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

TL;DR

This paper introduces a non-parametric estimator for transition intensities in interval-censored multi-state models, using an EM algorithm that handles mixed censoring types, validated through simulations and applied to dental development data.

Contribution

It presents a novel EM-based non-parametric estimation method for multi-state models with interval and right censoring, improving computational efficiency and flexibility.

Findings

Estimator performs comparably to existing methods with less computational cost.

Simulation studies confirm the estimator's accuracy and efficiency.

Application to children's dental data demonstrates practical utility.

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.