Multi-threshold Change Plane Model: Estimation Theory and Applications in Subgroup Identification

TL;DR

This paper introduces a multi-threshold change plane regression model for identifying subgroups with different covariate effects, providing a novel estimation approach with theoretical guarantees and practical medical applications.

Contribution

It proposes a new 2-stage estimation method for multi-threshold change plane models, including subgroup number determination and parameter estimation with asymptotic properties.

Findings

Effective in simulation studies for subgroup detection.

Applicable to high-dimensional covariates with sparse solutions.

Demonstrated usefulness in medical data analysis.

Abstract

We propose a multi-threshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of covariates and thus multiple thresholds form parallel change planes in the covariate space. We contribute a novel 2-stage approach to estimate the number of subgroups, the location of thresholds and all other regression parameters. In the first stage we adopt a group selection principle to consistently identify the number of subgroups, while in the second stage change point locations and model parameter estimates are refined by a penalized induced smoothing technique. Our procedure allows sparse solutions for relatively moderate- or high-dimensional covariates. We further establish the asymptotic properties of our proposed estimators under appropriate technical conditions. We evaluate the performance of the proposed methods by simulation studies and provide illustration using two medical data. Our proposal for subgroup identification may lead to an immediate application in personalized medicine.