Relevant Accessible Sensitivity Analysis for Clinical Trials with Missing Data

The statistical analysis of longitudinal randomised controlled trials is frequently complicated by the occurrence of protocol deviations which result in incomplete datasets for analysis. However analysis is approached, an unverifiable assumption about the distribution of the unobserved post-deviation data must be made. In such circumstances it is consequently important to assess the robustness of the primary analysis of the trial to different credible assumptions about the distribution of the missing data. Reference based multiple imputation procedures have been proposed for contextually relevant sensitivity analysis of longitudinal trials. Differences between the mean and variance of observed and missing data are specified with qualitative reference to trial arms and multiple imputation is used for estimation and inference. The primary analysis model is retained in the sensitivity analysis to assess the impact of alternative sampling behaviour on the original planned analysis. Rubin's rules are used to combine the treatment effect and variance estimates across imputed datasets, however it is unclear precisely what an appropriate measure of variance is in this setting and how Rubin's variance formula relates to this. We begin by defining a lower bound for variance estimation in the reference based settings as the variance estimate we would obtain were we able to observe the deviation data under the postulated post-deviation data assumption. We show Rubin's variance estimate always exceeds this and moreover it approximately preserves the loss of information in the primary analysis. We also explore Rubin's variance estimate in the δ-adjusted sensitivity analysis setting and show that Rubin's variance formula preserves the loss of information in this context. Alongside, we develop a new Stata command “mimix" for implementation of reference based sensitivity analyses. We illustrate the relevance and accessibility of the proposed methods of sensitivity analysis using data from a chronic asthma trial and a study of peer review.