Targeted Maximum Likelihood Based Estimation for Longitudinal Mediation Analysis

TL;DR

This paper develops a targeted maximum likelihood estimation method for longitudinal mediation analysis, effectively handling complex data structures with time-varying confounders and censoring, and introduces new estimators utilizing highly adaptive lasso.

Contribution

It introduces a novel TMLE approach for longitudinal natural direct and indirect effects, combining machine learning with semiparametric theory for improved robustness and efficiency.

Findings

Estimators are multiply robust and locally efficient.

The method uses HAL and projection representations for new influence curve estimators.

A fast one-step TMLE algorithm with preserved asymptotic properties is proposed.

Abstract

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox.