# Potassium sleep experiments

2 self-experiments on potassium citrate effects on sleep: harm to sleep when taken daily or in the morning (experiments, biology, statistics, Zeo, R, Bayes)
created: 21 December 2012; modified: 30 Sep 2017; status: finished; confidence: highly likely;

Potassium and magnesium are minerals that many Americans are deficient in. I tried using potassium citrate and immediately noticed difficulty sleeping. A short randomized (but not blinded) self-experiment of ~4g potassium taken throughout the day confirmed large negative effects on my sleep. A longer followup randomized and blinded self-experiment used standardized doses taken once a day early in the morning, and also found some harm to sleep, and I discontinued potassium use entirely.

# Potassium day use

In October 2012, I bought some potassium citrate on a lark after noting that the daily RDA and my diet suggested that I was massively deficient. (I chose potassium citrate rather than potassium chloride because they are priced similarly and no information suggested they differed meaningfully, but I don’t really like the idea of chlorine, so I went with citrate.) The first night I slept terribly, taking what felt like hours to fall asleep and then waking up frequently - due to either the potassium or a fan left on; the second night with potassium, I turned off the fan but slept poorly again. My suspicions were aroused. I began recording sleep data.

## Background

Partway through the process, I searched Google Scholar and Pubmed (human trials) for potassium sleep; I checked the first 70 results of both. A general Google search turned up mostly speculation on the relationship of potassium deficiency and sleep. The only useful citation was Potassium affects actigraph-identified sleep, Drennan et al 1991; actigraphs likely aren’t as good as a Zeo, and n=6, but the study is directly relevant. Only 2 actigraph results reached statistical significance: a small improvement in sleep efficiency (the percentage of time spent laying in bed and actually sleeping) and a bigger benefit in WASO (time awake during sleep time; this probably drove the sleep efficiency).

## Data

The first night (10/12) involved falling asleep in 30 minutes rather than my usual 19.6±11.9, waking up 12 times (5.9±3.4), and spending ~90 minutes awake (18.1±16.2) The next day (10/13) I took a similar dose and double-checked the fan before bed: 25 minutes to fall asleep, 10 awakenings, 35 minutes awake, but I woke fairly rested. So it seems like the fan was only partly to blame. The third day (10/14) I omitted any potassium: 21/8/29. Fourth (10/15) on again with an evening dose: 54/7/24. Fifth (10/16), off: 16/2/6. Sixth (10/17), on with a halved dose: 33/3/6. Seventh (10/18), off: 17/6/7. Eighth (10/20), half: 33/6/15.

At this point I began randomizing consumption between on and off; since this is preliminary, I didn’t bother with blinding potassium consumption. Ninth (10/21), on: 25/7/9. Tenth (10/22), on: 18/8/10. 11th (10/23), off: 26/4/10. 12th (10/24), off: 33/7/16. 13th (10/25), on: 32/7/13. 14th (10/26), on: 21/5/8. 15th, on: 34/2/1. 16th, off: 16/7/15. 17th, on: 29/8/20. 18th, on: 17/10/17. 19th, off: 36/9/24. 20th (11/1), on: 21/4/19. 21st (11/2), off: 29/7/16. 22nd (11/3), on: 26/7/10. 23rd (11/4), on: 16/4/11. 24th (11/5), off: 21/4/17. 25th (11/6), on: 19/9/24.

11 Nov, on: 15/3/08. 13 Nov, off: 11/8/21. 14 Nov, off: 18/8/22. 15 Nov, on: 30/8/16. 16 Nov, off: 20/7/12. 17 Nov, on: 34/8/20. 18 Nov, on: 12/8/22. 19 Nov, off: 24/8/14. 20 Nov, on: 26/4/39. 21 Nov, off: 15/6/14. 22 Nov, on: 26/8/29. 23 Nov, on: 23/4/8. 24 Nov, off: 24/3/5. 25 Nov, on: 27/7/15. 26 Nov, on: 30/10/17. 27 Nov, off: 42/12/13. 28 Nov, off: 40/11/42. 29 Nov, off: 19/14/50. 30 Nov, off: 32/8/39. (Here I counted the sample-sizes and realized the off days were drastically under-represented, reducing statistical power; so I have eliminated randomization and gone off potassium.) 1 Dec, off: 28/10/15. 2 Dec, off: 37/8/20. 3 Dec, off: 36/6/18. 4 Dec, off: 19/9/33. 5 Dec, off: 25/8/27. 6 Dec, off: 30/13/45. (Now balanced, resuming randomization.) 7 Dec, on: 31/9/60. 8 Dec, off: 22/9/23. 9 Dec, off: 11/5/21. 10 Dec, on: 30/4/10. 11 Dec, on: 22/9/50. 13 Dec, off: 20/5/6. 14 Dec, off: 33/13/25. 15 Dec, on: 26/11/22. 16 Dec, off: 33/12/28. 17 Dec, off: 42/9/31. 18 Dec, off: 31/9/61. 19 Dec, on: 23/8/18.

## Analysis

### Sleep disturbances

If potassium was disturbing my sleep, I didn’t necessarily want to wait for any one metric of wakefulness to reach significance; rather, I wanted to combine them into a single metric of sleep problems: time to fall asleep (latency), number of awakenings, and time spent awake. (With all 3, higher is worse.) Number of awakenings tends to vary over a smaller range than time to fall asleep or time spent awake - a normal value for the former might be 5, rather than 30 for the latter; to compensate for that, we convert each metric into a standard deviation indicating how unusual eg. 10 awakenings is and whether it is more unusual than it taking 15 minutes to fall asleep. Then we can do a standard test. To graph the data at each step, starting with graphing all the data on an overlapping chart1 (this is not per day):

Nights off potassium are colored blue and nights on potassium are red; it looks like red dots are higher than blues, overall, but the trend is not clear. So we convert each individual datapoint to its respective standard deviation2:

The trend has become much clearer, but the final step is to add each day’s scores to get an overall measure3:

Now the different has become dramatic: one can almost draw a line separating both groups without any errors. As one would expect given this graphical evidence, a Bayesian two-group test reports that there is ~0 chance that the true effect size is 0, and the most likely effect size is a dismaying d=-1.14:

A two-sample test agrees:5 p=0.0002168. (There is no need for multiple correction in this instance.) This confirms my subjective impression.

### Mood/productivity

A secondary question is whether potassium delivered any waking benefits. I write down at the end of each day my rating 2-4 how happy and/or productive I felt that day. Does this self-rating show any effect? Here’s a plot of each day colored by whether it was a potassium day:

There is little visible effect, and the formal Bayesian6 analysis is as weak as the sleep disturbances are strong:

So there is no apparent benefit from the potassium.

## Conclusion

This experiment was hastily done and has several weaknesses, some I mentioned before; in ascending order of importance:

1. dosage was not uniform

Number of dosages varied from day to day as was convenient and doses were measured approximately with a spoon (since 4 grams is a pretty substantial amount, after all). Here is another objection I don’t think matters: lower than average doses may contribute to an underestimate of the effect size… but that implies that the effect size is even more extreme than -1.1! We are interested in problems that would shrink the effect size back to 0, not imply that it’s even worse than -1.1.
2. the randomization was incomplete

As covered in the data section, there was a severe imbalance in sample size for each condition, so I stopped randomization for about a week. Intuitively, I don’t think there was anything special about that week in regard to getting very good sleep (as would be necessary to contribute to an overestimated effect size), but if anyone disagreed, it would not be hard to exclude those days and use the rest.
3. no blinding was done

I am not sure how much this matters. I had no expectation that potassium would affect my sleep at all, one user specifically denied any effect, the only study suggested I’d find improvements, I did not want to find a negative effect much less such a severe effect, and the sheer strength of the effect over a multi-month period is a bit more than I would expect from any expectancy or placebo effect.
4. timing was not uniform

Of the issues, this is the most important. If potassium has some stimulating effects as anecdotes claim, then timing may be causing all the sleep disturbances and not potassium per se. It might be exactly like vitamin D in this respect: taken in the evening, it badly damages sleep but taken in the morning, it does nothing or it improves sleep.

If I were to do a followup experiment, it would be blinded & randomized as usual, with consistent doses (eliminating objections 1-3), but more importantly, the dose would be consumed upon awakening.

I am not sure I will bother with a followup experiment. Potassium is not of particular interest to me, my existing supply is low after months of consumption, I observed no subjective improvements on consumption, and so I am not inclined to run the risk of damaging more months of sleep. Other people can do that.

# Potassium morning use

As it happened, I managed to retrieve my pill-making machine and spare gel capsules, and I do hate to waste perfectly good potassium citrate powder, so I decided to do a morning experiment. I made 3x24 potassium pills and 3x24 brown rice pills (out of flour); I take one set of 3 pills each morning, randomly picking. This procedure addresses all 4 issues, and will answer the question about whether potassium’s sleep disturbance is due to a timing issue like that of caffeine and vitamin D. Analysis will be the same as before: 3 metrics of sleep disturbance, and then daily self-rating. (I didn’t devise a paired-blocks setup since my marked containers were in use elsewhere; as often happens I ran out of one set of pills first, the rice placebo pills, on 10 February 2013, and made another batch of 24 rice placebo pills. The last potassium pill was 21 February 2013.)

## Analysis

Subjectively, I noticed nothing on what turned out to be the potassium days, unlike in the first experiment.

### Sleep disturbances

Running the analysis the same way as before, we get a small increase in sleep disturbances (d=0.15, higher is worse) but the effect could easily be nothing7:

I suspect there really is an underlying causal effect: the first experiment indicated a large increase in sleep disturbances, and a much smaller one is in line with my expectations of the effect of a smaller standardized dose first thing upon waking.

But practically speaking, this small disturbance would be acceptable if it came with some benefit.

### Mood/productivity

The results look almost identical to before8:

## Conclusion

A much higher-quality experiment with more favorable conditions for potassium showed a result consistent with some harm to my sleep, and no benefit. Since potassium showed harm in both circumstances with no suggestion of benefit, I will not continue using potassium.

1. The generating R code (see later analysis footnote for definitions of data variables like offtimeawake etc):

plot(c(1:32), offtimeawake, col="blue",
xlab="nth", ylab="latency/awakenings/awake (raw)")
points(c(1:32), offlatency, col="blue")
points(c(1:32), offawakenings, col="blue")
points(c(1:30), ontimeawake, col="red")
points(c(1:30), onlatency, col="red")
points(c(1:30), onawakenings, col="red")
2. After running zscore on each data variable, we repeat the previous code but with ylab="latency/awakenings/awake (standardized)" in the call to plot.

3. Assuming the zscore conversion has been done:

plot(c(1:32), offtimeawake+offlatency+offawakenings, col="blue",
xlab="nth", ylab="standardized sleep disturbance score")
points(c(1:30), ontimeawake+onlatency+onawakenings, col="red")
4. The previously described composite measure and BEST test:

# for interventions with dates, see https://www.gwern.net/docs/zeo/2012-2013-potassium.csv
# all the non-potassium days
offlatency <- c(11,15,16,16,17,18,20,21,21,24,24,26,29,33,36,42,40,19,32,28,37,36,19,25,
30,22,11,20,33,33,42,31)
offawakenings <- c(8,6,2,7,6,8,7,4,8,3,8,4,7,7,9,12,11,14,8,10,8,6,9,8,13,9,5,5,13,12,9,9)
offtimeawake <- c(21,14,6,15,7,22,12,17,29,5,14,10,16,16,24,13,42,50,39,15,20,18,33,27,45,
23,21,6,25,28,31,61)

# all the potassium days
onlatency <- c(12,15,16,17,18,19,21,21,23,25,25,26,26,26,27,29,30,30,32,33,33,34,34,
54,30,31,30,22,26,23)
onawakenings <- c(8,3,4,10,8,9,4,5,4,10,7,4,7,8,7,8,12,8,7,3,6,2,8,7,10,9,4,9,11,8)
ontimeawake <- c(22,08,11,17,10,24,19,8,8,35,9,39,10,29,15,20,90,16,13,6,15,1,20,24,
17,60,10,50,22,18)

# normalize
zscore <- function(x,y) mapply(function(a) (a - mean(y))/sd(y), x)
offlatency <- zscore(offlatency, c(offlatency, onlatency))
onlatency  <- zscore(onlatency,  c(offlatency, onlatency))
offawakenings <- zscore(offawakenings, c(offawakenings, onawakenings))
onawakenings  <- zscore(onawakenings,  c(offawakenings, onawakenings))
offtimeawake <- zscore(offtimeawake, c(offtimeawake, ontimeawake))
ontimeawake <- zscore(ontimeawake, c(offtimeawake, ontimeawake))

# zip together with sum to get a single measure of how deviate a night was
off <- offlatency + offawakenings + offtimeawake
on <- onlatency + onawakenings + ontimeawake

# usual Bayesian two-group test
source("BEST.R")
mcmcChain = BESTmcmc(off, on)
postInfo = BESTplot(off, on, mcmcChain) # graph
postInfo
#          SUMMARY.INFO
# PARAMETER      mean  median    mode  HDIlow HDIhigh pcgtZero
#   mu1        0.1664  0.1655  0.1421 -0.71894  1.0555       NA
#   mu2        2.4256  2.4210  2.4035  1.81175  3.0478       NA
#   muDiff    -2.2592 -2.2592 -2.2318 -3.34666 -1.1853    0.006
#   sigma1     2.3939  2.3607  2.2695  1.78291  3.0915       NA
#   sigma2     1.6189  1.5988  1.5786  1.11009  2.1614       NA
#   sigmaDiff  0.7750  0.7606  0.7341 -0.03236  1.6317   97.205
#   nu        32.0045 23.2730  9.6599  2.33645 88.0997       NA
#   nuLog10    1.3607  1.3669  1.4214  0.67234  2.0337       NA
#   effSz     -1.1141 -1.1107 -1.0959 -1.69481 -0.5433    0.006
5. Reusing the standardized data from before:

wilcox.test(off, on)
#     Wilcoxon rank sum test
#
# data:  off and on
# W = 224, p-value = 0.0002168
6. As before, we use BEST (the self-rating is mostly normal):

Potassium <- c(1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0,1,1,
0,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1)
MP <- c(4,4,3,4,4,3,3,2,3,3,3,3,4,4,3,4,2,2,2,3,4,3,4,3,4,3,4,4,3,3,2,3,2,4,4,3,4,2,3,4,2,
3,3,2,2,2,3,2,3,3,4,2,3,4,3,4,3,3,2,2,3,4,4,3,4,2,2,3,2)
pot <- data.frame(Potassium, MP)

# first graph:
library(ggplot2)
qplot(data=pot, y=MP, color=Potassium)

# analysis:
source("BEST.R")
off <- pot$MP[pot$Potassium == 0]
on <- pot$MP[pot$Potassium == 1]
mcmcChain = BESTmcmc(off, on)
postInfo = BESTplot(off, on, mcmcChain) # graph
postInfo
#            SUMMARY.INFO
# PARAMETER       mean   median     mode  HDIlow  HDIhigh pcgtZero
#   mu1        3.02651  3.02686  3.03576  2.7780   3.2677       NA
#   mu2        3.10432  3.10390  3.07921  2.7939   3.4127       NA
#   muDiff    -0.07782 -0.07736 -0.07786 -0.4728   0.3119    34.96
#   sigma1     0.75685  0.74855  0.73261  0.5834   0.9427       NA
#   sigma2     0.83168  0.81845  0.79169  0.6133   1.0677       NA
#   sigmaDiff -0.07483 -0.07033 -0.05617 -0.3755   0.2195    31.15
#   nu        47.52944 39.43237 23.78338  4.6350 111.4156       NA
#   nuLog10    1.58217  1.59585  1.63348  0.9931   2.1316       NA
#   effSz     -0.09844 -0.09761 -0.10476 -0.5879   0.3897    34.96

wilcox.test(off, on)
#     Wilcoxon rank sum test with continuity correction
#
# data:  off and on
# W = 552.5, p-value = 0.6789
7. See previously for explanation:

pot <- read.csv("https://www.gwern.net/docs/zeo/2013-gwern-potassium-morning.csv")

# standardize & combine into a single equally-weighted synthetic index z-score
pot$Disturbance <- scale(pot$Time.to.Z) + scale(pot$Awakenings) + scale(pot$Time.in.Wake)

on  <- pot[pot$Potassium==1,]$Disturbance
off <- pot[pot$Potassium==0,]$Disturbance

source("BEST.R")
mcmcChain = BESTmcmc(off, on)
postInfo = BESTplot(off, on, mcmcChain) # graph
postInfo
#            SUMMARY.INFO
# PARAMETER      mean   median     mode  HDIlow HDIhigh pcgtZero
#   mu1        0.1329  0.13224  0.11468 -0.6505  0.9203       NA
#   mu2       -0.2626 -0.26479 -0.22430 -1.1154  0.5966       NA
#   muDiff     0.3956  0.39838  0.37996 -0.7724  1.5327    75.39
#   sigma1     1.9961  1.96663  1.89699  1.3978  2.6302       NA
#   sigma2     1.9403  1.90682  1.86314  1.2797  2.6697       NA
#   sigmaDiff  0.0558  0.06166  0.04212 -0.8615  0.9499    55.85
#   nu        33.0593 24.28680  9.49415  1.7036 90.8230       NA
#   nuLog10    1.3674  1.38537  1.47058  0.6392  2.0655       NA
#   effSz      0.2054  0.20334  0.18368 -0.3619  0.8119    75.39
8. on/off defined and BEST loaded in previous analysis:

mcmcChain = BESTmcmc(off$MP, on$MP)
postInfo = BESTplot(off$MP, on$MP, mcmcChain) # graph
postInfo
#                SUMMARY.INFO
# PARAMETER        mean   median     mode  HDIlow  HDIhigh pcgtZero
#   mu1        2.999866  2.99993  2.99749  2.7134   3.2884       NA
#   mu2        2.955535  2.95571  2.95990  2.6391   3.2689       NA
#   muDiff     0.044331  0.04465  0.05384 -0.3831   0.4669    58.29
#   sigma1     0.739736  0.72787  0.71017  0.5371   0.9685       NA
#   sigma2     0.731523  0.71670  0.68979  0.5081   0.9827       NA
#   sigmaDiff  0.008212  0.01087  0.01340 -0.3210   0.3419    52.76
#   nu        41.545632 33.20153 18.29201  2.5717 103.6089       NA
#   nuLog10    1.502165  1.52116  1.55933  0.8486   2.1209       NA
#   effSz      0.060755  0.06100  0.07764 -0.5064   0.6339    58.29