Integration of Individual Participant and Aggregate Data Under Dataset Shift: Summary Statistic Comparison and Scalable Computation

TL;DR

This paper explores how different summary statistics from aggregate data affect the efficiency of integrating individual and aggregate data, especially under dataset shift, proposing methods for improved estimation and practical recommendations.

Contribution

It introduces a framework comparing summary statistics for data integration, highlights the benefits of outcome-stratified summaries, and develops scalable estimation methods under dataset shift.

Findings

Outcome-stratified summaries improve efficiency more than covariate-stratified ones.

Including outcome-stratified summaries for continuous outcomes enhances evidence synthesis.

A fast, non-iterative estimation procedure improves scalability and stability.

Abstract

Integrated IPD-AD analysis, which combines individual participant data (IPD) with aggregate data (AD), is increasingly recognized as an effective strategy for generating more reliable and generalizable inferences from heterogeneous studies. While most existing work has focused on algorithmic approaches, this paper investigates a complementary yet underexplored question: how different forms of AD influence the efficiency of data integration. Working within a constrained maximum likelihood estimation framework, we compare commonly reported summary statistics and show that subgroup-specific summaries can substantially improve estimation efficiency. In particular, we find that AD derived from outcome-stratified subgroups (e.g., cases and controls) consistently yield greater efficiency gains than those based on covariate-stratified subgroups (e.g., age or exposure categories), especially when the outcome is continuous. Although outcome-stratified summaries are commonly reported for discrete outcomes, they are rarely provided when the outcome is continuous. Our findings therefore support the routine inclusion of outcome-stratified summaries for continuous endpoints in trial reports and public data repositories to facilitate more efficient evidence synthesis. We further extend the constrained maximum likelihood framework to accommodate dataset shift and develop a fast, non-iterative estimation procedure to improve numerical stability and scalability. We illustrate the proposed methodology with two applications: an analysis of income data under covariate shift and an analysis of housing data under prior probability shift.