Handwashing for the avoidance of COVID-19: A Bayesian Meta Analysis

We’ve all had enough of this buffoon spouting rubbish for the last two years - but does the “Hands / Face / Space” message he promoted in lieu of actual governance or action have an evidence base? That’s the question that Talic et al tried to answer in their BMJ article this week, and presented their results with an elegant infographic:

However, despite strong evidence for social distancing and mask wearing, the 95% confidence interval for handwashing crossed the magical line of no effect (despite looking pretty strong), leading to Twitter publicly declaring its lack of understanding of p-values. But you know what the answer is when we want to judge the uncertainty of something…

The raw (limited) data on handwashing looks like this:

Study	COVID+ handwashers	All handwashers	COVID+ non-handwashers	All non-handwashers	RR (95% CI)	Comments
Doung-Ngern 2020	52	424	158	612	0.34 (0.13 to 0.88)	Used “always” vs “sometimes/never”
Lio 2021	12	975	12	162	0.30 (0.11 to 0.81)
Xu 2020	51	7895	6	263	0.58 (0.40 to 0.84)	Wrong reference in the article!

We’ll use the excellent {bayesmeta} package to analyse this. Firstly build a table of log-RR using the {metafor} package:

data.es <- metafor::escalc(measure="RR",
                   ai = hw_cases,  n1i = hw_total,
                   ci = nhw_cases, n2i = nhw_total,
                   slab = Study, data = raw_data)

Now lets perform a Bayesian random-effects meta-analysis, assuming a minimally-informative prior, and plot the results:

ma01 <- bayesmeta::bayesmeta(y = data.es[, "yi"],
                             sigma = sqrt(data.es[, "vi"]), # Convert variance to standard error
                             labels = data.es[, "Study"],
                             mu.prior.mean = 0, mu.prior.sd = 4,
                             tau.prior = function(t) bayesmeta::dhalfcauchy(t, scale = 0.5)
                             )

bayesmeta::forestplot.bayesmeta(ma01, exponentiate=TRUE)

As with a frequentist meta-analysis, this shows the estimated relative risks of each study along with the 95% confidence intervals of the standard errors, but additionally in grey the shrinkage intervals for each study, i.e. the posterior given each study’s effects on our minimally-informative prior. At the bottom the plot shows the 95% credible intervals for the effect (in this case handwashing has a relative risk of 0.33 for catching COVID-19, with a 95% credible interval of 0.15 to 0.63), and for the predictive distribution (0.34, 0.08 to 1.12), i.e. 95% of our unobserved values of the RR from handwashing in future studies will lie between 0.08 and 1.12, given the data we have so far.

This allows us to calculate the probability of handwashing having a non-beneficial effect:

1 - ma01$pposterior(mu = 0)

[1] 0.01111698

i.e. handwashing is 98.9% likely to reduce the risk of catching COVID-19. For an essentially free intervention, I have sufficient belief in it to keep going!

With that in mind, let’s plot the posterior distribution, i.e. the strength of our belief in handwashing, given the data from the three studies meta-analysed:

x <- seq(-3.5, 0.25, length=200)

library(ggplot2)

ggplot() +
  aes(x = exp(x), y = exp(ma01$dposterior(mu = x))) +
  geom_line() +
  geom_vline(xintercept = 1.0, lty = "dashed") +
  xlab("Relative risk") +
  ylab("Posterior density") +
  theme_bw()

Obviously this needs to be sensitivity tested with other distributions, etc, but hopefully this quick analysis demonstrates the power of a Bayesian analysis (how likely something is, given the data we have) over a frequentist approach (how likely the data is, assuming there is no effect).