity using our pooled-sam­ple meta-­analy­sis results from this paper, exclud­ing deCODE and with­out GC. While we believe this esti­mate is based on cohort results with­out GC, it is biased down­ward if any cohort in fact applied GC.) If we assume that the 12.7% is valid also for the cohorts con­sid­ered in this study, we would pre­dict an R 2 equal to 4.5%, some­what higher than we observe in HRS and STR but much clos­er. How­ev­er, the degree of cor­re­la­tion in coef­fi­cients across cohorts appears to be rel­a­tively high (Sup­ple­men­tary Table 1.10 reports esti­mates of the genetic cor­re­la­tion between selected cohorts and deCODE; although the cor­re­la­tion esti­mates vary a lot across cohorts, they tend to be large for the largest cohorts, and the weighted aver­age is 0.76). We do not know whether a pooled-­co­hort SNP her­i­tabil­ity of 12.7% or lower can be rec­on­ciled with the observed degree of cor­re­la­tion in coef­fi­cients across cohorts.

The results are reported in Sup­ple­men­tary Tables 6.3 and 6.4. In both the STR and the HRS, cog­ni­tive per­for­mance sig­nif­i­cantly medi­ates the effect of PGS on EduYears; in the HRS, Open­ness to Expe­ri­ence is also a sig­nif­i­cant medi­a­tor. The indi­rect effects for the other medi­at­ing vari­ables are not sig­nif­i­cant s . The results for cog­ni­tive per­for­mance are sim­i­lar across STR and HRS. In both datasets, a one-­s­tan­dard devi­a­tion increase in PGS is asso­ci­ated with ~0.6-0.7 more years of edu­ca­tion, and a one-­s­tan­dard devi­a­tion increase in cog­ni­tive per­for­mance is asso­ci­ated with ~0.15 more years of edu­ca­tion. In both datasets, the direct effect (θ 1 ) of PGS on EduYears is ~0.3-0.4 and the total indi­rect effect (β 1 θ 2 ) is ~0.19-0.31. This implies that a one-­s­tan­dard­-de­vi­a­tion increase in PGS is asso­ci­ated with ~0.3-0.4 more years of edu­ca­tion, keep­ing the medi­at­ing vari­ables con­stant, and that chang­ing the medi­at­ing vari­ables to the lev­els they would have attained had PGS increased by one stan­dard devi­a­tion (but keep­ing PGS fixed) increases years of edu­ca­tion by ~0.19-0.31 years. Last­ly, in both datasets, the par­tial indi­rect effect (θ 21 β 11 ) of cog­ni­tive per­for­mance is large and very sig­nif­i­cant: the esti­mates are equal to 0.29 and 0.14-or 42% and 23% of the total effect (γ 1 )-in STR and HRS, respec­tive­ly. The results also sug­gest that a one-­s­tan­dard devi­a­tion increase in Open­ness to Expe­ri­ence is asso­ci­ated with ~0.06 more years of edu­ca­tion, and the esti­mated par­tial indi­rect effect for Open­ness to Expe­ri­ence is equal to 0.04-or 7% of the total effect (γ 1 ).

Fine-map­ping: “Asso­ci­a­tion map­ping of inflam­ma­tory bowel dis­ease loci to sin­gle vari­ant res­o­lu­tion”, Huang et al 2017 https://www.biorxiv.org/content/early/2015/10/20/028688 Farh et al 2015 Gong et al 2013 van de Bunt et al 2015 “Eval­u­at­ing the Per­for­mance of Fine-Map­ping Strate­gies at Com­mon Vari­ant GWAS Loci” 1http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1005535 “Refin­ing the accu­racy of val­i­dated tar­get iden­ti­fi­ca­tion through cod­ing vari­ant fine-map­ping in type 2 dia­betes”, Maha­jan et al 2018: fine-map­ping sug­gests maybe a quar­ter of hits are causal?


let’s say we have 74 SNP can­di­dates with 2 lev­els each (on/off) which col­lec­tively deter­mine the depen­dent vari­able IQ with an effect of +0.2 IQ points or +0.0133SDs each; we want power=0.80/alpha=0.05 to detect the main effect for each SNP to see if it has a non-zero effect. In fac­to­r­ial ANOVA terms, this would be a design with 74^2=5476 pos­si­ble con­di­tions (since we are only inter­ested in main effects and not inter­ac­tions, I think it could be a par­tial fac­to­r­ial design where many of those are dropped). As a mul­ti­ple regres­sion, it’d be some­thing like IQ ~ A + B + C + ... ZZ. The effect of each vari­able is quite small, and so adding them all into a lin­ear model will explain only a small amount of vari­ance: (0.2/15)^2 * 74 = 0.0132.

G*Power 3.1 (http://www.gpower.hhu.de/ Win­dows ver­sion under Wine), test fam­ily ‘F test’, sta­tis­ti­cal test ‘Lin­ear mul­ti­ple regres­sion: Fixed mod­el, R increase’, a pri­ori power analy­sis:

l = 0.0133766? n=2711

Sup­pose we have a bud­get of 64 edits per embryo, and we want to be able to fill them all up with causal vari­ants; we know that around half will already be the good vari­ant, so we need to have at least 642=128 causal vari­ants. And since we know that each SNP can­di­date has a ~10% prob­a­bil­ity of being causal, we need to be test­ing 10 128 = >1280 SNPs to suc­cess­fully win­now down to >128 causal SNPs which will yield >64 avail­able edits.

We’ll drop the mean effect to 0.1 points and con­sider sam­ple size require­ments test­ing 1280 SNPs. (0.1/15)^2 * 1280 = 0.05688888889

l=0.06032045 n=2954

What does 80% power and 5% alpha mean here? We know that ~10% are causal (our base rate for a true find­ing is 10%), so there are 128 causal SNPs and 1152 non­causal SNPs here. There is a 5% false pos­i­tive rate, so there will be 0.051152=58 false pos­i­tive SNPs. There is 80% pow­er, so we will detect 0.8128=102 causal SNPs. So we will have 58+102=160 appar­ently causal SNPs, but only 58/160=36% are actu­ally causal. So we waste 64% of our edits. We need to do bet­ter.

let’s try with 0.9 and 0.01

l=0.06032045 n=3987

0.90.11280=115 0.01*(1280-115)=11 115/(115+11)=0.91

0.1 aver­age effect might be opti­mistic even though effect sizes decline slow­ly, so one last try with 0.05 mean effect size over those 1280 SNPs: (0.05/15)^2 * 1280 = 0.0142

l = 0.0144045 n=14197

n <- 1000
alpha <- 0.005
SNP_candidates <- 162
SNP_mean_effect <- 0.2
SNP_mean_frequency <- 0.5
SNP_causal_probability <- 0.12
SNP_effects <- sample(c(SNP_mean_effect, 0), SNP_candidates, replace=TRUE,
                      prob=c(SNP_causal_probability, 1-SNP_causal_probability))
which(SNP_effects>0)
r2 <- 0.01

generateSample <- function(n, SNP_effects, SNP_candidates=162, SNP_mean_frequency=0.5) {
    dm <- matrix(nrow=n, ncol=SNP_candidates+1)
    for (i in 1:n) {
        SNP_draw <- rbinom(SNP_candidates, 1, p=SNP_mean_frequency)
        SNPs_genetic <- sum(ifelse(SNP_draw, SNP_effects, 0))
        IQ <- rnorm(1, mean=100, sd=15) + SNPs_genetic
        dm[i,] <- c(round(IQ), SNP_draw)
        }
    df <- as.data.frame(dm)
    colnames(df) <- c("IQ", paste("SNP.", as.character(1:SNP_candidates), sep=""))
    return(df)
}
df <- generateSample(n, SNP_effects, SNP_candidates, SNP_mean_frequency)

power <- sapply(seq(1, n, by=500), function(i) {
    l <- summary(lm(IQ ~ ., data=df[1:i,]))
    # coefficients <- l$coefficients[,1]
    pvalues <- l$coefficients[,4][-1]
    causalPvalues <- na.omit(ifelse(SNP_effects>0, pvalues, NA))
    noncausalPvalues <- na.omit(ifelse(SNP_effects==0, pvalues, NA))

    alphas <- seq(from=0.001, to=0.05, by=0.001)
    alphaYields <- sapply(alphas, function(alpha) { sum(causalPvalues<alpha) / (sum(pvalues<alpha)) })
    alpha <- alphas[which.max(alphaYields)]

    positives <- sum(pvalues<alpha)
    falsePositives <- sum(noncausalPvalues<alpha)
    truePositives <- sum(causalPvalues<alpha)
    truePositiveFraction <- truePositives / length(causalPvalues)
    causalFraction <- (truePositives + falsePositives) / positives
    return(causalFraction) })




library(BGLR)
# n <- 1000
ns <- seq(100, 50000, by=400)
recovery <- sapply(ns, function(n) {
  mean(replicate(100, {
    ## bootstrap a new dataset
    d <- df[sample(nrow(df), n, replace=TRUE),]

    b <- BGLR(d$IQ, ETA=list(list(X=d[-1], model="BayesB", probIn=SNP_causal_probability)), R2=0.01, burnIn=0, verbose=FALSE)
    # plot((b$ETA[[1]]$b), SNP_effects!=0)
    estimate <- data.frame(Causal=SNP_effects!=0, Estimate=(b$ETA[[1]]$b))
    estimate <- estimate[order(estimate$Estimate),]
    truePositives <- sum(estimate$Causal[1:64])
    falseNegatives <- sum(estimate$Causal[-(1:64)])
    # truePositives;falseNegatives
    causalFraction <- truePositives / (truePositives+falseNegatives)
    print(causalFraction)
    return(causalFraction)
    })) })
recovery
library(ggplot2)
qplot(ns, recovery) + geom_smooth(method=lm)


library(glmnet)
cv <- cv.glmnet(as.matrix(df[-1]), df$IQ)
g <- glmnet(as.matrix(df[-1]), df$IQ, lambda=cv$lambda.min)
coef(g)
causalSNPs <- which(SNP_effects>0)
ridgeSNPs <- which(as.matrix(coef(g)[-1,])!=0)
intersect(causalSNPs, ridgeSNPs)

length(intersect(causalSNPs, ridgeSNPs)) / length(causalSNPs)
length(intersect(causalSNPs, ridgeSNPs)) / length(ridgeSNPs)



Thompson sampling with a subset/edit budget:

SNP_edit_limit <- 100
SNP_candidates <- 500
verbose <- TRUE
SNP_mean_effect <- 0.2
SNP_mean_frequency <- 0.5
SNP_causal_probability <- 0.12
r2 <- 0.05
iqError <- 0.55 ## 5yo IQ scores correlate r=0.55 with adult
SNP_effects <- sample(c(SNP_mean_effect, 0), SNP_candidates, replace=TRUE,
                      prob=c(SNP_causal_probability, 1-SNP_causal_probability))
which(SNP_effects>0)

measurementError <- function(r, IQ) {
    IQ.true.std <- (IQ-100)/15
    IQ.measured.std <- r*IQ.true.std + rnorm(length(IQ), mean=0, sd=sqrt(1 - r^2))
    IQ.measured <- 100 + 15 * IQ.measured.std
    return(IQ.measured) }
generateExperimentalSample <- function(n, r, SNP_effects, SNP_candidates, SNP_mean_frequency, SNP_draw_generator) {
    dm <- matrix(nrow=n, ncol=SNP_candidates+1+1) ## allocate space for all SNPs, true IQ, and measured IQ
    for (i in 1:n) {
        SNP_draw <- SNP_draw_generator() # which SNPs to toggle
        SNPs <- ifelse(SNP_draw, SNP_effects, 0) ## convert to effects
        SNP_genetic_score <- sum(SNPs, na.rm=TRUE)
        ## generate a N(100,15) - minus however much our candidate genes explain
        IQ <- round(rnorm(1, mean=100, sd= sqrt((15^2) * (1-r2))) + SNP_genetic_score)
        IQ_measured <- round(measurementError(r, IQ))
        dm[i,] <- c(IQ, IQ_measured, SNP_draw)
        }
    df <- as.data.frame(dm)
    colnames(df) <- c("IQ", "IQ.measured", paste("SNP.", as.character(1:SNP_candidates), sep=""))
    return(df)
}
generateRandomSample <- function(n, r=1, SNP_effects, SNP_candidates, SNP_mean_frequency) {
    generateExperimentalSample(n, r, SNP_effects, SNP_candidates, SNP_mean_frequency,
                               function() { rbinom(SNP_candidates, 1, p=SNP_mean_frequency) })
}

d <- generateRandomSample(1000, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency)
summary(d)

library(BGLR)
library(ggplot2)
maximumDays <- 10000
batch <- 10
lag <- 5*365
jumpForward <- lag*5
## initialize with a seed of n>=2; with less or an empty dataframe, BGLR will crash
d <- generateRandomSample(jumpForward, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency)
d$Date <- 1:jumpForward
# d$Date <- -lag # available immediately
regretLog <- data.frame(N=integer(), N.eff=integer(), Regret=numeric(), Fraction.random=numeric(), Fraction.causals=numeric(), Causal.found=integer(), Causal.notfound=integer())
for (i in jumpForward:maximumDays) {

    ## i=date; day 1, day 2, etc. A datapoint is only available if it was created more than 'lag' days ago; ie if we do 1 a day, then on day 20 with lag 18
    ## we will have 20-18=2 datapoints available. With a 5 year lag, we will go 1825 time-steps before any new data starts becoming available.
    dAvailable <- d[i >= (d$Date+lag),]
    ## quick Bayesian model of our data up to now, using Lasso priors and our SNP setup
    ## BGLR will randomly crash with a gamma/lambda range error every ~5k calls, so catch & retry until it succeeds:
    while(TRUE) {
    tryCatch({
      b <- BGLR(dAvailable$IQ.measured, ETA=list(list(X=dAvailable[-c(1, 2, length(colnames(dAvailable)))],
                                          model="BL", type="beta", probIn=0.12, counts=162, R2=r2, lambda=202, max=500)),
                verbose=FALSE)
      means <- b$ETA[[1]]$b; sds <- b$ETA[[1]]$SD.b
      break;
      }, error = function(e) { print(e) })
      }

    ## Thompson sampling: for Thompson sampling, we sample 1 possible value of each parameter from that parameter's
    ## posterior distribution. Normally, we would sample from the posterior samples returned by JAGS, but BGLR returns
    ## instead a mean+SD, so we sample from each parameter's normal distribution defined by the mean/sd. Then we see if it
    ## was positive (and hence worth editing); if it is positive, then we choose to edit it and toggle it to '1' (since
    ## we set the problem up as 1=increasing). This boolean is then passed into the simulation and a fresh datapoint generated according to
    ## that intervention. In the next loop, this new datapoint will be incorporated into the posterior and so on.
    ## For multiple-edit Thompson sampling where we can only edit _l_ out of _k_ possible SNPs, we sample 1 possible value
    ## as before, then we sort and take the top _l_ out of _k_ actions;
    ## then to decide whether to sample 1 or 0 in each arm, we do a second Thompson sample within each arm.
    ##
    ## To save computations while simulating, or to be more realistic, we might have batches: multiple datapoints in between
    ## updates. If batch=1, it is the conventional Thompson sample (and most data-efficient) but computationally demanding
    ## In the delayed-updates setting, 'batch' is how many get created each day
    for (j in 1:batch) {
     SNPs_Thompson_sampled <- function () {
         ## select the _l_ arms
         samplesArms <- rnorm(n=SNP_candidates, mean=means, sd=sds)
         cutoff <- sort(samplesArms, decreasing=TRUE)[SNP_edit_limit]
         l <- which(samplesArms>=cutoff)

         ## for each winner, do another Thompson sample, and record the losers as NA/not-played
         choices <- rep(NA, SNP_candidates)
         samplesActions <- rnorm(n=SNP_edit_limit, mean=means[l], sd=sds[l]) > 0
         choices[l] <- samplesActions
         return(choices)
         }
     newD <- generateExperimentalSample(1, iqError, SNP_effects, SNP_candidates, SNP_mean_frequency, SNPs_Thompson_sampled)
     newD$Date <- i
     d <- rbind(d, newD)
     }

    ## reports, evaluations, logging:
    estimate <- data.frame(Causal=SNP_effects!=0, Effect=SNP_effects, Estimate=(b$ETA[[1]]$b), SD=b$ETA[[1]]$SD.b)
    estimate <- estimate[order(estimate$Estimate, decreasing=TRUE),]
    regretLog[i,]$Causal.found <- sum(estimate$Causal[1:SNP_edit_limit])
    regretLog[i,]$Causal.notfound <- sum(estimate$Causal[-(1:SNP_edit_limit)])
    regretLog[i,]$Fraction.random  <- sum(estimate$Causal!=0) / SNP_candidates  ## base rate: random guessing
    regretLog[i,]$Fraction.causals <- round(regretLog[i,]$Causal.found / (regretLog[i,]$Causal.found+regretLog[i,]$Causal.notfound), digits=2)
    regretLog[i,]$Regret <- (sum(estimate$Effect) - sum(estimate$Effect[1:SNP_edit_limit])) * SNP_mean_frequency
    regretLog[i,]$N <- nrow(d)
    regretLog[i,]$N.eff <- nrow(dAvailable)

    if(verbose) { print(regretLog[i,]) }
}
qplot(regretLog$N, jitter(regretLog$Regret), xlab="Total N (not effective N)", ylab="Regret (expected lost IQ points compared to omniscience)", main=paste("Edits:", SNP_edit_limit, "; Candidates:", SNP_candidates)) + stat_smooth()

b <- BGLR(d$IQ.measured, ETA=list(list(X=d[-c(1, 2, length(colnames(d)))], model="BL", type="beta", probIn=0.12, counts=162, R2=r2, lambda=202, max=500)), verbose=FALSE)
means <- b$ETA[[1]]$b; sds <- b$ETA[[1]]$SD.b; qplot(SNP_effects, b$ETA[[1]]$b, color=b$ETA[[1]]$SD.b, main=paste("Edits:", SNP_edit_limit, "; Candidates:", SNP_candidates))
image(as.matrix(d[-c(1, 2, length(colnames(d)))]), col=heat.colors(2))

  1. Although it is hard to imag­ine any par­ent autho­riz­ing the cre­ation of nev­er-be­fore-seen muta­tions in their child, regard­less of how com­pelling a neu­ro­bi­o­log­i­cal mech­a­nis­tic case is made for it. In com­par­ison, switch­ing SNPs is know­ably safe because they all exist in the human pop­u­la­tion at high fre­quen­cies and can be observed to cor­re­late or not with health prob­lems. Ani­mal exper­i­ments can help but inher­ently are unrep­re­sen­ta­tive of effects in humans, so the first child will still be sub­ject to an unknown and prob­a­bly large risk.↩︎

  2. Indeed, most of the reported hits have bal­anced fre­quen­cies. I haven’t seen any­one specif­i­cally men­tion why this is so. My best guess is that it’s the same rea­son we expect to see SNPs with the largest effects detected first: it’s due to . Imbal­anced reduces power since the smaller group has larger stan­dard errors; hence, if there are two SNPs with the same effect, but one has a fre­quency of 10% (with 90% of peo­ple hav­ing the bad vari­ant) and another has an even 50-50 split, the sec­ond will be detected ear­lier by GWASes. This seems more sen­si­ble than expect­ing some force like to be oper­at­ing on most IQ-re­lated SNPs.↩︎

  3. For , or sim­ply pre­vent­ing , a major cause of mor­bid­ity & increased mor­tal­ity in the elder­ly.↩︎

  4. This may seem con­trary to the many reported cor­re­la­tions of mor­bid­ity & mor­tal­ity with shiftwork/less self­-re­ported sleep, or less resis­tance to infec­tion, but those results are always dri­ven by the gen­eral pop­u­la­tion suf­fer­ing from insom­nia, stress, dis­ease, etc, and not by the tiny minor­ity of short­-sleep­ers. The short­-sleep­ers them­selves do not report greater vul­ner­a­bil­ity to infec­tion or early mor­tal­i­ty, and I don’t believe any of the bad results focus on short­-sleep­ers.↩︎

  5. Inter­est­ing­ly, this was not even the first appli­ca­tion of CRISPR. That would appear to be DuPont in 2007, which began improved breed­ing of virus-re­sis­tant dairy cul­tures by intro­duc­ing trou­ble­some viral infec­tions, and select­ing for fur­ther use only those bac­te­ria with changed CRISPR-related genomes, indi­cat­ing they had acquired resis­tance to the virus.↩︎

  6. Novem­ber 2013: “‘But it is far too early to con­tem­plate using these meth­ods to alter the human germline’…Pro­fes­sor Dagan Wells, an IVF researcher at Oxford Uni­ver­si­ty, said that although there is still a long way to go before CRISPR could even be con­sid­ered for use on IVF embryos”↩︎

  7. Nature: “Jen­nifer Doud­na, a CRISPR pio­neer at the Uni­ver­sity of Cal­i­for­nia, Berke­ley, is keep­ing a list of CRISPR-altered crea­tures. So far, she has three dozen entries, includ­ing dis­ease-­caus­ing par­a­sites called try­panosomes and yeasts used to make bio­fu­els.” As of May 2017, some­where around 20 human tri­als (most in vivo) were report­edly under­way. Note that BGI’s com­mer­cial­ly-­sold micropigs, BGI’s myostatin/muscly pigs, and mus­cly sheep & cat­tle (Proud­foot et al 2015), were done using TALENs, not CRISPR; but report­ed­ly, BGI is redo­ing the mus­cly pigs with CRISPR↩︎

  8. Nature com­ments on the Liang work: “A Chi­nese source famil­iar with devel­op­ments in the field said that at least four groups in China are pur­su­ing gene edit­ing in human embryos.”↩︎

  9. Call­away 2015: “Sim­i­lar work is already being car­ried out in the lab of George Church, a geneti­cist at Har­vard Med­ical School in Boston. Using a tech­nol­ogy known as CRISPR/Cas9 that allows genes to be eas­ily edit­ed, his team claims to have engi­neered ele­phant cells that con­tain the mam­moth ver­sion of 14 genes poten­tially involved in cold tol­er­ance - although the team has not yet tested how this affects the ele­phant cells. Church plans to do these exper­i­ments in”organoids" cre­ated from ele­phant iPS cell­s."↩︎

  10. Rear­don 2016: “To address such con­cerns, fish geneti­cist Rex Dun­ham of Auburn Uni­ver­sity in Alabama has been using CRISPR to inac­ti­vate genes for three repro­duc­tive hor­mones - in this case, in cat­fish, the most inten­sively farmed fish in the United States. The changes should leave the fish ster­ile, so any fish that might escape from a farm, whether genet­i­cally mod­i­fied or not, would stand lit­tle chance of pol­lut­ing nat­ural stocks.”If we’re able to achieve 100% steril­i­ty, there is no way that they can make a genetic impact," Dun­ham says. Admin­is­ter­ing hor­mones would allow the fish to repro­duce for breed­ing pur­pos­es. And Dun­ham says that sim­i­lar meth­ods could be used in other fish species."↩︎

  11. Rear­don 2016: “CRISPR could also reduce the need for farm­ers to cull ani­mals, an expen­sive and arguably inhu­mane prac­tice. Biotech­nol­o­gist Ali­son van Eenen­naam at the Uni­ver­sity of Cal­i­for­nia, Davis, is using the tech­nique to ensure that beef cat­tle pro­duce only male or male-­like off­spring, because females pro­duce less meat and are often culled. She copies a Y-chro­mo­some gene that is impor­tant for male sex­ual devel­op­ment onto the X chro­mo­some in sperm. Off­spring pro­duced with the sperm would be either nor­mal, XY males, or XX females with male traits such as more mus­cle.”↩︎

  12. Rear­don 2016: “In the egg indus­try, male chicks from elite egg-lay­ing chicken breeds have no use, and farm­ers gen­er­ally cull them within a day of hatch­ing. Tizard and his col­leagues are adding a gene for green flu­o­res­cent pro­tein to the chick­ens’ sex chro­mo­somes so that male embryos will glow under ultra­vi­o­let light. Egg pro­duc­ers could remove the male eggs before they hatch and poten­tially use them for vac­cine pro­duc­tion.”↩︎

  13. Rear­don 2016: “Mol­e­c­u­lar geneti­cist Scott Fahrenkrug, founder of Recom­bi­net­ics in Saint Paul, Min­neso­ta, is using gene-edit­ing tech­niques to trans­fer the gene that elim­i­nates horns into elite breeds 12. The com­pany has pro­duced only two polled calves so far - both male - which are being raised at the Uni­ver­sity of Cal­i­for­nia, Davis, until they are old enough to breed.”↩︎

  14. Rear­don 2016: “But until the arrival of CRISPR, virol­o­gists lacked the tools to eas­ily alter fer­ret genes. Xiao­qun Wang and his col­leagues at the Chi­nese Acad­emy of Sci­ences in Bei­jing have used CRISPR to tweak genes involved in fer­ret brain devel­op­men­t14, and they are now using it to mod­ify the ani­mals’ sus­cep­ti­bil­ity to the flu virus. He says that he will make the model avail­able to infec­tious-dis­ease researchers.”↩︎

  15. from “Wel­come to the CRISPR zoo: Birds and bees are just the begin­ning for a bur­geon­ing tech­nol­ogy”, Rear­don 2016: “The group expects to hatch its first gen­er­a­tion of chicks with gene mod­i­fi­ca­tions later this year as a proof of con­cept. Doran real­izes that it could be some time before reg­u­la­tors would approve gene-edited eggs, and he hopes that his daugh­ter will have grown out of her allergy by then.”If not, I’ve got some­one ready and wait­ing to try the first egg," he says."↩︎

  16. Rear­don 2016: “Gillis has been study­ing the genomes of ‘hygienic’ bees, which obses­sively clean their hives and remove sick and infested bee lar­vae. Their colonies are less likely to suc­cumb to mites, fungi and other pathogens than are those of other strains, and Gillis thinks that if he can iden­tify genes asso­ci­ated with the behav­iour, he might be able to edit them in other breeds to bol­ster hive health. But the trait could be dif­fi­cult to engi­neer. No hygien­e-as­so­ci­ated genes have been defin­i­tively iden­ti­fied, and the roots of the behav­iour may prove com­plex, says Bart­Jan Fern­hout, chair­man of Arista Bee Research in Boxmeer, the Nether­lands, which stud­ies mite resis­tance. More­over, if genes are iden­ti­fied, he says, con­ven­tional breed­ing may be suf­fi­cient to con­fer resis­tance to new pop­u­la­tions, and that might be prefer­able given the wide­spread oppo­si­tion to genetic engi­neer­ing.”↩︎

  17. Rear­don 2016: “Other researchers are mak­ing cat­tle that are resis­tant to the try­panosome par­a­sites that are respon­si­ble for sleep­ing sick­ness.”↩︎

  18. Rear­don 2016: “BGI is also using CRISPR to alter the size, colour and pat­terns of koi carp. Koi breed­ing is an ancient tra­di­tion in Chi­na, and Jian Wang, direc­tor of gene-edit­ing plat­forms at BGI, says that even good breed­ers will usu­ally pro­duce only a few of the most beau­ti­fully coloured and pro­por­tioned, ‘cham­pion qual­ity’ fish out of mil­lions of eggs. CRISPR, she says, will let them pre­cisely con­trol the fish’s pat­terns, and could also be used to make the fish more suit­able for home aquar­i­ums rather than the large pools where they are usu­ally kept. Wang says that the com­pany will begin sell­ing koi in 2017 or 2018 and plans to even­tu­ally add other types of pet fish to its reper­toire.”↩︎

  19. For exam­ple, Liang et al 2015’s reported off-­tar­get muta­tion num­bers in human embryos was greeted with a com­ment from George Church that “the researchers did not use the most up-­to-­date CRISPR/Cas9 meth­ods and that many of the researchers’ prob­lems could have been avoided or less­ened if they had.”↩︎

  20. Power cal­cu­la­tion using the Rietveld et al 2013 poly­genic score:

    power.t.test(delta=0.03, sd=(1-0.025^2), power=0.80)
    
         Two-sample t test power calculation
    
                  n = 17421.11975
              delta = 0.03
                 sd = 0.999375
          sig.level = 0.05
              power = 0.8
        alternative = two.sided
    
    NOTE: n is number in *each* group
    17421 * 2
    # [1] 34842
    ↩︎