A Two-Part Framework for Estimating Individualized Treatment Rules From Semicontinuous Outcomes

Jared D. Huling, Maureen A. Smith, Guanhua Chen

Research output: Contribution to journalArticlepeer-review


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 semicontinuous 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 semicontinuous outcomes. In this article, 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. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)210-223
Number of pages14
JournalJournal of the American Statistical Association
Issue number533
StatePublished - 2021

Bibliographical note

Funding Information:
This project was supported by the University of Wisconsin (UW) Health Innovation Program and the UW School of Medicine and Public Health from The Wisconsin Partnership Program. We thank the editor, associate editor, and a reviewer for constructive comments, which helped greatly to improve the article.

Publisher Copyright:
© 2020 American Statistical Association.


  • Cooperative lasso
  • Electronic health records
  • Health services
  • Oracle inequality
  • Precision medicine


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