Censored linear regression in the presence or absence of auxiliary survival information

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.