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Updated: May 30, 2025

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Clustering Sequence Data with Mixture Markov Chains with Covariates Using Multiple Simplex Constrained Optimization

Priyam Das1, Deborshee Sen2, Debsurya De3

  • 1Department of Biostatistics, Virginia Commonwealth University, Richmond, VA.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|January 29, 2025
PubMed
Summary
This summary is machine-generated.

A new global optimization method improves Mixture Markov Model (MMM) performance for clustering event sequences, outperforming the Expectation-Maximization (EM) algorithm. This technique was applied to identify patient subgroups in multiple sclerosis (MS) based on treatment data.

Keywords:
Disease-modifying therapyGlobal optimizationMarkov chainMedical sequence dataMixture modelMultiple sclerosis

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Area of Science:

  • Computational Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Mixture Markov Models (MMM) are valuable for clustering event sequences but face challenges in likelihood maximization due to multi-modality.
  • The Expectation-Maximization (EM) algorithm, commonly used for MMM parameter estimation, does not guarantee convergence.
  • Maximizing MMM likelihood on constrained parameter spaces presents significant computational difficulties.

Purpose of the Study:

  • To develop a robust global optimization technique for maximizing Mixture Markov Model likelihood.
  • To enhance the performance of Mixture Markov Models in clustering complex event sequences.
  • To apply the improved MMM for clustering multiple sclerosis (MS) patients based on disease-modifying therapy (DMT) sequences and clinical covariates.

Main Methods:

  • Developed a pattern search-based global optimization technique capable of optimizing objective functions on collections of simplexes.
  • Utilized this technique to maximize the likelihood function for Mixture Markov Models.
  • Applied the enhanced MMM to cluster MS patients using DMT prescription data and associated clinical features (covariates).

Main Results:

  • The proposed pattern search-based global optimization method demonstrated superior performance compared to existing global optimization techniques.
  • In simulation experiments, the new method outperformed the Expectation-Maximization (EM) algorithm in Mixture Markov Model estimation.
  • Clustering of MS patients revealed three distinct subgroups based on DMT sequences and covariates, with significant differences identified across clusters.

Conclusions:

  • The novel pattern search-based global optimization technique effectively addresses the challenges of Mixture Markov Model likelihood maximization.
  • This approach offers improved accuracy and reliability for MMM parameter estimation compared to the traditional EM algorithm.
  • The application to MS patient data successfully identified clinically relevant subgroups, paving the way for personalized treatment strategies.