Public health measures for covid-19BMJ 2021; 375 doi: https://doi.org/10.1136/bmj.n2729 (Published 18 November 2021) Cite this as: BMJ 2021;375:n2729
Effectiveness of public health measures in reducing the incidence of covid-19, SARS-CoV-2 transmission, and covid-19 mortality
Re: Public health measures for covid-19
In their excellent editorial, Glasziou and colleagues combined two randomized controlled trials (RCT) considering the effect of masks on SARS-CoV-2 infections (1,2). The authors highlighted a statistically significant effect with 95% confidence interval compatible with 1% to 18% relative risk (RR) reduction when combined.
Between-study variance (tau-squared) is imprecisely estimated in random effects (RE) model with few studies, and several methods to estimate tau-squared and confidence interval for overall effect exist (3,4). Generally, the use of common effect model is not justifiable since some heterogeneity is expected.
I combined these two RCTs (1,2) using a Bayesian RE model with bayesmeta package in R (5). I used prior for tau-squared based on a study by Turner and coworkers [infection as outcome and non-pharma vs. non-pharma as comparison (6)] and normal prior of RR 1 (natural log scale 0 with standard deviation 0.354) for overall effect (7). In sensitivity analyses, I used half-normal prior of 0.5 for tau-squared and uniform prior for overall effect as well as frequentist RE model (DL-HKSJ) (8).
Posterior median for RR (95% credible interval) was 0.91 (0.63 to 1.33) and the probability of some (RR less than 1) and large (RR less than 0.5) benefit was 73% and 0.2%, respectively. In addition, 95% prediction interval for true effect in a new study ranged from 0.41 to 2.04. In sensitivity analysis, posterior median for RR (95% credible interval) was 0.89 (0.50 to 1.52) and with frequentist RE model RR was 0.90 (95% confidence interval 0.66 to 1.23).
Taken together, there is probably some benefit of masks for reducing SARS-CoV-2 infections although evidence is still limited. The priors used in calculations were based on published literature, yet one can argue for some other priors. Sensitivity analyses with different methods are warranted notably with few studies.
1. Bundgaard H, Bundgaard JS, Raaschou-Pedersen DET, et al. Effectiveness of adding a Mask Recommendation to Other Public Health Measures to Prevent SARS-CoV-2 Infection in Danish Mask Wearers: A Randomized Controlled Trial. Ann Intern Med 2021;174:335-343.
2. Abaluck J, Kwong LH, Styczynski A, et al. Impact of community masking on COVID-19: A cluster-randomized trial in Bangladesh. Science 2022;375(6577):eabi9069.
3. Veroniki AA, Jackson D, Viechtbauer W, et al. Methods to estimate the between-study variance and its uncertainty in meta-analysis. Res Synth Methods 2016;7:55-79.
4. Veroniki AA, Jackson D, Bender R, et al. Methods to calculate uncertainty in the estimated overall effect size from a random-effects meta-analysis. Res Synth Methods 2019;10:23-43.
5. Röver, C. Bayesian Random-Effects Meta-Analysis Using the bayesmeta R Package. J Stat Softw 2020;93:1-51. doi: 10.18637/jss.v093.i06
6. Turner RM, Jackson D, Wei Y, Thompson SG, Higgins JP. Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis. Stat Med 2015;34:984-98.
7. Pedroza C, Han W, Truong VTT, Green C, Tyson JE. Performance of informative priors skeptical of large treatment effects in clinical trials: A simulation study. Stat Methods Med Res 2018;27:79-96.
8. Friede T, Röver C, Wandel S, Neuenschwander B. Meta-analysis of two studies in the presence of heterogeneity with applications in rare diseases. Biom J 2017;59:658-671.
Competing interests: I like statistics.