Emmett B. Kendall: Beyond time-homogeneity for continuous-time multistate Markov models

Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over time, as is often the case in longitudinal medical data, for example. Assuming that a continuous-time Markov process is time-homogeneous, a closed-form likelihood function can be derived from the Kolmogorov forward equations -- a system of differential equations with a well-known matrix-exponential solution. Unfortunately, however, the forward equations do not admit an analytical solution for continuous-time, time-inhomogeneous Markov processes, and so researchers and practitioners often make the simplifying assumption that the process is piecewise time-homogeneous. In this talk, I provide intuition and illustrations of the potential biases for parameter estimation that may ensue in the more realistic scenario that the piecewise-homogeneous assumption is violated, and I advocate for a solution for likelihood computation in a truly time-inhomogeneous fashion. Particular focus is afforded to the context of multistate Markov models that allow for state label misclassifications, which applies more broadly to hidden Markov models (HMMs). Additionally, I will explore the utility of these types of regime switching models in applications such as medicine and sociology, as well as provide ideas for future research.