Marginal generalized raking with parametric working models
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 marginal generalized raking. We contrast our approach to a procedure that marginalizes a conditional GR estimator of regression parameters; while the former approach is doubly robust, i.e. is consistent if either the missing-data model or the optimal raking variable is estimated consistently, our proposed approach is multiply robust, allowing either the outcome regression or treatment propensity score to also be misspecified. We compare the approaches in both fully-synthetic simulations and in an application using data from an observational cohort of persons living with HIV.
Related
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BibTeX
@misc{williamson2026marginal,
title = {{Marginal generalized raking with parametric working models}},
author = {Brian D Williamson and Runjia Zou and Thomas Lumley and Bryan E Shepherd and Pamela A Shaw},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.29629},
eprint = {2607.29629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.29629},
}
RIS
TY - UNPB
TI - Marginal generalized raking with parametric working models
AU - Brian D Williamson
AU - Runjia Zou
AU - Thomas Lumley
AU - Bryan E Shepherd
AU - Pamela A Shaw
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2607.29629
UR - https://arxiv.org/abs/2607.29629
AB - 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 marginal generalized raking. We contrast our approach to a procedure that marginalizes a conditional GR estimator of regression parameters; while the former approach is doubly robust, i.e. is consistent if either the missing-data model or the optimal raking variable is estimated consistently, our proposed approach is multiply robust, allowing either the outcome regression or treatment propensity score to also be misspecified. We compare the approaches in both fully-synthetic simulations and in an application using data from an observational cohort of persons living with HIV.
ER -