How much compliance is enough? Estimating the Complier Average Causal Effect (CACE) for treatment efficacy with different definitions of compliance
*Scott F Grey, Kent State University 

Keywords: Causal inference, Compliance, Principal stratification

A recent solution to estimating treatment efficacy in studies with non-compliance has been the development of CACE estimates. Based on principal stratification, CACE classifies subjects who have received an adequate amount of the treatment as potential compliers and then compares them to control subjects who have an equal probability of being classified as compliers if they had been randomized to treatment. No studies have systematically examined how sensitive CACE estimates are to different definitions of compliance. This study hypothesizes that incorrect definitions of compliance can bias CACE estimates and seeks to determine under what circumstances bias can occur. The standard CACE method was compared to the partial compliance framework developed by Jin and Rubin (2009) where [1] there can be multiple principal strata of partial potential compliance and [2] there is a true minimum partial potential compliance principal stratum (T) where subjects would receive the minimum treatment exposure necessary to have a relevant outcome effect. In this framework, subjects in partial potential compliance principal strata above T can be incorrectly classified as non-compliers, and subjects in partial potential compliance principal strata below T can be incorrectly classified as compliers. Mathematical investigations and numeric analysis was conducted to understand the amount of bias that can be seen when deviations from the true minimum partial compliance principal stratum are used. When subjects in partial potential compliance principal strata below T are incorrectly classified as compliers, CACE estimates being no more than 18% different than their true value. On the other hand, when subjects in partial potential compliance principal strata above T are incorrectly classified as non-compliers, CACE estimates are grossly inflated to over 100% of their true value. These results remain when CACE estimates were calculated using the exclusion restriction or a covariate, when exclusion restriction is true and when is false. These findings suggest that misclassifying true non-compliers as compliers will introduce a substantial, but not necessarily large amount of bias into CACE estimates, but that misclassifying true compliers as non-compliers will introduce a very large amount of bias into CACE estimates. This divergence below or above T may provide researchers with a method of identifying the true partial compliance principal strata using sensitivity analysis.