Bayesian Inference in Augmented Designs for Assessing Principal Strata Causal Effects

Poster. Many research questions involving causal inference are often concerned with understanding the causal pathways by which an exposure or a treatment affects an outcome. Thus, researchers want to know not only if the treatment is effective, but also how the effect of the treatment on the outcome is mediated by the intermediate variable, and the concept of ’direct’ versus ’indirect’ effects comes to play. The use of this concept is common not only in statistics, but also in many area of social, economic and political sciences as well as in biomedical and pharmacological sciences, where there are the closely related concepts of ’biomarkers’ and ’surrogate outcomes’. We will pursue the potential outcomes framework to causal inference using the concept of the principal stratification (Frangakis and Rubin 2002, Biometrics 58(1), 21-29) for addressing the topic of direct and indirect causal effects. Principal stratification with respect to a posttreatment variable is a cross-classification of subjects defined by the joint potential values of that posttreatment variable under each of the treatments being compared. Principal Causal Effects (PCEs) are causal effects for specific (union of) strata. The role of principal stratification in clarifying the concepts of direct causal effects is well described by Mealli and Rubin (2003, J. Econometrics 112, 79-87), showing that some latent strata provide evidence on the direct effect of the treatment on the primary outcome: principal strata where the intermediate outcome is unaffected by treatment. PCE analysis is challenging, due to the latent nature of principal strata. In order to ease identification and estimation of PCEs, we will investigate new augmented designs, where the treatment is randomized, and the mediating variable is not forced, but only randomly encouraged. The design will be feasible in some clinical and social experiments, when partial control of the intermediate variable can be conceived. We will adopt a Bayesian approach for inference, which allows us to achieve valid estimates of quantities of interest and also properly account for our uncertainty about these quantities. This approach has the advantage of (a) gathering more information from the data, which may be useful for policy purposes; and (b) exploiting the constraints of the implicit conditional distributions that are compared. In addition, crucial structural (behavioral) assumptions can be distinguished from functional assumptions and clearly discussed. Our framework permits clear assessment of assumptions and evaluation of their consequences, by means of sensitivity analysis, by using posterior predictive checks, and investigating the posterior distribution of weakly identified models.