Treatment group outcome variance difference after dropout as an indicator of missing-not-at-random bias in randomized clinical trials

Randomized controlled trials (RCTs) are considered the gold standard for assessing the causal effect of an exposure on an outcome, but are vulnerable to bias from missing data. When outcomes are missing not at random (MNAR), estimates from complete case analysis (CCA) will be biased. There is no statistical test for distinguishing between outcomes missing at random (MAR) and MNAR, and current strategies rely on comparing dropout proportions and covariate distributions, and using auxiliary information to assess the likelihood of dropout being associated with the outcome. We propose using the observed variance difference across treatment groups as a tool for assessing the risk of dropout being MNAR. In an RCT, at randomization, the distributions of all covariates should be equal in the populations randomized to the intervention and control arms. Under the assumption of homogeneous treatment effects, the variance of the outcome will also be equal in the two populations over the course of followup. We show that under MAR dropout, the observed outcome variances, conditional on the variables included in the model, are equal across groups, while MNAR dropout may result in unequal variances. Consequently, unequal observed conditional group variances are an indicator of MNAR dropout and possible bias of the estimated treatment effect. Heterogeneity of treatment effect affects the intervention group variance, and is another potential cause of observing different outcome variances. We show that, for longitudinal data, we can isolate the effect of MNAR outcome-dependent dropout by considering the variance difference at baseline in the same set of patients that are observed at final follow-up. We illustrate our method in simulation and in applications using individual-level patient data and summary data.