Application of Multistate Model to Functional Recovery in Patients with Stroke
Date Issued
2007
Date
2007
Author(s)
Pan, Shin-Liang
DOI
zh-TW
Abstract
Purpose
Few attempts have been made to model the time needed for functional recovery after stroke and the related prognostic factors for functional outcomes. This study aimed to (1) investigate the dynamic process and predictors of function recovery after first-time stroke. (2) propose a multistate Markov regression model with random effects under the Bayesian framework to model the step-by-step process of functional recovery, to quantify the dwelling time and probabilities of functional transitions, and to tackle the individual heterogeneity and uncertainty in estimation and prediction. (3) develop novel analytic methods for non-homogeneous Markov process, including the application of Kologromov differential equations and compartmental analysis. These approaches are flexible and computationally efficient for modeling non-homogeneous Markov process in biomedical research.
Material and methods
(1)Data source
The stroke data used in this study were derived from an already completed randomized controlled trial for stroke. A total of 111 patients with first stroke were recruited between October 1992 and April 1995. A series of Barthel index of each patient was assessed at six time points after stroke. The hypertension data used in this study were part of the Keelung Community-based Integrated Screening (KCIS) program. This sample represented 18120 subjects aged greater than 50 years at the time of first participating KCIS between 1999 and 2002.
(2) Analytic methods
For modeling the dynamic process of functional recovery after stroke, the generalized linear mixed model was first used for time-dependent analyses. A three state homogeneous Markov regression model with random effects was then developed to estimate transition parameters and mean time to functional recovery, and to predict the probability of functional recovery by using Bayesian approach with Gibbs sampling technique. We further applied Kolmogorov differential equation and compartmental analysis to modeling continuous time non-homogeneous Markov process.
Results
(1)Dynamic process of functional recovery after stroke.
The mean total recovery time to good functional state (GFS) was 3.1 months for patients with poor functional state (PFS) at baseline and 1.3 months for patients with moderate functional state (MFS) at baseline. Age predominantly affected the probabilities of MFS-to-GFS transitions, younger patients had 4.5-fold faster transition; but age had only borderline effects on PFS-to-MFS transitions. In contrast, infarct size exerted substantial effects on PFS-to-MFS transitions; small-size infarct was correlated with a 10-fold higher transition rate, whereas only a borderline effect on MFS-to-GFS transitions was found. The baseline functional state significantly affected the MFS-to-GFS transitions. The results of non-homogeneous Markov regression analysis showed that the estimated shape parameter of the Weibull distribution for PFS-to-MFS transition was 0.45 (95% CI: 0.35-0.61). This suggests that the PFS-to-MFS transition rate decreased with time.
(2)Non-homogeneous Markov model with Kologromov differential equation solution
The estimated shape parameter of the Weibull distribution for the transition rate was 0.65 (95% CI: 0.41-0.92). The shape parameter less than one suggests that the transition rate decreases with time and reflects the non-homogeneous property.
(3)Non-homogeneous Markov process for modeling natural history of hypertension using compartmental analysis
The estimated shape parameter in each age subgroup was significantly higher than one, indicating that the transition rate from normal to prehypertension increases with time. The transition rate from prehypertension to stage 1 hypertension showed a tendency to increase with age. In contrast, the regression rate from prehypertension to normal tended to decline with age.
Conclusions
We developed a multi-state Markov random effects model under the Bayesian framework, and used it to analyze the dynamic process of functional recovery after stroke. The mean time to functional recovery to different functional states can be estimated and the effect of clinical predictors on step-by-step functional transitions can be precisely quantified. In addition, two novel analytic methods for non-homogeneous Markov process on the basis of Kologromov differential equations and compartmental analysis were proposed. The application of the methodology developed in the present study can be extended to other application fields in biomedical sciences.
Subjects
馬可夫鍊
隨機過程
貝式理論
蒙地卡羅方法
日常生活活動
腦中風
危險因子
Markov Chains
Stochastic Processes
Bayes Theorem
Monte Carlo Method
Activities of Daily Living
Cerebrovascular Accident
Risk factors
Type
thesis
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