  Missing data is unavoidable in longitudinal clinical trials, and outcomes are
not always normally distributed. In the presence of outliers or heavy-tailed
distributions, the conventional multiple imputation with the mixed model with
repeated measures analysis of the average treatment effect (ATE) based on the
multivariate normal assumption may produce bias and power loss. Control-based
imputation (CBI) is an approach for evaluating the treatment effect under the
assumption that participants in both the test and control groups with missing
outcome data have a similar outcome profile as those with an identical history
in the control group. We develop a general robust framework to handle
non-normal outcomes under CBI without imposing any parametric modeling
assumptions. Under the proposed framework, sequential weighted robust
regressions are applied to protect the constructed imputation model against
non-normality in both the covariates and the response variables. Accompanied by
the subsequent mean imputation and robust model analysis, the resulting ATE
estimator has good theoretical properties in terms of consistency and
asymptotic normality. Moreover, our proposed method guarantees the analysis
model robustness of the ATE estimation, in the sense that its asymptotic
results remain intact even when the analysis model is misspecified. The
superiority of the proposed robust method is demonstrated by comprehensive
simulation studies and an AIDS clinical trial data application.
