Bacopa Quasi-Experiment

A small 2014-2015 non-blinded self-experiment using Bacopa monnieri to investigate effect on memory/sleep/self-ratings in an ABABA design; no particular effects were found. (experiments, biology, statistics, Zeo, R, Bayes, psychology)
created: 6 May 2014; modified: 17 May 2018; status: finished; confidence: possible; importance: 3

Bacopa is a supplement herb often used for memory or stress adaptation. Its chronic effects reportedly take many weeks to manifest, with no important acute effects. Out of curiosity, I bought 2 bottles of Bacognize Bacopa pills and ran a non-randomized non-blinded ABABA quasi-self-experiment from June 2014 to September 2015, measuring effects on my memory performance, sleep, and daily self-ratings of mood/productivity. For analysis, a multi-level Bayesian model on two memory performance variables was used to extract per-day performance, factor analysis was used to extract a sleep index from 9 Zeo sleep variables, and the 3 endpoints were modeled as a multivariate Bayesian time-series regression with splines. Because of the slow onset of chronic effects, small effective sample size, definite temporal trends probably unrelated to Bacopa, and noise in the variables, the results were as expected, ambiguous, and do not strongly support any correlation between Bacopa and memory/sleep/self-rating (+/-/- respectively).

Bacopa monnieri (Examine, nootropics survey, Reddit discussions) is an herb prominent for its use in Ayurvedic medicine. Taken chronically over long time-periods, Bacopa may improve cognition and help with stress, but (like some other Ayurvedic remedies) has a potential drawback in the form of heavy metal contamination.

Background

The psychology & medical literature is sporadic and studies are somewhat uninterpretable due to variables of dosage & dose length, but overall the evidence for improvements is better than that for most nootropics. The Cognitive-Enhancing Effects of Bacopa monnieri: A Systematic Review of Randomized, Controlled Human Clinical Trials found evidence of benefits to memory in several >=12-week-long RCTs. Cognitive effects of two nutraceuticals Ginseng and Bacopa benchmarked against modafinil: a review and comparison of effect sizes reviewed mostly the same studies. Meta-analysis of randomized controlled trials on cognitive effects of Bacopa monnieri extract attempted to meta-analyze the studies (specifically: Stough et al 2001b, Roodenrys et al 2002, Raghav et al 2006, Barbhaiya et al 2008, Calabrese et al 2008, Stough et al 2008, Peth-Nui et al 2012, & Sathyanarayanan et al 2013) and found that of the 21 possible metrics/tests, the trail-making and reaction-time improvements had low heterogeneity between studies & also reached statistical-significance; unfortunately, heterogeneity was high in most metrics, few studies examined the same metrics, and the low study count renders impossible any estimate of how bad the publication bias is (typically severe) or other checks of quality/reliability, so the results are not as impressive as they might appear. Overall, it seems Bacopa likely has some useful effects.

Practically, I have 2 concerns about Bacopa:

  1. obtaining a heavy-metal-free product for long-term consumption (what good is it to benefit from Bacopa if you are simultaneously building up a long-term heavy metal burden?)

    CoAs are the first line of defense but availability differs: Ayur Sante, Nutrigold, Indigo Herbs, Banyan Botanical & Nutricargo reportedly provide CoAs as does NootropicsDepot; while Planetary Herbals, Himalaya, & Mind Nutrition have stonewalled requests.

    Probably the best bet is to go with Bacognize: NootropicsDepot’s CoA & an independent lab test confirms that the heavy metal levels are acceptably low in that standardized branded source. (May cost more, though.)
  2. how hard self-experimenting is.

    Self-experimenting is both easy and hard: it’s easy because there should be effects on memory recall which can be easily extracted from spaced repetition software like Mnemosyne, but hard because onset requires many weeks so a self-experiment must either have few blocks (limiting comparability) or be lengthy (to allow for multiple transitions between Bacopa and placebo conditions). I may have to settle for a lesser analysis like a before-after comparison, and only then if the results are positive consider the expense & difficulty of a full RCT over a number of months.

Bacopa sources

Bacopa can be bought from a number of retailers. There are several capsule sellers on Amazon, and NootropicsDepot sells both capsules & powder. More specifically (as of 11 September 2014, assuming using Amazon’s free shipping & NootropicsDepot’s regular S&H):

Seller Form Content/brand Dose (mg) Count Price ($) S&H mg/$
ProHealth Cap Bacognize 300 60 25.49 0 706
NootropicsDepot Cap Bacognize 250 120 11.99 7.25 1159
Vitacost Cap Bacognize 300 60 8.99 4.49 1335
Vitacost Cap Bacognize 300 120 20.49 4.49 1441
NootropicsDepot Cap Bacognize 250 240 22.99 7.25 1984
Swanson Cap Bacognize 250 90 11.25 0 2000
Nutrigold Cap BacoMind+generic 500 90 16.99 0 2649
NootropicsDepot Powder Bacognize 125000 1 24.99 7.25 3877
Vitacost Cap Bacognize 300 240 12.49 4.99 41191
NootropicsDepot Powder Bacognize 250000 1 45.99 7.25 4695
NootropicsDepot Powder Bacognize 500000 1 89.99 7.25 5142

The cheapest Bacognize, if one doesn’t want to cap one’s own pills (as one probably does since the powder reportedly tastes bad), would seem to be the Swanson. (The Nutrigold is substantially cheaper, but also comes with a different branded source and is half-generic, and if one wanted to roll the dice, there are probably much cheaper sources of Bacopa on Amazon.) At 90x250mg, the dose per pill is a little inconveniently low for daily usage (>=300mg would be better) but still usable, so the daily cost would be $0.13, and it’d cover 90 days - conveniently, the same time period used in a number of studies such as Stough et al 2008.

Quasi-experiment

Intervention

I ordered 2 bottles of the Swanson on 14 September, and began taking one pill in the morning with olive oil on 26 September 2014. I decided to do an ABABA trial (baseline/Bacopa/off/Bacopa/off), checking for correlated changes in my Mnemosyne spaced repetition memory scores/grades, Zeo sleep variables (changes are often reported anecdotally), and possibly other things such as my daily self-ratings or extracted factors. I used 90-day blocks because that is long enough for effects to manifest (~12 weeks) and conveniently matches up with the pill count in each Swanson bottle:

  1. Baseline/off (A): prior 90 days: 2014-06-28 - 2014-09-25
  2. On (B): 2014-09-26 - 2014-12-19
  3. Off (A): 2014-12-20 - 2015-03-19
  4. On (B): 2015-03-20 - 2015-06-05
  5. End/Off (A): 2015-06-06 - 2015-09-04

The quasi-experiment went reasonably well and I noticed no side-effects or visible changes.

Data prep

Daily ratings:

mp <- na.omit(read.csv("~/selfexperiment/mp.csv", colClasses=c("Date", "integer")))

(I am not using any productivity factors which might improve substantially on my MP self-ratings because in the analyses I try periodically with a large set of variables eg Git commits & number of emails sent, as of May 2018, I still haven’t found any clear productivity factor, to my disappointment.)

Query Mnemosyne spaced repetition logs (see Treadmill), get grades recorded each day (which reflects memory retrieval that day) and the next future grade for each card (reflects memory encoding/increase in memorization that day), along with easiness and hour/day covariates; then fit a Bayesian multilevel model with random effects for each card and day regressing on current & future grade; finally, extract the two random-effects for each day and sum them to get an index variable of my memory performance that day:

target <- "~/doc/mnemosyne/default.db"
library(sqldf)
# .schema log
# CREATE TABLE log(
#         _id integer primary key autoincrement,
#         event_type integer,
#         timestamp integer,
#         object_id text,
#         grade integer,
#         easiness real,
#         acq_reps integer,
#         ret_reps integer,
#         lapses integer,
#         acq_reps_since_lapse integer,
#         ret_reps_since_lapse integer,
#         scheduled_interval integer,
#         actual_interval integer,
#         thinking_time integer,
#         next_rep integer,
#         scheduler_data integer
#     );
grades <- sqldf("SELECT timestamp,object_id,grade,easiness,thinking_time,actual_interval,(SELECT grade \
                 FROM log AS log2 WHERE log2.object_id = log.object_id AND log2.timestamp > log.timestamp \
                 ORDER BY log2.timestamp DESC LIMIT 1) AS grade_future FROM log WHERE event_type==9;",
                dbname=target,
                method = c("integer", "factor","integer","numeric","integer","integer", "integer"))
grades$timestamp <- as.POSIXct(grades$timestamp, origin = "1970-01-01", tz = "EST")
grades$thinking_time.log <- log1p(grades$thinking_time); grades$thinking_time <- NULL
colnames(grades) <- c("Timestamp", "ID", "Grade", "Easiness", "Interval.length", "Grade.future",
                       "Thinking.time.log")
## extract the temporal covariates from the timestamp
grades$WeekDay <- as.factor(weekdays(grades$Timestamp))
grades$Hour    <- as.factor(as.numeric(format(grades$Timestamp, "%H")))
grades$Date    <- as.Date(grades$Timestamp)

## multilevel model: mean-field variational inference rather than MCMC to avoid days of computation
library(brms)
mb <- brm(cbind(Grade,Grade.future) ~ (1|ID) + (1|Date.int) + WeekDay + Hour + Easiness, data=grades, algorithm="mean")
summary(mb)
r <- as.data.frame(ranef(mb)$Date.int)
averageGrade <- r$Estimate.Grade_Intercept + r$Estimate.Gradefuture_Intercept
dates <- as.Date(as.integer(rownames(r)), origin = "1970-01-01")
gradeDaily <- data.frame(Date=dates, Mnemosyne.performance=averageGrade)

Zeo code largely borrowed from most-recent style of analysis in CO2/ZMA; for more details, see those, but the idea is to transform the variables into more Gaussian-looking variables for stabler model-fitting, specify a plausible amount of measurement error, define 2 latent variables for good and bad sleep (oddly, they don’t seem to be negations of each other), and like the Mnemosyne code, extract the latent variables for each day and sum into a single sleep quality score:

zeo <- read.csv("https://www.gwern.net/docs/zeo/gwern-zeodata.csv")
zeo$Date <- as.Date(sapply(strsplit(as.character(zeo$Rise.Time), " "), function(x) { x[1] }), format="%m/%d/%Y")
zeo <- subset(zeo, select=c("Date", "ZQ", "Total.Z", "Time.to.Z", "Time.in.Wake", "Time.in.REM",
    "Time.in.Light", "Time.in.Deep", "Awakenings", "Morning.Feel"))

zeo$Total.Z.2 <- zeo$Total.Z^2
zeo$ZQ.2 <- zeo$ZQ^2
zeo$Time.in.REM.2 <- zeo$Time.in.REM^2
zeo$Time.in.Light.2 <- zeo$Time.in.Light^2
zeo$Time.in.Wake.log <- log1p(zeo$Time.in.Wake)
zeo$Time.to.Z.log <- log1p(zeo$Time.to.Z)

model1 <- '
 ## single-indicator measurement error model for each sleep variable assuming decent reliability:
 ZQ.2_latent =~ 1*ZQ.2
 ZQ.2 ~~ 0.7*ZQ.2
 Total.Z.2_latent =~ 1*Total.Z.2
 Total.Z.2 ~~ 0.7*Total.Z.2
 Time.in.REM.2_latent =~ 1*Time.in.REM.2
 Time.in.REM.2 ~~ 0.7*Time.in.REM.2
 Time.in.Light.2_latent =~ 1*Time.in.Light.2
 Time.in.Light.2 ~~ 0.7*Time.in.Light.2
 Time.in.Deep_latent =~ 1*Time.in.Deep
 Time.in.Deep ~~ 0.7*Time.in.Deep
 Time.to.Z.log_latent =~ 1*Time.to.Z.log
 Time.to.Z.log ~~ 0.7*Time.to.Z.log
 Time.in.Wake.log_latent =~ 1*Time.in.Wake.log
 Time.in.Wake.log ~~ 0.7*Time.in.Wake.log
 Awakenings_latent =~ 1*Awakenings
 Awakenings ~~ 0.7*Awakenings

 GOOD_SLEEP =~ ZQ.2_latent + Total.Z.2_latent + Time.in.REM.2_latent + Time.in.Light.2_latent + Time.in.Deep_latent + Morning.Feel
 BAD_SLEEP  =~ Time.to.Z.log_latent + Time.in.Wake.log_latent + Awakenings_latent
 '
## Fit Bayesian SEM:
library(blavaan)
s1 <- bsem(model1, n.chains=8, test="none", burnin=10000, sample=10000,
    dp = dpriors(nu = "dnorm(0,1)", alpha = "dnorm(0,1)", beta = "dnorm(0,200)"),
    jagcontrol=list(method="rjparallel"), fixed.x=FALSE, data=scale(zeo[-1])); summary(s1)
sleepIndex <- predict(s1)[,9] - predict(s1)[,10] # GOOD_SLEEP - BAD_SLEEP
zeo$Sleep.performance <- sleepIndex

Merge the 3 datasets, restrict down to the ABABA time-range, classify by Bacopa status:

df <- merge(zeo, merge(gradeDaily, mp, all=TRUE), all=TRUE)
df <- df[!is.na(df$Date),]
df <- df[df$Date>=as.Date("2014-06-28") & df$Date<=as.Date("2015-09-04"),]
df$Date.int <- as.integer(df$Date)

df$Bacopa <- FALSE
df[df$Date>=as.Date("2014-06-28") & df$Date<=as.Date("2014-09-25"),]$Bacopa <- FALSE
df[df$Date>=as.Date("2014-09-26") & df$Date<=as.Date("2014-12-19"),]$Bacopa <- TRUE
df[df$Date>=as.Date("2014-12-20") & df$Date<=as.Date("2015-03-19"),]$Bacopa <- FALSE
df[df$Date>=as.Date("2015-03-20") & df$Date<=as.Date("2015-06-05"),]$Bacopa <- TRUE
df[df$Date>=as.Date("2015-06-06") & df$Date<=as.Date("2015-09-04"),]$Bacopa <- FALSE

write.csv(df, row.names=FALSE, file="2018-05-17-gwern-bacopa.csv")

Analysis

df <- read.csv("https://www.gwern.net/docs/nootropics/2018-05-17-gwern-bacopa.csv")
#       Date                  ZQ               Total.Z           Time.to.Z         Time.in.Wake        Time.in.REM
#  Min.   :2014-06-28   Min.   : 14.00000   Min.   : 70.0000   Min.   : 1.00000   Min.   :  0.00000   Min.   : 12.0000
#  1st Qu.:2014-10-14   1st Qu.: 85.00000   1st Qu.:496.2500   1st Qu.: 7.00000   1st Qu.: 12.00000   1st Qu.:138.0000
#  Median :2015-01-30   Median : 95.00000   Median :544.0000   Median :20.00000   Median : 23.00000   Median :163.0000
#  Mean   :2015-01-30   Mean   : 93.11521   Mean   :530.2465   Mean   :19.64286   Mean   : 29.20507   Mean   :157.4816
#  3rd Qu.:2015-05-18   3rd Qu.:103.00000   3rd Qu.:579.0000   3rd Qu.:27.00000   3rd Qu.: 37.00000   3rd Qu.:183.0000
#  Max.   :2015-09-04   Max.   :129.00000   Max.   :682.0000   Max.   :95.00000   Max.   :167.00000   Max.   :263.0000
#                       NA's   :1           NA's   :1          NA's   :1          NA's   :1           NA's   :1
#  Time.in.Light       Time.in.Deep        Awakenings         Morning.Feel        Total.Z.2             ZQ.2           Time.in.REM.2
#  Min.   : 38.0000   Min.   :  5.0000   Min.   : 0.000000   Min.   :0.000000   Min.   :  4900.0   Min.   :  196.000   Min.   :  144.00
#  1st Qu.:292.0000   1st Qu.: 48.0000   1st Qu.: 4.000000   1st Qu.:2.000000   1st Qu.:246264.2   1st Qu.: 7225.000   1st Qu.:19044.00
#  Median :317.0000   Median : 57.0000   Median : 6.000000   Median :3.000000   Median :295936.0   Median : 9025.000   Median :26569.00
#  Mean   :313.9516   Mean   : 59.3318   Mean   : 6.341014   Mean   :2.562212   Mean   :287184.9   Mean   : 8915.078   Mean   :26341.23
#  3rd Qu.:344.7500   3rd Qu.: 69.0000   3rd Qu.: 8.000000   3rd Qu.:3.000000   3rd Qu.:335241.0   3rd Qu.:10609.000   3rd Qu.:33489.00
#  Max.   :459.0000   Max.   :142.0000   Max.   :16.000000   Max.   :4.000000   Max.   :465124.0   Max.   :16641.000   Max.   :69169.00
#  NA's   :1          NA's   :1          NA's   :1           NA's   :1          NA's   :1          NA's   :1           NA's   :1
#  Time.in.Light.2    Time.in.Wake.log   Time.to.Z.log       Sleep.performance    Mnemosyne.performance       MP
#  Min.   :  1444.0   Min.   :0.000000   Min.   :0.6931472   Min.   :-1.8207928   Min.   :-0.81207471   Min.   :1.000000
#  1st Qu.: 85264.0   1st Qu.:2.564949   1st Qu.:2.0794415   1st Qu.:-0.1382757   1st Qu.:-0.08138984   1st Qu.:3.000000
#  Median :100489.0   Median :3.178054   Median :3.0445224   Median : 0.2507222   Median : 0.02087041   Median :3.000000
#  Mean   :100831.6   Mean   :3.091542   Mean   :2.6811233   Mean   : 0.2215090   Mean   : 0.00790124   Mean   :3.262069
#  3rd Qu.:118852.8   3rd Qu.:3.637586   3rd Qu.:3.3322045   3rd Qu.: 0.6038839   3rd Qu.: 0.12563885   3rd Qu.:4.000000
#  Max.   :210681.0   Max.   :5.123964   Max.   :4.5643482   Max.   : 1.8661274   Max.   : 1.68682336   Max.   :4.000000
#  NA's   :1          NA's   :1          NA's   :1           NA's   :1            NA's   :77
#     Date.int         Bacopa
#  Min.   :16249.0   Mode :logical
#  1st Qu.:16357.5   FALSE:271
#  Median :16465.0   TRUE :164
#  Mean   :16465.4   NA's :0
#  3rd Qu.:16573.5
#  Max.   :16682.0
cor(subset(df, select=c("Sleep.performance", "Mnemosyne.performance", "MP", "Bacopa")), use="pairwise.complete.obs")
#                       Sleep.performance Mnemosyne.performance             MP         Bacopa
# Sleep.performance        1.000000000000
# Mnemosyne.performance   -0.008373508585        1.000000000000
# MP                       0.019296978791        0.029580496779  1.00000000000
# Bacopa                  -0.013829613334       -0.083324462060 -0.02286848706  1.00000000000

library(gridExtra)
p1 <- qplot(Date, Mnemosyne.performance, color=Bacopa, data=df) + stat_smooth()
p2 <- qplot(Date, MP, color=Bacopa, data=df) + stat_smooth()
p3 <- qplot(Date, Sleep.performance, color=Bacopa, data=df) + stat_smooth()
grid.arrange(p1, p2, p3, ncol=1)
Graph of daily sleep, memory, and productivity self-ratings over time during Bacopa quasi-experiment
Graph of daily sleep, memory, and productivity self-ratings over time during Bacopa quasi-experiment

For analysis, the baseline linear model and then a Bayesian model with a B-spline to model the time-series/autocorrelation aspect2:

summary(lm(cbind(Mnemosyne.performance, Sleep.performance, MP) ~ Bacopa, data=df))
# Response Mnemosyne.performance :
# ...Coefficients:
#                Estimate  Std. Error  t value Pr(>|t|)
# (Intercept)  0.02091904  0.01377171  1.51899  0.12966
# BacopaTRUE  -0.03534109  0.02256296 -1.56633  0.11816
#
# Residual standard error: 0.2061161 on 355 degrees of freedom
#   (78 observations deleted due to missingness)
# Multiple R-squared:  0.00686354,  Adjusted R-squared:  0.004065972
# F-statistic: 2.453396 on 1 and 355 DF,  p-value: 0.1181619
#
# Response Sleep.performance :
# ...Coefficients:
#                Estimate  Std. Error  t value   Pr(>|t|)
# (Intercept)  0.24477449  0.03711767  6.59455 1.5485e-10
# BacopaTRUE  -0.06054636  0.06081197 -0.99563    0.32011
#
# Residual standard error: 0.5555265 on 355 degrees of freedom
#   (78 observations deleted due to missingness)
# Multiple R-squared:  0.002784573, Adjusted R-squared:  -2.44843e-05
# F-statistic: 0.9912838 on 1 and 355 DF,  p-value: 0.320107
#
# Response MP :
# ...Coefficients:
#                Estimate  Std. Error  t value Pr(>|t|)
# (Intercept)  3.29464286  0.04072128 80.90716  < 2e-16
# BacopaTRUE  -0.03900376  0.06671595 -0.58462  0.55917
#
# Residual standard error: 0.6094603 on 355 degrees of freedom
#   (78 observations deleted due to missingness)
# Multiple R-squared:  0.0009618499,    Adjusted R-squared:  -0.001852342
# F-statistic: 0.3417855 on 1 and 355 DF,  p-value: 0.5591718
bacopa <- brm(cbind(Mnemosyne.performance, Sleep.performance, MP) ~ s(Date.int) + Bacopa, data=df); summary(bacopa)
#  Family: MV(gaussian, gaussian, gaussian)
#   Links: mu = identity; sigma = identity
#          mu = identity; sigma = identity
#          mu = identity; sigma = identity
# Formula: Mnemosyne.performance ~ s(Date.int) + Bacopa
#          Sleep.performance ~ s(Date.int) + Bacopa
#          MP ~ s(Date.int) + Bacopa
#    Data: df (Number of observations: 357)
# Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#          total post-warmup samples = 4000
#
# Smooth Terms:
#                                       Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
# sds(Mnemosyneperformance_sDate.int_1)     3.44      1.19     1.79     6.52        914 1.00
# sds(Sleepperformance_sDate.int_1)         3.30      1.43     1.24     6.89       1006 1.00
# sds(MP_sDate.int_1)                       0.80      0.85     0.02     3.13        871 1.01
#
# Population-Level Effects:
#                                  Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
# Mnemosyneperformance_Intercept      -0.02      0.02    -0.05     0.02       3372 1.00
# Sleepperformance_Intercept           0.28      0.05     0.19     0.39       2946 1.00
# MP_Intercept                         3.30      0.05     3.22     3.39       4000 1.00
# Mnemosyneperformance_BacopaTRUE      0.07      0.05    -0.02     0.16       3097 1.00
# Mnemosyneperformance_sDate.int_1     0.63      0.21     0.23     1.05       2168 1.00
# Sleepperformance_BacopaTRUE         -0.16      0.11    -0.40     0.04       2461 1.00
# Sleepperformance_sDate.int_1         1.23      0.47     0.39     2.21       1697 1.00
# MP_BacopaTRUE                       -0.07      0.08    -0.23     0.09       4000 1.00
# MP_sDate.int_1                      -0.15      0.23    -0.72     0.24       1444 1.00
#
# Family Specific Parameters:
#                                               Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
# sigma_Mnemosyneperformance                        0.19      0.01     0.17     0.20       4000 1.00
# sigma_Sleepperformance                            0.52      0.02     0.48     0.56       4000 1.00
# sigma_MP                                          0.61      0.02     0.57     0.66       4000 1.00
# rescor(Mnemosyneperformance,Sleepperformance)    -0.00      0.05    -0.11     0.10       4000 1.00
# rescor(Mnemosyneperformance,MP)                   0.02      0.05    -0.09     0.12       4000 1.00
# rescor(Sleepperformance,MP)                      -0.01      0.05    -0.11     0.09       4000 1.00
mean(posterior_samples(bacopa, "Mnemosyneperformance_BacopaTRUE")[,1] > 0)
# [1] 0.93025
mean(posterior_samples(bacopa, "Sleepperformance_BacopaTRUE")[,1] < 0)
# [1] 0.94525
mean(posterior_samples(bacopa, "MP_BacopaTRUE")[,1] < 0)
# [1] 0.803

Unsurprisingly given a de facto sample size n=5 due to the long-term chronic effects forcing a small ABABA quasi-experimental design, the results are largely inconclusive; using multilevel Mnemosyne scores and latent sleep indexes can help reduce measurement error but can only do so much.

The strongest result, in terms of posterior probability of a nonzero correlation between Bacopa & the 3 variables, is, perhaps as one would predict based on the Bacopa literature, on my Mnemosyne memory performance: a 0.07 (95% credible interval: -0.02-0.16) SD increase in retention, P=0.93. If real & causal, that would be a small effect, but perhaps worthwhile in some contexts like medical school cramming (especially since it comes on top of an already quite powerful memory enhancement intervention - spaced repetition). The other two estimated correlations, unfortunately, are negative and also of similar posterior probability (P=0.95, P=0.80).

Conclusion

So on net, I’d say the results neither encourage nor discourage Bacopa use and are uninformative mostly as I expected due to the small sample size and difficulty of distinguishing any temporal trends from actual Bacopa effects. Given the difficulty of investigating Bacopa, it probably isn’t worthwhile to try to experiment further with a randomized blinded self-experiment because it would require extremely long time investments.


  1. This is calculated assuming Vitacost is still offering the 2-for-1 sale which it was on 26 September 2014.

  2. In the past I’ve used bsts with brms for time-series, but the author now strongly discourages its use, saying it is integrated into brms in an ad hoc and unmaintainable matter and thinks splines are a better approach in general, so I’ve switched over although I’m not as familiar with Bayesian splines as I’d like.