🤖 AI Summary
This study addresses the lack of a unified and efficient estimation framework for complex causal inference problems involving time-varying treatments, mediation effects, and censored data. Building on the Riesz representation theorem, the authors propose a general recursive Riesz representer framework that integrates targeted minimum loss-based estimation (TMLE) with semiparametric efficiency theory to construct efficient estimators for nested linear functionals in a unified manner. The approach substantially simplifies the construction of estimators for a broad class of causal parameters while guaranteeing asymptotic efficiency and robustness. Numerical experiments demonstrate its favorable performance, and an open-source software implementation is provided. The method is successfully applied to a reanalysis of data from an HIV vaccine efficacy trial.
📝 Abstract
As research in causal inference has sought to address more complex scientific questions, the number of specialized estimands in the field has proliferated. Recognition that many of these estimands share a common linear form has generated interest in simplifying estimation procedures using Riesz representers. In this work, we construct a targeted minimum loss-based estimation procedure for nested linear functionals, leveraging Riesz representers of a general recursive form. The proposed method unifies asymptotically efficient estimation for a variety of statistical estimands that originate in causal inference, including the effects of time-varying treatments under treatment-confounder feedback and direct and indirect effects from causal mediation analysis. We demonstrate how our proposal reduces the need for laborious and technically challenging mathematical derivations when constructing estimators of common statistical estimands under complex forms of censoring and sampling. We investigate and validate the properties of the proposed procedures in numerical experiments, discuss open-source software facilitating their implementation, and illustrate their application in a re-analysis of data from an HIV vaccine efficacy trial.