Clustering Sequence Data with Mixture Markov Chains with Covariates Using Multiple Simplex Constrained Optimization Routine (MSiCOR)
提出一种基于模式搜索的全局优化方法MSiCOR，用于最大化混合马尔可夫模型的似然，在模拟和真实多发性硬化患者治疗序列数据中优于EM算法，并引入协变量实现更精准的聚类。
Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However, the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization (EM) algorithm remains one of the most popular ways to estimate the MMM parameters, however, convergence of EM algorithm is not always guaranteed. Given the computational challenges in maximizing the mixture likelihood on the constrained parameter space, we develop a pattern search-based global optimization technique which can optimize any objective function on a collection of simplexes, which is eventually used to maximize MMM likelihood. This is shown to outperform other related global optimization techniques. In simulation experiments, the proposed method is shown to outperform the expectation-maximization (EM) algorithm in the context of MMM estimation performance. The proposed method is applied to cluster Multiple sclerosis (MS) patients based on their treatment sequences of disease-modifying therapies (DMTs). We also propose a novel method to cluster people with MS based on DMT prescriptions and associated clinical features (covariates) using MMM with covariates. Based on the analysis, we divided MS patients into three clusters. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters. Supplementary materials for this article are available online.