Multi-threshold Accelerate Failure Time Model

TL;DR

This paper introduces a novel two-stage method for detecting multiple thresholds and selecting models in segmented accelerate failure time models, with proven consistency and demonstrated effectiveness through simulations and real data analysis.

Contribution

It develops a new two-stage procedure combining group selection and refinement for threshold detection in AFT models, with theoretical guarantees.

Findings

Method achieves strong consistency in threshold and coefficient estimates.

Performs well in extensive simulation studies.

Successfully applied to follicular lymphoma data.

Abstract

A two-stage procedure for simultaneously detecting multiple thresholds and achieving model selection in the segmented accelerate failure time (AFT) model is developed in this paper. In the first stage, we formulate the threshold problem as a group model selection problem so that a concave 2-norm group selection method can be applied. In the second stage, the thresholds are finalized via a refining method. We establish the strong consistency of the threshold estimates and regression coefficient estimates under some mild technical conditions. The proposed procedure performs satisfactorily in our extensive simulation studies. Its real world applicability is demonstrated via analyzing a follicular lymphoma data.