Maximum likelihood estimation in discrete mixed hidden Markov models using the SAEM algorithm

Mixed hidden Markov models have been recently defined in the literature as an extension of hidden Markov models for dealing with population studies. The notion of mixed hidden Markov models is particularly relevant for modeling longitudinal data collected during clinical trials, especially when distinct disease stages can be considered. However, parameter estimation in such models is complex, especially due to their highly nonlinear structure and the presence of unobserved states. Moreover, existing inference algorithms are extremely time consuming when the model includes several random effects. New inference procedures are proposed for estimating population parameters, individual parameters and sequences of hidden states in mixed hidden Markov models. The main contribution consists of a specific version of the stochastic approximation EM algorithm coupled with the BaumWelch algorithm for estimating population parameters. The properties of this algorithm are investigated via a Monte-Carlo simulation study, and an application of mixed hidden Markov models to the description of daily seizure counts in epileptic patients is presented.