Targeted maximum likelihood based estimation for longitudinal mediation analysis

Wang Zeyi (), Laan Lars van der (), Petersen Maya (), Gerds Thomas (), Kvist Kajsa () and Laan Mark van der ()
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Wang Zeyi: Division of Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, United States of America
Laan Lars van der: Division of Environmental Health Sciences, School of Public Health, University of California, Berkeley, Berkeley, United States of America
Petersen Maya: Division of Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, United States of America
Gerds Thomas: Department of Public Health, Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark
Kvist Kajsa: Novo Nordisk, Søborg, Denmark
Laan Mark van der: Division of Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, United States of America

Journal of Causal Inference, 2025, vol. 13, issue 1, 39

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 article, 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 (EICs) 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.

Keywords: longitudinal mediation analysis; stochastic intervention; random intervention; targeted maximum likelihood estimation; efficient influence curve; efficient estimator; highly adaptive lasso (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:13:y:2025:i:1:p:39:n:1001

DOI: 10.1515/jci-2023-0013

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