Efficient Estimation of the Accelerated Failure Time Model with Auxiliary Aggregate Information

With the rapidly increasing availability of aggregate data in the public domain, there has been a growing interest in synthesizing information from individual-level data and aggregate data.This article studies the maximum full likelihood estimation method to integrate the auxiliary information in the estimation of the accelerated failure time model.To overcome the computational challenges in maximizing full likelihood, we propose a novel one-step estimator, where the maximum conditional likelihood estimator without combining any auxiliary information is chosen as an initial estimator.We establish the consistency and asymptotic normality of the proposed one-step estimator and show that it is more efficient than the initial estimator.The asymptotic variance of the proposed one-step estimator has a closed form and is easily estimated by the plug-in rule.Simulation studies show that the proposed one-step estimator yields an efficiency gain over existing approaches.The proposed methodology is illustrated with an analysis of a chemotherapy study for Stage III colon cancer.