Abstract

Consider fitting a general parametric regression model, such as a generalized linear model, with individual data. It is common to have summary information,

such as parameter estimates, available from external studies that use similar regression models. Many methods have been developed to incorporate this external

information into internal model fitting to improve parameter estimation. Some

of these methods aim to reduce estimation variance without introducing estimation bias that could result from study population heterogeneity. Others allow

introduction of bias in exchange for substantial variance reduction, based on the

bias-variance trade-off consideration. We take the latter approach and develop

James-Stein shrinkage estimators to integrate the external information. These

estimators can reduce the asymptotic risk compared to not using the external information, regardless of the degree of heterogeneity between internal and external

populations. This is a highly desirable property as it provides a safe passage for

the utility of external information. Few existing methods provide such a guaranteed improvement. We also conduct simulation studies and apply the method to

a prostate cancer dataset to illustrate the numerical performance.

Information

Preprint No.SS-2025-0225
Manuscript IDSS-2025-0225
Complete AuthorsPeisong Han, Haoyue Li, Jeremy M. G. Taylor
Corresponding AuthorsPeisong Han
Emailspeisong@umich.edu

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Acknowledgments

We would like to thank the Editor, Associate Editor, and two referees for

their helpful comments that improved the quality of this work. This research was partially supported by National Institutes of Health grants CA-

129102 and CA-46592 to Taylor.