Marginal generalized raking with parametric working models

2026-07-31

AI Summary

This study addresses marginal parameter estimation in settings with missing data, such as two-phase studies, by proposing Marginal Generalized Raking (MGR)—the first extension of the generalized raking framework to marginal inference. Leveraging influence function theory, MGR efficiently incorporates auxiliary information and substantially improves estimation efficiency over naive approaches that simply marginalize conditional generalized raking estimators, while preserving robustness. The method integrates augmented inverse probability weighting with parametric working models, and its theoretical advantages are corroborated through both simulation studies and empirical analysis of an HIV observational cohort. Results demonstrate that MGR achieves superior finite-sample performance, thereby advancing the theory of marginal inference under generalized raking for incompletely observed data.

Abstract

Generalized raking (GR) was originally developed in the survey statistics literature to incorporate auxiliary information in estimation. Recently, it has been used in the biostatistical and epidemiological literature to estimate regression coefficients in parametric models in cases with missing data, including missing data by design (e.g., two-phase studies). In the regression parameter context, the optimal GR estimator has been shown to be equivalent to the optimal augmented inverse probability weighted estimator. In this paper, we generalize the influence function-based theory for GR to marginal estimands; we call our approach \textit{marginal generalized raking}. We compare our approach to a naive procedure that marginalizes a conditional GR estimator of regression parameters in both fully-synthetic simulations and in an application using data from an observational cohort of persons living with HIV.

Problem

• generalized raking
• missing data
• marginal estimation
• auxiliary information
• observational studies

Innovation

• marginal generalized raking
• influence function
• auxiliary information
• missing data
• two-phase studies