Simple Bayesian models for missing binary outcomes in randomized controlled trials

Missing outcomes are commonly encountered in randomized controlled trials (RCT) involving human subjects and present a risk for substantial bias in the results of a complete case analysis. While response rates for RCTs are typically high there is no agreed upon universal threshold under which the amount of missing data is deemed to not be a threat to inference. We focus here on binary outcomes that are possibly missing not at random, that is, the value of the outcome influences its possibility of being observed. Salient information that can assist in addressing these missing outcomes in such situations is the anticipated response rate in each study arm; these can often be anticipated based on prior research in similar populations using similar designs and outcomes. Further, in some areas of human subjects research, we are often confident or we suspect that response rates among RCT participants with successful treatment outcomes will be at least as great as those among participants without successful treatment outcomes. In other settings we may suspect the opposite relationship. This direction of the differential response between those with successful and unsuccessful outcomes can further aid in addressing the missing outcomes. We present simple Bayesian pattern-mixture models that incorporate this information on response rates to analyze the relationship between a binary outcome and an intervention while addressing the missing outcomes. We assess the performance of this method in simulation studies and apply this method to the results of an RCT of a smoking abstinence intervention.