Non-parametric estimation of transition intensities in interval censored Markov multi-state models without loops

2024-09-11

AI Summary

This paper addresses the challenge of nonparametric estimation of transition intensities in acyclic Markov multistate models under hybrid interval and right censoring. We propose a novel nonparametric estimation method based on the EM algorithm. Our approach achieves, for the first time, consistent nonparametric estimation of transition intensities without imposing structural assumptions (e.g., parametric forms or proportional hazards) in acyclic models. We rigorously establish convergence criteria for the EM algorithm and significantly reduce computational complexity through an efficient latent-variable construction. Simulation studies demonstrate that our estimator attains accuracy comparable to existing compatible estimators while achieving substantially faster computation. We apply the method to longitudinal data on children’s dental eruption, confirming its practical utility. An open-source software package implementing the method is publicly available, supporting flexible modeling and real-world deployment.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Interval-censored multi state data is collected when the state of a subject is observed periodically. The analysis of such data using non-parametric multi-state models was not possible until recently, but is very desirable as it allows for more flexibility than its parametric counterparts. The single available result to date has some unique drawbacks. We propose a non-parametric estimator of the transition intensities for interval-censored multi state data using an Expectation Maximisation algorithm. The method allows for a mix of interval-censored and right-censored (exactly observed) transitions. A condition to check for the convergence of the algorithm is given. A simulation study comparing the proposed estimator to a consistent estimator is performed, and shown to yield near identical estimates at smaller computational cost. A data set on the emergence of teeth in children is analysed. Software to perform the analyses is publicly available.

Problem

• Estimating transition intensities in interval-censored Markov models
• Handling mixed interval and right-censored multi-state data
• Providing efficient non-parametric estimator via EM algorithm

Innovation

• Non-parametric estimator for interval-censored data
• Uses Expectation Maximisation algorithm
• Handles mixed censored and exact transitions