Subgroup Analysis of a Single-Index Threshold Penalty Quantile Regression Model Based on Variable Selection

In clinical research, subgroup analysis can help identify patient groups that respond better or worse to specific treatments, improve therapeutic effect and safety, and is of great significance in precision medicine. This article considers subgroup analysis methods for longitudinal data containing multiple covariates and biomarkers. We divide subgroups based on whether a linear combination of these biomarkers exceeds a predetermined threshold, and assess the heterogeneity of treatment effects across subgroups using the interaction between subgroups and exposure variables. Quantile regression is used to better characterize the global distribution of the response variable and sparsity penalties are imposed to achieve variable selection of covariates and biomarkers. The effectiveness of our proposed methodology for both variable selection and parameter estimation is verified through random simulations. Finally, we demonstrate the application of this method by analyzing data from the PA.3 trial, further illustrating the practicality of the method proposed in this paper.