The Analysis of Censored Covariates in Observational Studies

After treatment is found to be effective in a clinical study, attention often focuses on the effect of treatment duration on outcome. Such an analysis facilitates recommendations on the most beneficial treatment duration. In many studies, treatment duration is left to the discretion of the investigators. Occasionally, however, treatment may be terminated prematurely due to an adverse event, in which case a recommended treatment duration is part of a policy that treats patients for a specified length of time or until a treatment-terminating event occurs, whichever comes first. Evaluating mean response for a particular treatment duration policy from observational data is difficult due to censoring and the fact that it may not be reasonable to assume patients are prognostically similar across all treatment strategies. First, we propose an estimator for mean response as a function of treatment duration policy under these conditions. Second, we characterize mean response as a continuous function of treatment duration policy and propose an estimator for this functional relationship. The method uses potential outcomes and embodies assumptions that allow consistent estimation of the mean response. The estimator is evaluated through simulation studies and demonstrated by application to the ESPRIT infusion trial coordinated at Duke University Medical Center.