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.

Effect of the root parameter on the stability of the Non-stationary <em>D/M/1 </em> queue’s <em>GI/M/1 </em> model with PSFFA applications to the Internet of Things (IoT)

“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [4][5][6]], namely ( ) = + ( + ), for more details see [7,8]. Thus, the required model reads as:…”

“…Notably, (7) is extremely general in nature, since the closed form represention of can be computed for many queues. However, we can numerically or by data of an existing system's fitting curve calculate .…”

<strong></strong>The Fine Thread between Stability and Randomness of the Non-stationary D/M/1 Queue’s GI/M/1 Pointwise of Stationary Fluid Flow Approximation Model with Application Ultra-Low Latency of Autonomous Driving Service

“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [2][3][4][5][6], namely 𝜆(𝑡) = 𝐴 + 𝐵𝑠𝑖𝑛(𝑤𝑡 + 𝐷), for more details see [7][8][9].…”

“…Notably, (7) is extremely general in nature, since the closed form represention of 𝐺 1 can be computed for many queues. However, we can numerically or by data of an existing system's fitting curve calculate 𝐺 1 .…”

<strong></strong>The Fine Thread between Stability and Randomness of the Non-stationary D/M/1 Queue’s GI/M/1 Pointwise of Stationary Fluid Flow Approximation Model with Application Ultra-Low Latency of Autonomous Driving Service

“…We believe that the non-stationary load will exhibit sinusoidal mean behaviour, which will describe the cyclic load pattern over a specified time period (for example, day) in accordance with the prior research on non-stationary analysis of communication networks [2][3][4][5][6], namely 𝜆(𝑡) = 𝐴 + 𝐵𝑠𝑖𝑛(𝑤𝑡 + 𝐷), for more details see [7][8][9].…”