SMART-MC: Characterizing the Dynamics of Multiple Sclerosis Therapy Transitions Using a Covariate-Based Markov Model

Treatment switching is a common occurrence in the management of Multiple Sclerosis (MS), where patients transition across various disease-modifying therapies (DMTs) due to heterogeneous treatment responses, differences in disease progression, patient characteristics, and therapy-associated adverse effects. To investigate how patient-level covariates influence the likelihood of treatment transitions among DMTs, we adopt a Markovian framework, <i>Sparse Matrix Estimation with Covariate-Based Transitions in Markov Chain Modeling</i> (SMART-MC), in which the transition probabilities are modeled as functions of these covariates. Modeling real-world treatment transitions under this framework presents several challenges, including ensuring parameter identifiability and handling sparse transitions without overfitting. To address identifiability, we constrain each transition-specific covariate coefficient vectors to have a fixed L2 norm. Furthermore, our method automatically estimates transition probabilities for sparsely observed transitions as constants and enforces zero transition probabilities for transitions that are empirically unobserved. This approach mitigates the need for additional model complexity to handle sparsity while maintaining interpretability and efficiency. To optimize the multi-modal likelihood function, we develop a scalable, parallelized global optimization routine, which is validated through benchmark comparisons and supported by key theoretical properties. Our analysis uncovers meaningful patterns in DMT transitions, revealing variations across MS patient subgroups defined by age, race, and other clinical factors.