Doubly Robust Regression Analysis for Data Fusion

TL;DR

This paper introduces doubly robust semiparametric estimators for regression analysis using fused data from two sources with different observed variables, ensuring consistent inference even with complex missing data patterns.

Contribution

It develops a class of doubly robust estimators tailored for data fusion scenarios, extending regression analysis methods to handle extreme missing data configurations.

Findings

Estimators are consistent and asymptotically normal under correct model specifications.

Simulation studies demonstrate the estimators' robustness and efficiency.

Application to U.S. household data reveals relationships between net asset value and expenditure.

Abstract

This paper investigates the problem of making inference about a parametric model for the regression of an outcome variable $Y$ on covariates $(V,L)$ when data are fused from two separate sources, one which contains information only on $(V, Y)$ while the other contains information only on covariates. This data fusion setting may be viewed as an extreme form of missing data in which the probability of observing complete data $(V,L,Y)$ on any given subject is zero. We have developed a large class of semiparametric estimators, which includes doubly robust estimators, of the regression coefficients in fused data. The proposed method is DR in that it is consistent and asymptotically normal if, in addition to the model of interest, we correctly specify a model for either the data source process under an ignorability assumption, or the distribution of unobserved covariates. We evaluate the performance of our various estimators via an extensive simulation study, and apply the proposed methods to investigate the relationship between net asset value and total expenditure among U.S. households in 1998, while controlling for potential confounders including income and other demographic variables.