A two-part framework for estimating individualized treatment rules from semi-continuous outcomes

Health care payments are an important component of health care utilization and are thus a major focus in health services and health policy applications. However, payment outcomes are semi-continuous in that over a given period of time some patients incur no payments and some patients incur large costs. Individualized treatment rules (ITRs) are a major part of the push for tailoring treatments and interventions to patients, yet there is a little work focused on estimating ITRs from semi-continuous outcomes. In this paper, we develop a framework for estimation of ITRs based on two-part modeling, wherein the ITR is estimated by separately targeting the zero part of the outcome and the strictly positive part. To improve performance when high-dimensional covariates are available, we leverage a scientifically-plausible penalty that simultaneously selects variables and encourages the signs of coefficients for each variable to agree between the two components of the ITR. We develop an efficient algorithm for computation and prove oracle inequalities for the resulting estimation and prediction errors. We demonstrate the effectiveness of our approach in simulated examples and in a study of a health system intervention.