Causal estimation using semiparametric transformation models under prevalent sampling

This article presents methods and inference for causal estimation in semiparametric transformation models for the prevalent survival data. Through the estimation of the transformation models and covariate distribution, we propose a few analytical procedures to estimate the causal survival function. As the data are observational, the unobserved potential outcome (survival time) may be associated with the treatment assignment, and therefore there may exist a systematic imbalance between the data observed from each treatment arm. Further, due to prevalent sampling, subjects are observed only if they have not experienced the failure event when data collection began, causing the prevalent sampling bias. We propose a unified approach, which simultaneously corrects the bias from the prevalent sampling and balances the systematic differences from the observational data. We illustrate in the simulation study that standard analysis without proper adjustment would result in biased causal inference. Large sample properties of the proposed estimation procedures are established by techniques of empirical processes and examined by simulation studies. The proposed methods are applied to the Surveillance, Epidemiology, and End Results (SEER) and Medicare-linked data for women diagnosed with breast cancer.