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Digitized material from "'Shin shinfujin' kaisetsu, sōmokuji, sakuin"
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Application of Multistate Model to Functional Recovery in Patients with Stroke
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對於初次中風患者功能的恢復過程很少有研究探討恢復至不同功能狀態所需之時間及預測因子。本論文目的為： (1) 探求初次中風後患者功能隨時間恢復的過程以及預後因子。(2) 提出使用以貝氏法分析含有隨機效應的多階段馬可夫模型以探求初次中風病人的功能恢復過程，量化功能恢復所需之時間與功能轉移機率，並處理個體間異質性以及估計與預測的不確定性，建構以機率為基礎的動態功能恢復模型。(3)探討非均質性馬可夫模型在生物醫學的應用，並發展新的分析方法，包括應用Kologormov differential equation與應用compartmental analysis以處理非均質性的時間連續性馬可夫模型。
材料與方法
(1) 資料來源
(A) 中風後功能恢復過程的資料是來自先前一個多中心隨機對照試驗。其中一家大型醫學中心對於其所收納111位中風病患進行功能狀態的長期追蹤。(B)高血壓資料取自基隆地區的整合式篩檢計畫(KCIS)，該樣本涵蓋18,120名50歲以上第一次於1999年及2002年之間參KCIS者。
(2)分析模式
對於中風後功能長期追蹤的資料，先使用線性混合模型進行時間相依的分析，以瞭解功能隨時間的變化。但該線性混合模型僅能描繪二階段之變化，故進一步使用多階段均質馬可夫模型分析中風後功能進步的動態過程，並以貝氏方法加入隨機效應以處理個體間異質性，並有效解決估計參數與預測時的不確定性。其次再以貝氏法結合Kologormov differential equation分析連續時間非均質馬可夫模型以應用於中風後的功能恢復過程。最後發展以分室分析（compartmental analysis）為基礎，具有高運算效率的連續時間非均質馬可夫模型之分析方法，並應用於大型資料庫以建立高血壓自然史。
結果
(1) 中風後功能恢復的動態過程
首先以線性混合模型分析中風後功能恢復的預後因子，結果與功能恢復的顯著預後因子包括年齡、初始功能狀態、時間、梗塞位置、梗塞大小。其次，應用貝氏法分析含有隨機效應的時間均質性馬可夫迴歸模型，發現在較差功能到中間功能（PFS->MFS）的轉移機率方面，年齡僅有邊界顯著的效應；而在中間功能到良好功能（MFS->GFS）轉移機率70歲以下病患的轉移速率為70歲以上病患的4.5倍。小於1 cm的梗塞在PFS->MFS轉移上相對於大於1cm者有10倍的轉移速率，但梗塞大小在MFS->GFS的轉移則無顯著效果。應用多階段功能恢復模型可以估計各階段之間功能恢復所需要的時間，由PFS進步到GFS所需要的時間（即total recovery time）平均為3.1個月。如果考慮預後因子年齡與梗塞大小，其平均total recovery time的範圍為1到11個月。此外，並且可以將total recovery time分解成PFS->MFS與MFS->GFS兩段，以PFS->MFS而言，其平均recovery time範圍為一周到四個月，而以 MFS->GFS而言，其平均 recovery time範圍為一至七個月，取決於年齡與梗塞大小。我們並依據年齡及梗塞大小分類的4個族群中，不同時間的轉移機率估計。結果亦顯示梗塞大小為PFS->MFS轉移的重要因素，而年齡主要影響MFS->GFS的轉移。
另外，本研究亦發展非均質性馬可夫模型應用於中風的功能恢復，以貝氏法與Kologormov differential equation分析, 由PFS->MFS轉移速率以Weibull分佈呈現，其shape parameter估計為0.45 (95% CI: 0.35-0.61)這表示PFS->MFS轉移速率會顯著的隨著時間而下降，而其它預後因子對於功能轉移的作用與均質性模型所估計的結果接近，年齡主要影響MFS->GFS，而梗塞大小主要影響PFS->MFS的轉移。
(2)貝氏分析與Kologormov differential equation分析具有可逆性轉移之連續時間非均質性馬可夫模型
以兒童戒煙之行為治療為例，轉移速率的Weibull分佈的shape參數r的估計值為0.65 (95% CI：0.41-0.92)，由於r < 1，表示轉移速率會隨著時間而降低。此外，高危險群的學童從抽菸到戒菸的轉移機率較低。
(3)以分室分析為基礎發展高運算效率的非均質性馬可夫模型的分析法，應用於高血壓自然史的分析
結果由正常進展至高血壓前期的發生率之Weibll分佈的shape parameter在每一個年齡性別分層下都顯著的大於1，顯示高血壓的發生率隨年齡增加而增加。此外，我們發現由高血壓前期至第一期高血壓的轉移速率隨年齡層增加而增加，顯示年紀大的個案有較大的危險性發生高血壓。另一方面，由高血壓前期返回正常血壓的轉移速率隨年紀增加而減少。
結論
本研究建立中風後功能恢復的多階段模型，可以定量各預後因子在中風後功能逐步恢復的過程的角色，並且可以估計功能恢復所需要的時間以及預測功能恢復的機率，這些訊息對於中風相關的病生理研究以及臨床決策等都有很大的應用價值。本研究並有下列分析方法的創新發展：(1)將貝氏分析應用於多階段模式，以處理個體間異質性以及估計與預測的不確定性。（2）應用Kologormov differential equation與發展基於compartmental analysis的分析方法，有效處理可逆性的時間連續非均質馬可夫模型，並且有較高的運算效率，這將有助於擴大非均多階段質馬可夫模型在生物醫學的應用。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.目錄
I. 前言 6
II. 文獻回顧 7
II.1. 中風後功能恢復的預後因子 7
II.1.1. 中風後功能狀態的測量 7
II.1.2. 中風之後失能的盛行率 8
II.1.3. 中風後功能恢復的預後因子 8
II.2. 分析長期追蹤資料的方法學 10
II.2.1. 臨床的問題與需求 10
II.2.2. 廣義線性混和模型（generalized linear mixed model, GLMM） 10
II.2.3. 廣義估計方程式 (generalized estimating equation, GEE) 11
II.2.4. 多階段模型應用在長期追蹤資料分析 11
II.2.5. 時間非均質性多階段馬可夫過程(time non-homogeneous multistate model, NHMP) 14
II.3. 缺血性中風後的失能對於長期存活的影響 17
III. 材料與方法 18
III.1. 初次缺血性中風後功能狀態長期追蹤資料分析 18
III.1.1. 資料來源 18
III.1.2. 應用線性混和模型分析初次梗塞中風其功能表現的預後因子 19
III.1.3. 應用貝氏法分析含有隨機效應的時間均質性馬可夫迴歸模型：初次梗塞中風其功能表現的預後因子 19
III.2. 連續時間的非均質馬可夫過程（CONTINUOOUS TIME NHMP）的建構與分析 24
III.2.1. 以貝氏法與FKDE微分方程組分析進行性（progressive）之連續時間NHMP：以中風後功能恢復為例 24
III.2.2. 以貝氏分析與FKDE微分方程分析具有可逆性（reversible）轉移之連續時間NHMP：以兒童戒煙之行為治療為例 28
III.2.3. 以分室模型分析（compartmental analysis）估計具有可逆性轉移之連續時間NHMP：高血壓自然史的應用 31
III.3. 初次中風後的失能對於長期存活的影響 36
IV. 結果 37
IV.1. 初次缺血性中風後功能狀態長期追蹤資料分析 37
IV.1.1. 以線性混合模型分析中風後功能恢復的預後因子 37
IV.1.2. 應用貝氏法分析含有隨機效應的時間均質性馬可夫迴歸模型 37
IV.2. 進行性與可逆性的連續時間NHMP之分析 39
IV.2.1. 以貝氏法與FKDE微分方程組分析進行性之連續時間NHMP：以中風後功能恢復為例 39
IV.2.2. 以貝氏分析與FKDE微分方程組分析具有可逆性轉移之連續時間NHMP：以兒童戒煙之行為治療為例 40
IV.2.3. 以分室分析（compartmental analysis）估計具有可逆性轉移之連續時間NHMP：高血壓自然史的應用 41
IV.3. 初次中風後的失能的減少對於長期存活的影響 42
V. 討論 43
V.1. 以含有隨機效應的多階段馬可夫模式分析中風後功能恢復過程 43
V.1.1. 含有隨機效應的多階段模型在中風功能恢復的應用價值 43
V.1.2. 使用貝式法在多階段分析的優點 44
V.1.3. 預後因子的作用討論 45
V.1.4. 研究限制 45
V.2. 進行性與可逆性的連續時間PARAMETRIC NHMP之建構 45
V.2.1. 以Forward Kolmogorov differential equation（FKDE）於Bayesian架構下分析parametric NHMP 46
V.2.2. 以compartmental analysis分析parametric NHMP 47
V.3. 初次中風後的失能的減少對於長期存活的影響 48
VI. 結論 49
VII. 參考文獻 50
VIII. 圖 67
IX. 表 80
圖目錄
圖 1：中風區域的分類，包括 ANTERIOR CEREBRAL ARTERY TERRITORY, MIDDLE CEREBRAL ARTERY TERRITORY, POSTERIOR CEREBRAL ARTERY TERRITORY, BASAL GANGLION, CORONA RADIATA, THALAMUS, AND BRAIN STEM. 67
圖 2：中風後功能恢復的多階段轉移模型圖說 68
圖 3： 無隨機效應的三階段馬可夫功能轉移模型之ACYCLIC GRAPHIC MODEL 69
圖 4：含有隨機效應的三階段馬可夫功能轉移模型之ACYCLIC GRAPHIC MODEL 70
圖 5：中風後功能狀態隨在各時間點的分佈 71
圖 6：在不同年齡與梗塞大小分組估算由不良功能(PFS)到較佳功能狀態的轉移機率 72
圖 7：在不同年齡與梗塞大小分組估算由中間功能(MFS)到良好功能狀態（GFS）的轉移機率 73
圖 8：在不同年齡與梗塞大小分組估算由不良功能(PFS)到較佳功能狀態的轉移機率分佈。 74
圖 9： 估計的轉移速率，由狀態2 (目前吸煙) 到狀態 3 (戒煙) 75
圖 10：估計的高危險群的轉移機率，由狀態1 (未曾吸煙) 到狀態 2或3 (曾經吸煙) 76
圖 11：估計的低危險群轉移機率，由狀態1 (未曾吸煙) 到狀態 2或3 (曾經吸煙) 77
圖 12： 由正常到各血壓狀態的三年轉移機率 78
圖 13： 依照巴氏量表進步分數分組的存活曲線 79
表目錄
表 1：巴氏量表 80
表 2： 在各時間點的巴氏量表，以平均值（標準差）表示 81
表 3： 以線性混和模型分析影響功能表現的預後因子 82
表 4：以線性混和模型分析影響功能表現的預後因子，不包括基礎的巴氏量表值. 83
表 5： 影響中風後各功能狀態之間轉移速率的單因子分析 84
表 6： 影響中風後功能轉移速率的多變項因子分析 85
表 7： 含有隨機效應的指數迴歸分析結果 86
表 8： 比較固定效應與隨機效應模型的DIC 87
表 9： 依據預後因子分組估計的功能恢復時間（月） 88
表 10： 使用不含隨機效應的非均質馬可夫模型分析影響中風後功能轉移的預後因子 89
表 11：使用含隨機效應的非均質馬可夫模型分析影響中風後功能轉移的預後因子 90
表 12： 比較各種中風功能恢復的多階段模型的DIC與BAYESIAN CHI-SQUARE 統計值 91
表 13：使用數種非均質馬可夫模型分析戒煙行為介入的資料 92
表 14： 比較戒煙研究之數種非均質馬可夫模型的DIC值 93
表 15： 各種轉移的觀察值與預測值之比較 94
表 16： 高血壓狀態的分佈，依照JNC 7 的分類方式，KCIS 1999-2002 95
表 17： 高血壓自然史轉移參數之估計結果 96
表 18： 由PREHYPERTENSION進行到STATE 1 HYPERTENSION的平均停留時間 97
表 19： 各年齡與性別分層的DEVIANCE STATISTICS 98
表 20： 影響缺血性中風後的長期存活的單因子分析 99
表 21：影響缺血性中風後的長期存活的多因子分析 10
In Conversation with Daniel Liang
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Poetry Reading: Sun Yung Shin
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The event is co-sponsored with the St. Thomas English Department.
Sun Yung Shin is the editor of A Good Time for the Truth: Race in Minnesota and the author of two previous poetry/essay collections—Rough, and Savageand Skirt Full of Black (both from Coffee House Press). She is also the co-editor of Outsiders Within: Writing on Transracial Adoption, and the author of bilingual illustrated book for children Cooper’s Lesson. She has received artist grants from the Bush Foundation, the Minnesota State Arts Board, the McKnight Foundation, and the Jerome Foundation. She is teaching or has taught at St. Catherine University, Hamline University, Macalester College, the University of Minnesota, the Perpich Center for Arts Education, Intermedia Arts, Minneapolis public schools, and the Loft Literary Center
Asymptotic Performance Analysis of Time-Frequency-Domain Spread MC DS-CDMA Systems Employing MMSE Multiuser Detection
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Time-Varying Markov Regression Random-Effect Model with Bayesian Estimation Procedures: Application to Dynamics of Functional Recovery in Patients with Stroke
No full textThe rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual's covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear model. We further built up Bayesian directed acyclic graphic model to obtain full joint posterior distribution. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke
Effects of Age and Degree of Hearing Loss on the Agreement and Correlation Between Sound Field Audiometric Thresholds and Tone Burst Auditory Brainstem Response Thresholds in Infants and Young Children
No full textIntervention on Blood Pressure Control in Communities
No full textIn order to investigate the effect of health intervention on the control of adult blood pressure, 590 cases residing in 50 communities in northern Taiwan were selected. Those cases with BP levels >= 140/90 mmHg were randomly assigned to a relaxation, BP-measurement, self-learning, or comparison groups. Intervention activities had been implemented in 1989. It was found that: (1) the dropout rates of the groups were high, but no significant difference among groups was found; (2)three interventions including relaxations, BP-measurement, and self-learning showed significant reductions in systolic BP; (3) some of the subjects in the self-learning group significantly changed their BP from ab-normal to normal. Overall, the introduction of educational strategies for blood pressure control in communities was ascertained
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