Integrating external summary information in the presence of prior probability shift: an application to assessing essential hypertension.

Recent years have witnessed a rise in the popularity of information integration without sharing of raw data. By leveraging and incorporating summary information from external sources, internal studies can achieve enhanced estimation efficiency and prediction accuracy. However, a noteworthy challenge in utilizing summary-level information is accommodating the inherent heterogeneity across diverse data sources. In this study, we delve into the issue of prior probability shift between two cohorts, wherein the difference of two data distributions depends on the outcome. We introduce a novel semi-parametric constrained optimization-based approach to integrate information within this framework, which has not been extensively explored in existing literature. Our proposed method tackles the prior probability shift by introducing the outcome-dependent selection function and effectively addresses the estimation uncertainty associated with summary information from the external source. Our approach facilitates valid inference even in the absence of a known variance-covariance estimate from the external source. Through extensive simulation studies, we observe the superiority of our method over existing ones, showcasing minimal estimation bias and reduced variance for both binary and continuous outcomes. We further demonstrate the utility of our method through its application in investigating risk factors related to essential hypertension, where the reduced estimation variability is observed after integrating summary information from an external data.