Improving Efficiency of Regression Analyses by Integrating Data from Population-Representative Surveys: A Model-Assisted Calibration Approach

2026-06-30

AI Summary

Existing data integration methods struggle to accommodate complex survey designs and typically assume that multiple data sources originate from the same population, rendering them unsuitable for non-probability samples. This work proposes a model-assisted calibration framework that extends such integration to multiple probability survey samples—a first in the literature—accepting either individual-level data or aggregated summary statistics as input. The approach guarantees design-consistent estimation without requiring correct specification of the outcome model and naturally accommodates complex sampling designs. Coupled with Taylor linearization for variance estimation, the method substantially enhances the efficiency of regression analysis while preserving validity for finite-population inference. Simulation studies and empirical analyses using NHANES and NHIS data demonstrate consistent efficiency gains across diverse scenarios.

Abstract

The increasing availability of diverse data sources has motivated great interest in data integration for improving regression efficiency. Existing data integration methods primarily focus on integrating nonprobability samples and typically assume that the integrated data sources represent the same target population. While this assumption is often difficult to justify for nonprobability samples, it is naturally satisfied when integrating probability-based surveys designed to represent a common target population. Such surveys are important research data sources because they provide representative samples and collect rich information on diverse variables, making them well suited to data integration. However, existing integration methods do not accommodate complex sampling designs. We propose model-assisted calibration methods to improve regression efficiency by integrating multiple probability-based survey samples. The proposed framework accommodates settings in which either individual-level data or only summary statistics are available from external surveys while preserving valid finite-population inference without requiring correct specification of the outcome model. We establish the design consistency of the proposed estimators and develop Taylor linearization variance estimators accounting for the complex sampling designs of both surveys. Simulation studies and an application integrating National Health and Nutrition Examination Survey and National Health Interview Survey demonstrate substantial efficiency gains while maintaining valid finite-population inference.

Problem

• data integration
• probability-based surveys
• complex sampling designs
• regression efficiency
• finite-population inference

Innovation

• model-assisted calibration
• data integration
• probability-based surveys
• complex sampling design
• finite-population inference