  Missing data is inevitable in longitudinal clinical trials. Conventionally,
the missing at random assumption is assumed to handle missingness, which
however is unverifiable empirically. Thus, sensitivity analysis is critically
important to assess the robustness of the study conclusions against untestable
assumptions. Toward this end, regulatory agencies often request using
imputation models such as return-to-baseline, control-based, and washout
imputation. Multiple imputation is popular in sensitivity analysis; however, it
may be inefficient and result in an unsatisfying interval estimation by Rubin's
combining rule. We propose distributional imputation (DI) in sensitivity
analysis, which imputes each missing value by samples from its target
imputation model given the observed data. Drawn on the idea of Monte Carlo
integration, the DI estimator solves the mean estimating equations of the
imputed dataset. It is fully efficient with theoretical guarantees. Moreover,
we propose weighted bootstrap to obtain a consistent variance estimator, taking
into account the variabilities due to model parameter estimation and target
parameter estimation. The finite-sample performance of DI inference is assessed
in the simulation study. We apply the proposed framework to an antidepressant
longitudinal clinical trial involving missing data to investigate the
robustness of the treatment effect. Our proposed DI approach detects a
statistically significant treatment effect in both the primary analysis and
sensitivity analysis under certain prespecified sensitivity models in terms of
the average treatment effect, the risk difference, and the quantile treatment
effect in lower quantiles of the responses, uncovering the benefit of the test
drug for curing depression.
