ON THE USE OF NONPARAMETRIC BOUNDS FOR CAUSAL EFFECTS IN NULL RANDOMIZED TRIALS

The goal of randomized experiments is to estimate the causal effect of an intervention on a clinically relevant outcome. When study subjects are missing outcome information due to factors related to the intervention, compliance, or the outcome, the causal effect is not identifiable from the observed data alone (1). When there is no missing data, randomization allows identification of the effect of assignment to the intervention, sometimes called the intent-to-treat effect; this is only equivalent to the intervention effect if subjects comply with their assigned intervention as directed. When this is not the case, the intervention effect is nonidentifiable, even with no missing data, without making additional assumptions (2).

The Danish randomized trial studying the effect of mask recommendation (DANMASK-19) was widely discussed in the media (3). In the study, 3,030 participants were randomly assigned to the mask group, and 2,994 to the control group; 638 and 524, respectively, did not complete the study. The reported infection risk difference comparing the mask recommendation arm with the control arm was −0.3% (95% confidence interval: −1.2, 0.4). The primary analysis excluded subjects missing data (a complete-case analysis), and the authors used multiple imputation with additional covariates in secondary analyses. The complete-case analysis is valid if the missingness is completely random, and the imputation analysis is valid if the missingness depends only on included observed covariates. However, neither produce valid estimates of the causal effect of the mask recommendation when the missingness depends on unmeasured factors, which is always a possibility.