Methods for Comparing Two Treatments for a Dichotomous Outcome for a Two-Period Design with Treatment Switching of Control Group Period 1 Nonresponders

This chapter considers a two-period clinical trial in which patients are randomized to either a placebo (or control) arm or a test treatment arm. At the end of the first period of the trial, the patients are assessed for treatment failure via a dichotomous outcome, and all patients who are identified as having treatment failure receive test treatment for the second period. All patients are assessed for their dichotomous response at the end of the second period. While the risk difference in period 1 will appropriately estimate the treatment effect in period 1, the intention-to-treat (ITT) risk difference in period 2 will underestimate the treatment effect in period 2 for an effective treatment because it does not account for such treatment switching. Estimators for the treatment difference in period 2 are proposed, and they have similar structure to the ITT risk difference and account for treatment switching. Properties of the proposed estimators are evaluated under various simulation scenarios using means, standard errors, standardized effect sizes, powers, and confidence interval coverages, and the estimators are illustrated in a hypothetical data example and a real data example.