Sensitivity analysis of incomplete longitudinal data departing from the missing at random assumption: Methodology and application in a clinical trial with drop-outs

Statistical analyses of longitudinal data with drop-outs based on direct likelihood, and using all the available data, provide unbiased and fully efficient estimates under some assumptions about the drop-out mechanism. Unfortunately, these assumptions can never be tested from the data. Thus, sensitivity analyses should be routinely performed to assess the robustness of inferences to departures from these assumptions. However, each specific scientific context requires different considerations when setting up such an analysis, no standard method exists and this is still an active area of research. We propose a flexible procedure to perform sensitivity analyses when dealing with continuous outcomes, which are described by a linear mixed model in an initial likelihood analysis. The methodology relies on the pattern-mixture model factorisation of the full data likelihood and was validated in a simulation study. The approach was prompted by a randomised clinical trial for sleep-maintenance insomnia treatment. This case study illustrated the practical value of our approach and underlined the need for sensitivity analyses when analysing data with drop-outs: some of the conclusions from the initial analysis were shown to be reliable, while others were found to be fragile and strongly dependent on modelling assumptions. R code for implementation is provided.