Using Machine Learning to Improve Control for Confounding in the Dynamic Weighted Ordinary Least Squares Estimator of Optimal Adaptive Treatment Strategies

Abstract

Estimating optimal adaptive treatment strategies (ATSs) can be done in several ways, including dynamic weighted ordinary least squares (dWOLS). This approach is doubly robust as it requires modeling both the treatment and the response, but only one of those models needs to be correctly specified to obtain a consistent estimator. For estimating an average treatment effect, doubly robust methods have been shown to combine better with machine learning methods than alternatives. However, the use of machine learning within dWOLS has not yet been investigated. Using simulation studies, we evaluate and compare the performance of the dWOLS estimator when the treatment probability is estimated either using machine learning algorithms or a logistic regression model. We further investigate the use of an adaptive $m$-out-of-$n$ bootstrap method for producing inferences. SuperLearner performed at least as well as logistic regression in terms of bias and variance in scenarios with simple data-generating models and often had improved performance in more complex scenarios. Moreover, the $m$-out-of-$n$ bootstrap produced confidence intervals with nominal coverage probabilities for parameters that were estimated with low bias. We also apply our proposed approach to the data from a breast cancer registry in Québec, Canada, to estimate an optimal ATS to personalize the use of hormonal therapy in breast cancer patients. Our method is implemented in the R software and available on GitHub https://github.com/kosstre20/MachineLearningToControlConfoundingPersonalizedMedicine.git. We recommend routine use of machine learning to model treatment within dWOLS, at least as a sensitivity analysis for the point estimates.