The timing of time-dependent treatment---e.g., when to perform kidney transplantation---is an important factor for evaluating treatment efficacy. A naive comparison between the treatment and nontreatment groups, while ignoring the timing of treatment, typically yields results that might biasedly favor the treatment group, as only patients who survive long enough will get treated. On the other hand, studying the effect of 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 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). *Joint work with Zhe Fei, Yi Li.
