A Data Augmentation Method for Estimating the Causal Effect of Adherence to Treatment Regimens Targeting Control of an Intermediate Measure

Abstract

A dynamic treatment regimen is a rule or set of rules which define how a subject’s treatment at repeated visits depends on their evolving history of time-dependent covariates. In this manuscript we focus on regimens that are characterized by intermediate target ranges [b 1,b 2] which are used clinically to modify treatment such that longitudinal measures of the intermediate stay within a tolerance defined by [b 1,b 2]. For observational data, survival under a particular regimen can be consistently estimated by artificially censoring subjects when they become nonadherent to the regimen and then weighting subjects by the inverse probability of remaining uncensored. In many settings subjects are not identified at baseline as individuals who are following a pre-specified regimen. In addition, it may be possible for subjects to be adherent to multiple regimens at the same time. In order to compare alternative regimens we present a data augmentation methodology in which regimen membership is stochastically imputed multiple times and parameter estimates are aggregated to provide a final point estimate of a causal hazard ratio, and for which sandwich variance estimation methods provide consistent inference. The method is illustrated through simulation results as well as a preliminary analysis comparing epoetin therapy regimens with different target hemoglobin ranges in a cohort of hemodialysis subjects from the United States Renal Data System.