The reverse propensity score to detect selection bias and correct for baseline imbalances

The propensity score has been proposed, and for the most part accepted, as a tool to allow for the evaluation of medical interventions in the presence of baseline imbalances arising in the context of observational studies. The lack of an analogous tool to allow for the evaluation of medical interventions in the presence of potentially systematic baseline imbalances in randomized trials has required the use of ad hoc methods. This, in turn, leads to challenges to the conclusions. For example, much of the controversy surrounding recommendations for or against mammography for some age groups stems from the fact that all the randomized trials to study mammography had baseline imbalances, to some extent, in important prognostic covariates. While some of these trials used cluster randomization, baseline imbalances are prevalent also in individually randomized trials. We provide a systematic approach for evaluating medical interventions in the presence of potentially systematic baseline imbalances in individually randomized trials with allocation concealment. Specifically, we define the reverse propensity score as the probability, conditional on all previous allocations and the allocation procedure (restrictions on the randomization), that a given patient will receive a given treatment. We demonstrate how the reverse propensity score allows for both detection of and correction for selection bias, or systematic baseline imbalances.