A semiparametrically efficient estimator of the time-varying effects for survival data with time-dependent treatment.

The timing of a time-dependent treatment-e.g., when to perform a kidney transplantation-is an important factor for evaluating treatment efficacy. A naïve comparison between the treated and untreated groups, while ignoring the timing of treatment, typically yields biased results that might favor the treated group because only patients who survive long enough will get treated. On the other hand, studying the effect of a time-dependent treatment is often complex, as it involves modeling treatment history and accounting for the possible time-varying nature of the treatment effect. We propose a varying-coefficient Cox model that investigates the efficacy of a time-dependent treatment by utilizing a global partial likelihood, which renders appealing statistical properties, including consistency, asymptotic normality and semiparametric efficiency. Extensive simulations verify the finite sample performance, and we apply the proposed method to study the efficacy of kidney transplantation for end-stage renal disease patients in the U.S. Scientific Registry of Transplant Recipients (SRTR).