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There has been a rising interest in better exploiting auxiliary summary information from large databases in the analysis of smaller‐scale studies that collect more comprehensive patient‐level information. The purpose of this paper is twofold: first, we propose a novel approach to synthesize information from both the aggregate summary statistics and the individual‐level data in censored linear regression. We show that the auxiliary information amounts to a system of nonsmooth estimating equations and thus can be combined with the conventional weighted log‐rank estimating equations by using the generalized method of moments (GMM) approach. The proposed methodology can be further extended to account for the potential inconsistency in information from different sources. Second, in the absence of auxiliary information, we propose to improve estimation efficiency by combining the overidentified weighted log‐rank estimating equations with different weight functions via the GMM framework. To deal with the nonsmooth GMM‐type objective functions, we develop an asymptotics‐guided algorithm for parameter and variance estimation. We establish the asymptotic normality of the proposed GMM‐type estimators. Simulation studies show that the proposed estimators can yield substantial efficiency gain over the conventional weighted log‐rank estimators. The proposed methods are applied to a pancreatic cancer study for illustration. [ABSTRACT FROM AUTHOR]

Summary: Length‐biased survival data subject to right‐censoring are often collected from a prevalent cohort. However, informative right censoring induced by the sampling design creates challenges in methodological development. While certain conditioning arguments could circumvent the problem of informative censoring, related rank estimation methods are typically inefficient because the marginal likelihood of the backward recurrence time is not ancillary. Under a semiparametric accelerated failure time model, an overidentified set of log‐rank estimating equations is constructed based on the left‐truncated right‐censored data and backward recurrence time. Efficient combination of the estimating equations is simplified by exploiting an asymptotic independence property between two sets of estimating equations. A fast algorithm is studied for solving non‐smooth, non‐monotone estimating equations. Simulation studies confirm that the overidentified rank estimator can have a substantially improved estimation efficiency compared to just‐identified rank estimators. The proposed method is applied to a dementia study for illustration. [ABSTRACT FROM AUTHOR]