AIM: Amortized Inference for Multistate Transition Models

Interval censored continuous time multistate transition models (MSTMs) are widely used to characterize disease progression and other dynamic processes.

Existing inference procedures are predominantly likelihood-based and require a separate model fit for each dataset, involving repeated evaluation of transition probability matrices.

This repeated computation can become burdensome when the same model is applied across centers, time periods, or newly collected cohorts.

We propose AIM, an amortized Bayesian inference framework for interval censored continuous time MSTMs.

AIM learns the relationship between informative summary statistics and model parameters from simulated datasets generated during an offline training stage.

Once trained for a prespecified model class, AIM provides posterior inference for new datasets without repeated likelihood optimization.

Under fixed observation schedules and discretized covariate strata, we show that interval-specific transition counts are sufficient for the observed panel likelihood and establish identifiability of the corresponding population summaries.

We further prove consistency of the induced summary posterior and its neural approximation, yielding a consistent posterior mean estimator.

Simulation studies under progressive and competing-pathway MSTMs demonstrate accurate point estimation and reliable uncertainty quantification.

AIM completed online inference in milliseconds, with median speedups ranging from approximately 154-fold to 2308-fold relative to repeated likelihood-based estimation.

These results establish AIM as a scalable and theoretically grounded framework for reusable Bayesian inference in interval censored MSTMs.