Analysis of subgroup effects in randomized trials when subgroup membership is missing: Application to the second Multicenter Automatic Defibrillator Intervention Trial

We develop and implement a methodology for drawing inference about subgroup effects in a two-arm randomized trial when subgroup status is known only for a non-random sample in each of the trial arms. Since the subgroup effects are not point identified from the distribution of the observed data, we show how to compute bounds on these effects by using scientifically plausible assumptions. We characterize the uncertainty of our procedure by using the Bayesian paradigm. The methodology is developed in the context of the second Multicenter Automatic Defibrillator Intervention Trial, which was a randomized trial designed to evaluate the effectiveness of implantable defibrillators on survival.