Survival data collected from prevalent cohorts are subject to left-truncation and the analysis is challenging. Conditional approaches for left-truncated data under the Cox model are inefficient as they typically ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods can improve the estimation efficiency but only when the stationarity assumption of the disease incidence holds, i.e., the truncation distribution is uniform; otherwise they may generate biased estimates. In this paper, we propose a semi-parametric method for the Cox model under general left-truncation, where the truncation distribution is unspecified. Our approach is to make inference based on the conditional likelihood augmented with a pairwise likelihood which eliminates the unspecified truncation distribution, yet retains the information about the regression coefficients and the baseline hazard function in the marginal likelihood. An iterative algorithm is provided to solve for the regression coefficients and the baseline hazard simultaneously. The proposed estimator is consistent and asymptotically normal with a closed-form consistent variance estimator. Simulations show a substantial efficiency gain in both the regression coefficients and the cumulative baseline hazard over the conditional approach estimator. Even when the stationarity assumption holds, our estimator results in better efficiency than some length-biased sampling estimators. An application to the analysis of a chronic kidney disease cohort study illustrates the utility of the method.


Biostatistics | Statistical Models | Survival Analysis

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