A plug-in estimator of the non-iterative conditional expectation g-formula using long short-term memory models
Abstract
The non-iterative conditional expectation (NICE) plug-in estimator of the g-formula can be used to estimate the causal effects of sustained treatment strategies, even in the presence of treatment-confounder feedback, under the assumptions of exchangeability, positivity, and consistency. In practical applications, parametric models are commonly used to estimate the joint distribution of confounders, treatments, and outcomes over time. As an alternative to parametric models, long short-term memory (LSTM) models, designed to capture both short-term patterns and long-range dependencies in sequential data, may better accommodate complex temporal dependencies among time-varying confounders, treatments, and outcomes. However, the validity of statistical inferences of a plug-in estimator based on LSTM models has not yet been investigated. Here, we provide proof of principle that, under a complex data generation mechanism that resembles data from a cohort of persons with HIV and sufficiently large sample sizes, an LSTM-based NICE g-formula plug-in estimator results in less bias than parametric estimators while achieving near-nominal coverage for 95\% confidence intervals. This work is intended to spur the development of a theoretical framework that encompasses deep learning plug-in estimators for causal inference based on high-dimensional longitudinal data.
Related
- The conditional expectation of the product of the first n−1 Hermite polynomials in a multivariate normal distribution with respect to the n-th variable. A fresh perspective on the Kibble-Slepian formula
- Learning Conditional Expectation Operators via Functional Newton Updates
- Dimension Reduction for the Trivariate Normal Product Distribution: An Efficient Numerical Algorithm via Conditional Expectation
- Continuous Distributional Characterizations via a Single Characterizing Function and Lambert W Conditional Expectation Identities
- Beyond Tweedie's Formula: Conditional Score Modeling for Empirical Bayes Inference
BibTeX
@misc{li2026plugin,
title = {{A plug-in estimator of the non-iterative conditional expectation g-formula using long short-term memory models}},
author = {Jing Li and Sophia M. Rein and Zilong Wang and Zixiao Wang and Sean McGrath and James M. Robins and Thomas Kolokotrones and Rajarshi Mukherjee and Miguel A. Hernán},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27354},
eprint = {2610.27354},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27354},
}
RIS
TY - UNPB
TI - A plug-in estimator of the non-iterative conditional expectation g-formula using long short-term memory models
AU - Jing Li
AU - Sophia M. Rein
AU - Zilong Wang
AU - Zixiao Wang
AU - Sean McGrath
AU - James M. Robins
AU - Thomas Kolokotrones
AU - Rajarshi Mukherjee
AU - Miguel A. Hernán
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27354
UR - https://arxiv.org/abs/2610.27354
AB - The non-iterative conditional expectation (NICE) plug-in estimator of the g-formula can be used to estimate the causal effects of sustained treatment strategies, even in the presence of treatment-confounder feedback, under the assumptions of exchangeability, positivity, and consistency. In practical applications, parametric models are commonly used to estimate the joint distribution of confounders, treatments, and outcomes over time. As an alternative to parametric models, long short-term memory (LSTM) models, designed to capture both short-term patterns and long-range dependencies in sequential data, may better accommodate complex temporal dependencies among time-varying confounders, treatments, and outcomes. However, the validity of statistical inferences of a plug-in estimator based on LSTM models has not yet been investigated. Here, we provide proof of principle that, under a complex data generation mechanism that resembles data from a cohort of persons with HIV and sufficiently large sample sizes, an LSTM-based NICE g-formula plug-in estimator results in less bias than parametric estimators while achieving near-nominal coverage for 95\% confidence intervals. This work is intended to spur the development of a theoretical framework that encompasses deep learning plug-in estimators for causal inference based on high-dimensional longitudinal data.
ER -