Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data

TL;DR

This paper extends a unifying theory for semiparametric data fusion to include complex scenarios like two-sample IV analysis and epidemiological data integration, enabling more flexible and efficient inference from diverse data sources.

Contribution

It introduces a generalized framework for data fusion that accommodates non-factorized conditional distributions, broadening applicability to real-world complex data integration problems.

Findings

Provides universal influence function characterizations for complex data fusion scenarios.

Enables machine-learning debiased, semiparametric efficient estimation.

Extends existing theories to more general data alignment conditions.

Abstract

We address the goal of conducting inference about a smooth finite-dimensional parameter by utilizing individual-level data from various independent sources. Recent advancements have led to the development of a comprehensive theory capable of handling scenarios where different data sources align with, possibly distinct subsets of, conditional distributions of a single factorization of the joint target distribution. While this theory proves effective in many significant contexts, it falls short in certain common data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological studies with diverse designs (e.g., prospective cohorts and retrospective case-control studies), and studies with variables prone to measurement error that are supplemented by validation studies. In this paper, we extend the aforementioned comprehensive theory to allow for the fusion of individual-level data from sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution. Assuming conditional and marginal distribution alignments, we provide universal results that characterize the class of all influence functions of regular asymptotically linear estimators and the efficient influence function of any pathwise differentiable parameter, irrespective of the number of data sources, the specific parameter of interest, or the statistical model for the target distribution. This theory paves the way for machine-learning debiased, semiparametric efficient estimation.