Causal inference in a placebo-controlled clinical trial with binary outcome and ordered compliance

We propose a likelihood-based method to analyze the causal effect of partial compliance (i.e., unplanned partial exposure to treatment or placebo) in the LRC-CPPT data, a prevention trial with long term follow-up previously analyzed by Efron and Feldman. Initially, we construct ordered compliance categories and dichotomize response. Assuming increased exposure to cholestyramine does not increase cholesterol, we estimate exposure-response curves in different compliance subsets. Subjects in different arms with similar levels of compliance to the assignment may have a different placebo prognosis (i.e., success probability under a possible zero exposure level). The sole assumption that the placebo group reflects response to zero exposure for the treatment group as a whole allows estimation of a causal parameter in a special case only. When a single parameter represents the association between responses to possible treatment exposures and treatment compliance, simple estimates are derived for a set of causal parameters. The example is analyzed in detail, and more general applicability and extensions of the method are discussed.