Identification and estimation of principal causal effects in randomized experiments with treatment switching

Abstract

In randomized clinical trials designed to evaluate the effect of a treatment on patients with advanced disease stages, treatment switching is often allowed for ethical reasons. Because the switching is a prognosis-related choice, identification and estimation of the effect of the actual receipt of the treatment becomes problematic. Existing methods in the literature try to reconstruct the ideal situation that would be observed if the switchers had not switched. Rather than focusing on reconstructing the a-priori counterfactual outcome for the switchers, had they not switched, we propose to identify and estimate effects for (latent) subgroups of units according to their switching behaviour. The reference framework of the proposed method is the potential outcome approach. In order to estimate causal effects for sub- groups of units not affected by treatment, we rely on the principal stratification approach (Frangakis and Rubin in Biometrics 58(1): 21–29 2002) [1]. To illustrate the proposed method and evaluate the maintained assumptions, we analyse a dataset from a randomized clinical trial on patients with asymptomatic HIV infection assigned to immediate (the active treatment) or deferred (the control treatment) Zidovudine (ZDV). The results, obtained through a full-Bayesian estimation approach, are promising and emphasize the high heterogeneity of the effects for different latent subgroups defined according to the switching behaviour.