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Abstract:
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The study of the long-term survival of end stage renal disease patients using the transplant registry is challenging due to left-truncated survival time and time-dependent covariates of interest. Ignoring the information in the truncation times, conventional conditional approaches yield consistent estimates but are less efficient. We introduce a semi-parametric estimation method for the Cox model under left-truncation that shows substantially improved efficiency. Rather than impose parametric forms on the truncation distribution, we rely on a pairwise likelihood argument to eliminate it. The greatest advantage of this approach is that, even when the time-dependent covariate depends on the truncation time, the proposed estimator is still accurate with better precision. Large sample properties have been shown using techniques in empirical process and U-process, and finite sample properties based on the asymptotic normality with a closed-form variance estimator have been demonstrated by extensive simulation studies. The proposed method is applied to the OPTN/UNOS kidney transplant data.
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