Using Longitudinal Targeted Maximum Likelihood Estimation in Complex Settings with Dynamic Interventions

TL;DR

This paper demonstrates that longitudinal targeted maximum likelihood estimation (LTMLE) can effectively estimate dynamic treatment effects in complex, realistic epidemiological settings with long follow-up, high-dimensional data, and multiple confounders, using HIV treatment as an example.

Contribution

It provides practical guidance and empirical evidence that LTMLE can be successfully applied in complex longitudinal studies, highlighting its robustness and the importance of machine learning and quality checks.

Findings

LTMLE yields stable, accurate estimates even with small samples.

Simple machine learning models can outperform complex ones in LTMLE.

Performance varies with intervention support and data complexity.

Abstract

Longitudinal targeted maximum likelihood estimation (LTMLE) has very rarely been used to estimate dynamic treatment effects in the context of time-dependent confounding affected by prior treatment when faced with long follow-up times, multiple time-varying confounders, and complex associational relationships simultaneously. Reasons for this include the potential computational burden, technical challenges, restricted modeling options for long follow-up times, and limited practical guidance in the literature. However, LTMLE has desirable asymptotic properties, i.e. it is doubly robust, and can yield valid inference when used in conjunction with machine learning. We use a topical and sophisticated question from HIV treatment research to show that LTMLE can be used successfully in complex realistic settings and compare results to competing estimators. Our example illustrates the following practical challenges common to many epidemiological studies 1) long follow-up time (30 months), 2) gradually declining sample size 3) limited support for some intervention rules of interest 4) a high-dimensional set of potential adjustment variables, increasing both the need and the challenge of integrating appropriate machine learning methods 5) consideration of collider bias. Our analyses, as well as simulations, shed new light on the application of LTMLE in complex and realistic settings: we show that (i) LTMLE can yield stable and good estimates, even when confronted with small samples and limited modeling options; (ii) machine learning utilized with a small set of simple learners (if more complex ones can't be fitted) can outperform a single, complex model, which is tailored to incorporate prior clinical knowledge; (iii) performance can vary considerably depending on interventions and their support in the data, and therefore critical quality checks should accompany every LTMLE analysis.