Section: New Results

Inference in mixed hidden Markov models

Participants : Maud Delattre, Marc Lavielle.

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.

We have proposed new inference procedures for estimating population parameters, individual parameters and sequences of hidden states in mixed hidden Markov models [1] . The main contribution consists of a specific version of the stochastic approximation EM algorithm coupled with the Baum-Welch algorithm for estimating population parameters. The properties of this algorithm were investigated via a Monte-Carlo simulation study.

An application of mixed hidden Markov models to the description of daily seizure counts in epileptic patients was then considered. We proposed to describe exposure-response relationship of gabapentin in epileptic patients using MHMM approach. Longitudinal seizure frequency data from six clinical studies were available for the analysis. The model describes daily seizure frequencies to be governed by an unobserved, yet present, underlying disease dynamics, defined by states of high or low epileptic activity. Individual day-to-day states are dependent exhibiting their own dynamics with patients transitioning between disease states, according to a set of transition probabilities. MHMM estimates both unobserved disease dynamics and daily seizure frequencies in all disease states. Novel drug action modes are achievable: drug may influence both seizure frequencies and transition probabilities. The model showed that gabapentin significantly reduced seizure frequencies in both disease states, without altering disease dynamics. Novel methodology offers additional insights into understanding epilepsy time course, gabapentin mode of action and provides a tool for realistic clinical trial simulations.