Non‐homogeneous continuous‐time Markov chain with covariates: Applications to ambulatory hypertension monitoring

Abstract

Hypertension significantly increases the risk for many health conditions including heart disease and stroke. Hypertensive patients often have continuous measurements of their blood pressure to better understand how it fluctuates over the day. The continuous‐time Markov chain (CTMC) is commonly used to study repeated measurements with categorical outcomes. However, the standard CTMC may be restrictive, because the rates of transitions between states are assumed to be constant through time, while the transition rates for describing the dynamics of hypertension are likely to be changing over time. In addition, the applications of CTMC rarely account for the effects of other covariates on state transitions. In this article, we considered a non‐homogeneous continuous‐time Markov chain with two states to analyze changes in hypertension while accounting for multiple covariates. The explicit formulas for the transition probability matrix as well as the corresponding likelihood function were derived. In addition, we proposed a maximum likelihood estimation algorithm for estimating the parameters in the time‐dependent rate function. Lastly, the model performance was demonstrated through both a simulation study and application to ambulatory blood pressure data.