Multi-state model with temporal-consistent survival analysis for homogeneous Markov chains

TL;DR

This paper introduces a novel temporal-consistent survival analysis method for estimating hitting-time distributions in homogeneous Markov chains, with theoretical guarantees and practical applications.

Contribution

It develops a new approach for estimating first hitting-time distributions and cure rates in Markov chains, with non-asymptotic guarantees and kernel-based estimators.

Findings

Method provides consistent estimators from transition data.

The approach includes a cure rate estimator for chains that never reach terminal states.

Simulation and real-life application demonstrate effectiveness.

Abstract

In this study, we consider sequences drawn from time-homogeneous Markov chains and introduce a novel approach for estimating first hitting-time distributions to specified terminal states. Our method- ology is based on the temporal-consistent survival analysis that facilitates the construction of consistent estimators of the distributions from any estimates of the transition rate and transition probabilities. In this line of work, we also discuss the issue of cured individuals with chains that never reach a termi- nal state, and propose an estimator of the cure rate. Furthermore, we derive non-asymptotic theoretical guarantees for our approach and apply our methodology with kernel type estimators. The latter approach is illustrated in a simulation study using generic data and a real-life application involving patients un- dergoing bone marrow transplants.