Department of Biostatistics and Data Science, University of Texas Health Science Center at Houston, Houston, Texas, USA.
Stat Med. 2023 May 30;42(12):1965-1980. doi: 10.1002/sim.9707. Epub 2023 Mar 10.
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.
高血压显著增加了许多健康状况的风险，包括心脏病和中风。高血压患者通常需要持续测量血压，以更好地了解血压在一天中的波动情况。连续时间马尔可夫链（CTMC）常用于研究具有分类结果的重复测量。然而，标准 CTMC 可能具有限制性，因为假设状态之间的转移率在整个时间内是恒定的，而描述高血压动态的转移率可能随时间变化。此外，CTMC 的应用很少考虑其他协变量对状态转移的影响。在本文中，我们考虑了一个具有两个状态的非齐次连续时间马尔可夫链，以分析高血压的变化，同时考虑了多个协变量。推导出了转移概率矩阵的显式公式和相应的似然函数。此外，我们提出了一种最大似然估计算法，用于估计时变率函数中的参数。最后，通过模拟研究和应用于动态血压数据来演示模型性能。
