Censoring-robust estimation in observational survival studies: Assessing the relative effectiveness of vascular access type on patency among end-stage renal disease patients.

The proportional hazards model is commonly used in observational studies to estimate and test a predefined measure of association between a variable of interest and the time to some event T. For example, it has been used to investigate the effect of vascular access type in patency among end-stage renal disease patients (Gibson et al., J Vasc Surg 34:694-700, 2001). The measure of association comes in the form of an adjusted hazard ratio as additional covariates are often included in the model to adjust for potential confounding. Despite its flexibility, the model comes with a rather strong assumption that is often not met in practice: a time-invariant effect of the covariates on the hazard function for T. When the proportional hazards assumption is violated, it is well known in the literature that the maximum partial likelihood estimator is consistent for a parameter that is dependent on the observed censoring distribution, leading to a quantity that is difficult to interpret and replicate as censoring is usually not of scientific concern and generally varies from study to study. Solutions have been proposed to remove the censoring dependence in the two-sample setting, but none has addressed the setting of multiple, possibly continuous, covariates. We propose a survival tree approach that identifies group-specific censoring based on adjustment covariates in the primary survival model that fits naturally into the theory developed for the two-sample case. With this methodology, we propose to draw inference on a predefined marginal adjusted hazard ratio that is valid and independent of censoring regardless of whether model assumptions hold.