Adaptive Incorporation of External Summary Information in the Cox Regression Under Population Heterogeneity

With the increasing availability of data from different sources, there is a growing interest in leveraging summary information from external studies to improve parameter estimation efficiency for the internal study that collects individual-level data. However, when analyzing right-censored survival data, covariate effects often vary across studies due to differences in study environments, research designs, and patients' inclusion criteria. Such heterogeneity, if not accounted for properly, can lead to biased estimates of covariate effects. In this article, we develop a Privacy-preserving and Heterogeneity-aware Integration (PHI) method to improve efficiency in estimating regression parameters of the internal Cox model under population heterogeneity. The PHI method characterizes parameter heterogeneity by assuming an unknown cluster structure across datasets, and constructs an augmented log partial likelihood function with a fusion penalty to simultaneously estimate the cluster structure and adaptively incorporate summary statistics from external datasets. Estimation consistency and asymptotic normality are established for the proposed estimator. We further prove that the proposed estimator is asymptotically more efficient than the traditional maximum partial likelihood estimator under mild conditions. The PHI method also achieves consistency in estimating the underlying cluster structure across datasets. Simulation studies and brain tumor data analysis are used to investigate the finite-sample performance of the proposed method.