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Mixture Markov Model (MMM) is a widely used tool to cluster sequences ofevents coming from a finite state-space. However the MMM likelihood beingmulti-modal, the challenge remains in its maximization. AlthoughExpectation-Maximization (EM) algorithm remains one of the most popular ways toestimate the MMM parameters, however convergence of EM algorithm is not alwaysguaranteed. Given the computational challenges in maximizing the mixturelikelihood on the constrained parameter space, we develop a patternsearch-based global optimization technique which can optimize any objectivefunction on a collection of simplexes, which is eventually used to maximize MMMlikelihood. This is shown to outperform other related global optimizationtechniques. In simulation experiments, the proposed method is shown tooutperform the expectation-maximization (EM) algorithm in the context of MMMestimation performance. The proposed method is applied to cluster Multiplesclerosis (MS) patients based on their treatment sequences of disease-modifyingtherapies (DMTs). We also propose a novel method to cluster people with MSbased on DMT prescriptions and associated clinical features (covariates) usingMMM with covariates. Based on the analysis, we divided MS patients into 3clusters. Further cluster-specific summaries of relevant covariates indicatepatient differences among the clusters.

Clustering sequence data with mixture Markov chains with covariates using multiple simplex constrained optimization routine (MSiCOR)