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Face mask and Covid-19 (DANMASK study): a Bayesian interpretation
In the famous study, DANMASK, the authors conclude that wearing surgical mask together with social distancing practice did not reduce the risk of SARS-Cov-2 infection. However, using a Bayesian inference, I show that their result is consistent with a risk reduction of up to 28%.
Rarely a scientific study generates a lot of controversies, but that is the case for the DANMASK study [1]. In this study, the authors found that face mask wearing did not reduce the risk of infection with SARS-Cov-2 (odds ratio, 0.82; 95% CI, 0.54 to 1.23; P = 0.33) [1]. However, most newspapers and health experts were not swayed by the evidence, and they categorically say that “you need to wear them anyway” [2]. Here, I would like to offer my interpretation of the study’s result within context of previous data.
First, about the DANMASK study: it was designed as a randomized controlled trial in Denmark. Ultimately the study included 6024 individuals who were randomly assigned to either the intervention (n = 3030) or control group (n = 2994). The intervention was social distancing recommendation plus mask wearing. The control group was also recommended to follow the social distancing rule but face mask wearing was not recommended. This sample size was calculated based on the assumption that wearing face mask cuts the risk of infection by 50% (eg 2% in the control and 1% in the intervention group). The primary outcome was the incidence of SARS-Cov-2 infection confirmed by antibody testing and PCR. In a per-protocol analysis, the outcome can be summarized as follows:
· 42 / 2392 individuals (1.76%) in the intervention group were infected;
· 53 / 2470 individuals (2.15%) in the control group were infected;
· the risk ratio (RR) = 0.82, with 95% confidence interval [CI] ranging from 0.55 to 1.22; P = 0.33.
As you can see, the result is not consistent with the hypothesis of 50% risk reduction at all. Actually, the result is consistent with a risk reduction of 45%, but it is also consistent with an increased risk of 22%. Some people may tempt to say that the result is inconclusive.
Well, not so soon.