Augmented transfer regression learning for completely missing covariates

TL;DR

This paper introduces an augmented transfer regression learning method to address the challenge of completely missing covariates in large-scale population datasets, leveraging invariance assumptions and doubly robust estimation.

Contribution

It proposes a novel transfer learning approach that combines importance weighting and imputation, achieving consistency and efficiency under covariate invariance assumptions.

Findings

Estimator is doubly robust and consistent under model misspecification.

Method attains the semiparametric efficiency bound with correct models.

Estimator is $n^{1/2}$-consistent and asymptotically normal.

Abstract

Large-scale population-level datasets, such as the UK Biobank and the All of Us Research Program, often lack covariates needed for a specific analysis, such as genetic or lifestyle measures, while related studies measure them. This creates a cross-population missing data problem in which covariates are completely unobserved in the target population, rather than partially missing within one dataset. We propose an augmented transfer regression learning method for this setting. The key identifying condition is a sub-population shift assumption: the joint distribution of the outcome and observed covariates may differ across source and target populations, but the conditional distribution of the missing covariates given observed variables is invariant. We combine importance-weighted estimating equations with imputation terms for first- and second-order moments of the missing covariates. The resulting estimator is doubly robust, remaining consistent if either the density ratio model or both imputation models are correctly specified. It is $n^{1/2}$-consistent and asymptotically normal, and attains the semiparametric efficiency bound when both nuisance models are correctly specified.