Eliciting and using expert opinions about dropout bias in randomized controlled trials

Background The analysis of clinical trials with dropout usually assumes the missing data are 'missing at random', i.e. given an individual's past observed data, their probability of dropout does not depend on their present outcome. However, in many settings this assumption is implausible, so it is sensible to assess the robustness of conclusions to departures from missing at random. Purpose To develop a practical, accessible, approach that allows expert opinions about the degree of departure from missing at random in the analysis of a clinical trial to be meaningfully and accurately elicited and incorporated in sensitivity analysis. Methods We elicit experts' prior beliefs about the mean difference between missing and observed outcomes in each trial arm. Then we perform a Bayesian synthesis of the information in the trial data with that in the experts' prior, using (i) a full Bayesian analysis for which we give WinBUGS code, and (ii) a simple approximate formula for the estimated treatment effect and its standard error. We illustrate our approach by re-analysing a recent trial of interventions to improve the quality of peer review. Results In the peer review trial, the approximate formula agreed well with the full Bayesian analysis, and both showed substantially larger standard errors than an analysis assuming missing at random. Limitations Strictly, the method is only applicable if the outcome is normally distributed. We did not elicit the full bivariate prior distribution, and instead used a sensitivity analysis. Our approach is not designed to incorporate prior beliefs about the intervention effect itself. Conclusions Our proposed approach allows for the greater uncertainty introduced by missing data that are potentially informatively missing. It can therefore claim to be a truly conservative method, unlike methods such as 'last observation carried forward'. It is practical and accessible to non-statisticians. It should be considered as part of the design and analysis of future clinical trials.