A Change-Point Model for Detecting Heterogeneity in Ordered Survival Responses

TL;DR

This paper introduces a new change-point detection model for ordered survival data, utilizing a constrained Hidden Markov Model and EM algorithm to identify heterogeneity in survival responses based on an ordering covariate.

Contribution

It presents a novel breakpoint model for survival analysis, combining HMM and EM methods, applicable to various hazard functions, and demonstrates its effectiveness on real data.

Findings

Effective detection of heterogeneity in survival data.

Flexible modeling with parametric and nonparametric hazards.

Successful application to diabetes survival times.

Abstract

In this article we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time to event variables. The survival responses need to be ordered according to a numerical covariate. Our esti- mation method will aim at detecting heterogeneity that could arise through the or- dering covariate. We formally introduce our model as a constrained Hidden Markov Model (HMM) where the hidden states are the unknown segmentation (breakpoint locations) and the observed states are the survival responses. We derive an efficient Expectation-Maximization (EM) framework for maximizing the likelihood of this model for a wide range of baseline hazard forms (parametrics or nonparametric). The posterior distribution of the breakpoints is also derived and the selection of the number of segments using penalized likelihood criterion is discussed. The performance of our survival breakpoint model is finally illustrated on a diabetes dataset where the observed survival times are ordered according to the calendar time of disease onset.