Non-parametric causal effects based on longitudinal modified treatment policies

TL;DR

This paper introduces longitudinal modified treatment policies (LMTPs), a non-parametric approach for causal inference that addresses issues with positivity and practical relevance in continuous or multi-valued treatments, providing efficient estimators and software.

Contribution

It proposes LMTPs as a novel non-parametric method for causal effects, ensuring positivity and interpretability, with multiple estimators and an open-source R package.

Findings

Two estimators are efficient.

One estimator is sequentially doubly robust.

Simulation and ICU study demonstrate estimator performance.

Abstract

Most causal inference methods consider counterfactual variables under interventions that set the treatment deterministically. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Furthermore, violations to the positivity assumption, necessary for identification, are exacerbated with continuous and multi-valued treatments and deterministic interventions. In this paper we propose longitudinal modified treatment policies (LMTPs) as a non-parametric alternative. LMTPs can be designed to guarantee positivity, and yield effects of immediate practical relevance with an interpretation that is familiar to regular users of linear regression adjustment. We study the identification of the LMTP parameter, study properties of the statistical estimand such as the efficient influence function, and propose four different estimators. Two of our estimators are efficient, and one is sequentially doubly robust in the sense that it is consistent if, for each time point, either an outcome regression or a treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on hypoxemia and mortality in Intensive Care Unit (ICU) patients. Software implementing our methods is provided in the form of the open source \texttt{R} package \texttt{lmtp} freely available on GitHub (\url{https://github.com/nt-williams/lmtp}).