A Generalized Quantile Tree Method for Subgroup Identification

Abstract

One primary goal of subgroup analysis is to identify subgroups of subjects with differential treatment effects. Existing methods have focused on the mean treatment effect and may be ineffective when the two distributions differ in scales or in the upper or lower tails. We develop a new generalized quantile tree method for subgroup identification. The method first uses quantile rank score tests to select split variables and then estimates the split point by minimizing a composite quantile loss. The proposed split rule is free of variable selection bias and robust against outliers and heavy-tailed distributions. In addition, we introduce a generalized quantile treatment effect estimator and a testing method for the selection and confirmation of predictive subgroups. Simulation shows that the proposed method gives more accurate subgroup identification than existing methods for cases with heteroscedastic or heavy-tailed errors. The practical value of the method is demonstrated through the analysis of an AIDS clinical trial data. Supplementary materials for this article are available online.

Keywords:

• Quantile treatment effect
• Rank score
• Recursive partitioning
• Regression tree
• Subgroup analysis

Supplementary materials

Technical proofs, the R code of the proposed GQ method and some additional simulation results are provided in the supplementary materials.

Acknowledgments

The authors gratefully acknowledge Dr. Xiaogang Su for sharing their R code.

Funding

This work is partly supported by the IR/D program and grant DMS-1712760 from the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Additional information

Funding

This work is partly supported by the IR/D program and grant DMS-1712760 from the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.