Deterministic Uniformization for Estimation and Latent Trajectory Inference in Interval-Censored Multistate Triansition Models

Abstract

Interval-censored multistate data arise when subjects are observed at irregular visit times, leaving transition times and intermediate states unobserved. Likelihood-based inference for continuous-time Markov models often requires computationally intensive matrix exponential evaluations. We propose a deterministic uniformization expectation-maximization (EM) algorithm for parameter estimation and latent trajectory inference. By representing the continuous-time process through an embedded Markov chain indexed by latent Poisson event counts, the method enables deterministic E-step calculations without repeated matrix exponential evaluations. The M-step reduces to transition-specific Poisson regressions with exposure offsets, accommodating covariate-dependent transition intensities. We establish uniform truncation error bounds and show that the procedure is an asymptotically monotone generalized EM algorithm. Under standard regularity conditions, the estimator is consistent and asymptotically normal. Simulations demonstrate accurate estimation and computational advantages over direct likelihood optimization, particularly for complex transition structures. We also develop an exact dynamic programming method to calculate posterior probabilities of candidate latent pathways and identify the most probable pathway between observations. Posterior expected transition counts and state occupancy times provide additional subject-specific summaries, while expected-count ratios offer a computational shortcut for classification in simple mutually exclusive pathway structures. The framework supports both population-level inference and individualized characterization of disease progression.