Sensitivity analysis for the probability of benefit in randomized controlled trials with a binary treatment and a binary outcome

For a comprehensive understanding of the effect of a given treatment on an outcome of interest, quantification of individual treatment heterogeneity is essential, alongside estimation of the average causal effect. However, even in randomized controlled trials, quantities such as the probability of benefit or the probability of harm are not identifiable, since multiple potential outcomes cannot be observed simultaneously for the same individual. We propose a sensitivity analysis for the probability of benefit in randomized controlled trial settings with a binary treatment and a binary outcome, by quantifying the deviation from conditional independence of the two potential outcomes, given a set of measured prognostic baseline covariates. We do this using a marginal sensitivity analysis parameter that does not depend on the number or complexity of the measured covariates. We provide a guide to estimation and interpretation, and illustrate our method in simulations, as well as using a real data example from a randomized controlled trial studying the effect of umbilical vein oxytocin administration on the need for manual removal of the placenta during birth.