Performance and Application of Estimators for the Value of an Optimal Dynamic Treatment Rule

TL;DR

This paper evaluates estimators for the expected outcomes of optimal dynamic treatment rules, emphasizing the benefits of cross-validated targeted maximum likelihood estimation (CV-TMLE) in maintaining performance amid data-adaptive estimation, with applications to mental health interventions.

Contribution

It demonstrates the effectiveness of CV-TMLE in estimating the value of dynamic treatment rules, especially under highly data-adaptive scenarios, and applies this methodology to a real trial for mental health treatment.

Findings

CV-TMLE maintains performance with data-adaptive algorithms

Using CV-TMLE reduces bias and improves efficiency

Application to a mental health trial shows practical utility

Abstract

Given an (optimal) dynamic treatment rule, it may be of interest to evaluate that rule -- that is, to ask the causal question: what is the expected outcome had every subject received treatment according to that rule? In this paper, we study the performance of estimators that approximate the true value of: 1) an $a$ $priori$ known dynamic treatment rule 2) the true, unknown optimal dynamic treatment rule (ODTR); 3) an estimated ODTR, a so-called "data-adaptive parameter," whose true value depends on the sample. Using simulations of point-treatment data, we specifically investigate: 1) the impact of increasingly data-adaptive estimation of nuisance parameters and/or of the ODTR on performance; 2) the potential for improved efficiency and bias reduction through the use of semiparametric efficient estimators; and, 3) the importance of sample splitting based on CV-TMLE for accurate inference. In the simulations considered, there was very little cost and many benefits to using the cross-validated targeted maximum likelihood estimator (CV-TMLE) to estimate the value of the true and estimated ODTR; importantly, and in contrast to non cross-validated estimators, the performance of CV-TMLE was maintained even when highly data-adaptive algorithms were used to estimate both nuisance parameters and the ODTR. In addition, we apply these estimators for the value of the rule to the "Interventions" Study, an ongoing randomized controlled trial, to identify whether assigning cognitive behavioral therapy (CBT) to criminal justice-involved adults with mental illness using an ODTR significantly reduces the probability of recidivism, compared to assigning CBT in a non-individualized way.