Semi-Markov Multistate Model with Interval-Censored Transition Times

A Cox-based multistate model is proposed for analyzing a multicohort event history process with interval-censored transition times. The cohort is included as a stratum variable when modeling each transition hazard, while testing the compliance with the Markov property conditional on the prognostic covariates. Whenever the Markovian assumption does not hold for a given transition, the time of entry into the current state is incorporated in the modeling procedure, yielding a semi-Markov process. To deal with interval censoring, an easy-to-implement procedure is based on performing a multiple imputation of the unknown transition times within the specified intervals. The corresponding artificially completed datasets are separately fitted using the proposed multistate model, each providing inference on the target population quantity. Finally, the overall collected information is properly combined. The described methodology is applied to a three-wave dataset of COVID-19-hospitalized adults.