Transportable inference using target population summary statistics under covariate shift

Transporting findings from a study population to a target population is central to evidence-based decision-making in real-world settings. Most existing methods require individual-level data from both populations to account for covariate shift. However, privacy regulations and data-sharing constraints often preclude access to such data from the target population, leaving only covariate summaries available for analysis. In this paper, we develop transportability methods that enable valid inference using source individual-level data and target covariate summaries. First, we apply entropy balancing (EB) to transportability, enabling source individual-level data to be adjusted to match the target covariate moments. We establish asymptotic normality for the EB estimator and propose a variance estimator to account for uncertainty in covariate summaries. Second, we develop a new transportability method that allows more flexible modeling of covariate shift, thereby accounting for covariate shift and uncertainty in covariate summaries simultaneously. Asymptotic normality for the proposed estimator is established, and its asymptotic variance is consistently estimated. The proposed method offers greater flexibility in accounting for covariate shift and thus permits consistent estimation and valid inference when the validity of EB is not guaranteed. The proposed methods are evaluated by simulations and illustrated with an analysis of Surveillance, Epidemiology, and End Results breast cancer data.