A pairwise pseudo-likelihood approach for left-truncated and interval-censored data under the Cox model

Left truncation commonly occurs in many areas, and many methods have been proposed in the literature for the analysis of various types of left-truncated failure time data. For the situation, a common approach is to conduct the analysis conditional on truncation times, and the method is relatively simple but may not be efficient. In this paper, we discuss regression analysis of such data arising from the proportional hazards model that also suffer interval censoring. For the problem, a pairwise pseudo-likelihood approach is proposed that aims to recover some missing information in the conditional methods. The resulting estimator is shown to be consistent and asymptotically normal. A simulation study is conducted to assess the performance of the proposed method and suggests that it works well in practical situations and is indeed more efficient than the existing method. The approach is also applied to a set of real data arising from an AIDS cohort study.