Information-anchored sensitivity analysis: theory and application

Analysis of longitudinal randomized clinical trials is frequently complicated because patients deviate from the protocol. Where such deviations are relevant for the estimand, we are typically required to make an untestable assumption about post-deviation behaviour to perform our primary analysis and to estimate the treatment effect. In such settings, it is now widely recognized that we should follow this with sensitivity analyses to explore the robustness of our inferences to alternative assumptions about post-deviation behaviour. Although there has been much work on how to conduct such sensitivity analyses, little attention has been given to the appropriate loss of information due to missing data within sensitivity analysis. We argue that more attention needs to be given to this issue, showing that it is quite possible for sensitivity analysis to decrease and increase the information about the treatment effect. To address this critical issue, we introduce the concept of information-anchored sensitivity analysis. By this we mean sensitivity analyses in which the proportion of information about the treatment estimate lost because of missing data is the same as the proportion of information about the treatment estimate lost because of missing data in the primary analysis. We argue that this forms a transparent, practical starting point for interpretation of sensitivity analysis. We then derive results showing that, for longitudinal continuous data, a broad class of controlled and reference-based sensitivity analyses performed by multiple imputation are information anchored. We illustrate the theory with simulations and an analysis of a peer review trial and then discuss our work in the context of other recent work in this area. Our results give a theoretical basis for the use of controlled multiple-imputation procedures for sensitivity analysis.