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  • 學位論文

多元縱向變數與邏輯斯之聯合模型-腦中風病患之姿態性低血壓實例研究

Joint model of a binary response variable and multiple longitudinal variables - an application to stroke patients with orthostatic hypotension

指導教授 : 黃怡婷
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摘要


腦血管突然阻塞或破裂,引起神經功能障礙,且持續24小時以上仍未恢復,稱為腦中風。在病情穩定之後,就可進行復健計畫,復健情形會直接影響日後殘障的情況,所以復健對於中風病患是極為重要的,但若在復健時引發姿態性低血壓,常會使病患感到不適,進而影響治療的時間,不僅增加痛苦,也增加醫療的成本。 臨床上常藉由重複觀測血壓值來決定病患是否有姿態性低血壓,但若將此重複觀測血壓值放入邏輯斯歸模型是不適當的。Tsiatis 和 Wulfsohn (1997) 提出聯合模型,可建立存活時間和單一重複觀測變數之間的關聯,蔡昊澐 (2007) 修改並提出了結合隨機效應模型與邏輯斯迴歸模型的聯合模型,利用收縮壓判斷有姿態性低血壓的機率,但除了收縮壓外,還有其他隨時間變動之縱向變數會與姿態性低血壓有關,且縱向變數之間會有某種程度的相關,所以不行直接使用隨機效應與邏輯斯迴歸之聯合模型。 Lin 等人 (2002) 提出多元縱向變數與存活時間之聯合模型,本論文將模型延伸至多元縱向變數與邏輯斯迴歸模型之模型,考慮連續時間變數之間可能的相關性,參數的估計方法是利用最大化縱向變數及事件因子之聯合概似函數,並用 EM 演算法處理隱藏變數估計問題,並以ROC曲線來評估模型的預測能力,最後將模型應用到臨床實務資料上。

並列摘要


Orthostatic hypotension (OH) is one kind of hypotension. Major characteristics of OH include dizziness and falls. A stroke patient with OH may fall when he or she performs the physical recovery. This may result in severe burden of medical costs. It is of important to verified whether a stroke patient has OH. To identify OH clinically, sequences of measurements such as systolic and diastolic pressures are needed and observed repeatedly. Owing to biological variations and measurement errors, the observed measures can not be directly used. Furthermore, although a logistic regression can be used to predict a binary outcome, the parameter estimation may be problematic if covariates are highly correlated. Tsai (2008) extended the two-stage model proposed by Tsiatis, DeGruttola, and Wulfsohn (1995) and the joint model proposed by Tsiatis and Wulfsohn (1997) for estimating the survival based on one repeated measure to predict a binary outcome based on one repeated measure. However, for OH, more than one repeated measures are observed. Adapting the method by Lin, McCulloch and Mayne (2002), this thesis extends the joint model by Tsai (2008) to predict a binary outcome using many repeated measures. Monte Carlo simulations are performed to evaluate the feasibility of the proposed method. The model is then implemented in a real example.

參考文獻


蔡昊澐 (2008),邏輯斯與長期資料之聯合模型-腦中風病患之姿態性低血壓實例研究, 國立台北大學統研所碩士論文
Fitzmaurice, G. M., Laird, N. M., and Ware, J. H. (2004), Applied longitudinal analysis, ASA.
Lagarias, J. C., Reeds, J. A., Wright, M. H., and Wright, P. E. (1999), "Convergence properties of the nelder-mead simplex method in low dimensions", SIAM Journal on Optimization, 9(1), 112-147.
Lin, H., McCulloch, C. E., and Mayne, S. T. (2002), "Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables", Statistics in Medicine, 21(16), 2369-2382.
Magnus, J. R. and Neudecker, H. (1999), Matrix differential calculus with applications in statistics and econometrics, John Wiley, Chichester.

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