Abstract

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.

Information

Preprint No.SS-2024-0105
Manuscript IDSS-2024-0105
Complete AuthorsHuijuan Ma, Manli Cheng, Yukun Liu, Donglin Zeng, Yong Zhou
Corresponding AuthorsYukun Liu
Emailsykliu@sfs.ecnu.edu.cn

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Acknowledgments

This work is partly supported by the National Key R&D Program of China (2021Y-

FA1000100 and 2021YFA1000101), the National Natural Science Foundation of China (12471253, 72331005 and 12171157), and the Natural Science Foundation of

Shanghai (23JS1400500)

The authors would like to thank the editor associate

editor, and two reviewers for their insightful comments which have helped improve

the manuscript substantially.

Supplementary Materials

The online Supplementary Material includes notations, the asymptotic results of ˆβau,

proofs of Theorems 1 and 2, the relationship between (ˆβau, ˆρau) and (˜β, ˜ρ), additional

simulation studies, as well as the heterogeneous case with heterogeneity in covariate

distributions and uncertainty in external information.

Supplementary materials are available for download.