Data Fusion for Errors-in-Variables

2026-10-04

AI Summary

This study addresses the problem of measurement error correction in target studies containing only a single error-prone proxy variable by leveraging repeated measurement data from an external heterogeneous source. To identify the error distribution, we propose a conditional transportability assumption. Methodologically, we construct a unified spectral theory framework accommodating both diffuse and finite atomic spectra, and develop a data fusion estimator that integrates conditional deconvolution with orthogonal correction. Theoretically, we establish consistency and convergence rate bounds for the proposed estimator. Empirically, an analysis of NHANES data demonstrates that accounting for source-target heterogeneity substantially alters existing conclusions, thereby validating the effectiveness of the proposed approach.

Abstract

We study errors-in-variables problems in which a target study contains only a single error-prone surrogate of an unobserved exposure, while an external source study provides repeated surrogate measurements from a different population. The measurement error distribution is allowed to depend on the observed error-free variables, and the error-free variable distribution itself may differ between studies. We introduce a conditional transportability assumption that enables the use of external repeated measurements under source-target heterogeneity. Together with additional replicate-error conditions, it identifies the target conditional measurement-error distribution. Building on this identification result, we develop a data-fusion estimator for a broad class of target functionals. The estimator combines conditional deconvolution, flexible nuisance estimation, and orthogonal correction that reduces first-order sensitivity to nuisance estimation. For the proposed estimator, we develop a unified spectral theory covering both diffuse-spectrum and finite atomic-spectrum target functionals, derive a general asymptotic expansion, and establish consistency and target-specific convergence-rate bounds. The resulting convergence-rate bounds depend jointly on the spectral properties of the measurement error, the latent exposure, and the target functional. For finite atomic-spectrum targets, we further establish joint Gaussian and bootstrap limits, yielding inference for smooth moment transformations under an additional centering condition. In the reported simulations, Fuse-EIV has small bias for the primary exposure-related coefficient. Applications to the National Health and Nutrition Examination Survey illustrate how accounting for population heterogeneity and error heteroscedasticity can change empirical conclusions.

Problem

• Errors-in-Variables
• Data Fusion
• Measurement Error
• Transportability
• Surrogate Measurements

Innovation

• errors-in-variables
• data fusion
• conditional transportability
• deconvolution
• orthogonal correction