Clustering Multiple Sclerosis Medication Sequence Data with Mixture Markov Chain Analysis with covariates using Multiple Simplex Constrained Optimization Routine (MSiCOR)

Multiple sclerosis (MS) is an autoimmune disease of the central nervous system that causes neurodegeneration. While disease-modifying therapies (DMTs) reduce inflammatory disease activity and delay worsening disability in MS, there are significantly varying treatment responses across people with MS (pwMS). pwMS often receive serial monotherapies of DMTs. Here, we propose a novel method to cluster pwMS according to the sequence of DMT prescriptions and associated clinical features (covariates). This is achieved via a mixture Markov chain analysis with covariates, where the sequence of prescribed DMTs for each patient is modeled as a Markov chain. Given the computational challenges to maximize 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 and shown to outperform other related global optimization techniques. In simulation experiments, the proposed method is shown to outperform the Expectation-Maximization (EM) algorithm based method for clustering sequence data without covariates. Based on the analysis, we divided MS patients into 3 clusters: inferon-beta dominated, multi-DMTs, and natalizumab dominated. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters. This method may guide the DMT prescription sequence based on clinical features

An Expository Note on Unit - Gompertz Distribution with Applications

In a recent paper, Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. It is a continuous distribution with bounded support, and hence may be useful for modelling life-time phenomena. We present counter-examples to point out some subtle errors in their work, and subsequently correct them. We also look at some other interesting properties of this new distribution. Further, we also study some important reliability measures and consider some stochastic orderings associated with this new distribution

Utilizing biologic disease-modifying anti-rheumatic treatment sequences to subphenotype rheumatoid arthritis

Abstract Background Many patients with rheumatoid arthritis (RA) require a trial of multiple biologic disease-modifying anti-rheumatic drugs (bDMARDs) to control their disease. With the availability of several bDMARD options, the history of bDMARDs may provide an alternative approach to understanding subphenotypes of RA. The objective of this study was to determine whether there exist distinct clusters of RA patients based on bDMARD prescription history to subphenotype RA. Methods We studied patients from a validated electronic health record-based RA cohort with data from January 1, 2008, through July 31, 2019; all subjects prescribed ≥ 1 bDMARD or targeted synthetic (ts) DMARD were included. To determine whether subjects had similar b/tsDMARD sequences, the sequences were considered as a Markov chain over the state-space of 5 classes of b/tsDMARDs. The maximum likelihood estimator (MLE)-based approach was used to estimate the Markov chain parameters to determine the clusters. The EHR data of study subjects were further linked with a registry containing prospectively collected data for RA disease activity, i.e., clinical disease activity index (CDAI). As a proof of concept, we tested whether the clusters derived from b/tsDMARD sequences correlated with clinical measures, specifically differing trajectories of CDAI. Results We studied 2172 RA subjects, mean age 52 years, RA duration 3.4 years, and 62% seropositive. We observed 550 unique b/tsDMARD sequences and identified 4 main clusters: (1) TNFi persisters (65.7%), (2) TNFi and abatacept therapy (8.0%), (3) on rituximab or multiple b/tsDMARDs (12.7%), (4) prescribed multiple therapies with tocilizumab predominant (13.6%). Compared to the other groups, TNFi persisters had the most favorable trajectory of CDAI over time. Conclusion We observed that RA subjects can be clustered based on the sequence of b/tsDMARD prescriptions over time and that the clusters were correlated with differing trajectories of disease activity over time. This study highlights an alternative approach to consider subphenotyping of patients with RA for studies aimed at understanding treatment response

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

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 3 clusters. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters.</p