# 臺灣博碩士論文加值系統

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 在臨床試驗中，我們常常收集兩種型態的資訊，一種是生物個體的存活資訊，另外一種則是我們感興趣疾病的生物指標資訊。而聯合模型則可以有效地同時處理這兩種型態資料形式的一種統計方法。首先，長期追蹤資料模型裡，在某些疾病中，影響疾病發病風險的生物指標可能不只有一種，因此，我們這裡考慮的是多個生物指標進行模型推倒。而存活模型中，傳統的存活模型上常用的是COX模型，然而，如果其中有部分或全部我們所感興趣疾病的生物指標未服從比例風險的假設時，COX模型則不能使用。因此，我們改採用另外一種存活模型，AFT模型，來解決不服從比例風險原則的問題。在整個統計方法中，我們使用的是蒙地卡羅期望最大值演算法來求得我們要估計的參數，其中，AFT模型中未特定的準線風險函數上，我們使用核心平滑函數來估計，因此我們則可以使用牛頓法來提高我們尋找回歸參數的最大值的效率。在本篇的第三章，我們使用模擬的方式來驗證我們聯立模型的效用。而第四章中，我們採用的是台灣愛滋病的疾病資料來對我們的模型進行實際醫學研究的案例分析。
 In many clinic trials, it become very common to collect survival time and time-dependent covariates simultaneously.In this situation, we are interested not only in the event time but also in the longitudinal covariates.Joint modeling approach has been successfully handle this kind of data.In many the literature, the Cox model is mostly widely used survival model.However, it must follow the proportional hazards assumption, which fails in many medical studies or clinic trials.In particular, when the data contains several longitudinal biomarkers, it is usually the case that proportionality doesn't hold for part of the biomarkers.To overcome this case, we propose a joint modeling approach for the accelerated failure time model with multivariate longitudinal covariates.The estimation is based on a joint likelihood function using Monte Carlo EM algorithm.The unspeified baseline hazard function is approximated by a kernel smooth function so that Newton-Raphson method can be applied to derive the estimates without closed form in the EM steps.Simulation studies are conducted to evaluate the performance of the proposed joint model approach.A case study on Taiwanese AIDS cohort study is used to demonstrate the usefulness of the estimating procedures.
 ContentsChapter 1 Introduction 11.1 The background . . . . . . . . . . . . . . . . . . . . . . . 11.2 The aim of the study . . . . . . . . . . . . . . . . . . . . 6Chapter 2 Statistical methods 102.1 The multivariate longitudinal model . . . . . . . . . . . 122.2 The accelerated failure time model . . . . . . . . . . . . 132.3 The joint model . . . . . . . . . . . . . . . . . . . . . . . 152.4 The Expectation-Maximization Algorithm . . . . . . . . 17Chapter 3 Simulation 25Chapter 4 Data analysis for AIDS 294.1 Introduction of AIDS data . . . . . . . . . . . . . . . . . 294.2 Linear mixed effect model . . . . . . . . . . . . . . . . . 304.3 The joint model of multivariate longitudinal and survivalmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Chapter 5 Discussion 37APPENDIX 39Reference 42List of Figures1 Figure 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 322 Figure 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 33List of Tables1 Table 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Table 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Table 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 31ii4 Table 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Table 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Table 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Table 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 Table 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Table 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
 ReferenceBrown, E. R., Ibrahim, J. G. and Degruttola. (2005). A Flexible B-spline Model for Multivariate Longitudinal Biomarker and Survival.Biometrics, 61, 64-73.Cox, D. R. (1972). Regression models and life table. Journal of theRoyal Statistical Society, Series B 34, 187-220.Hsieh, F., Tseng, Y. K. and Wang, J. L. (2006). Joint Modeling ofSurvival and Longitudinal Data: Likelihood Approch Revisited. Bio-metrics, 62, 1037-1043.42Hwang YT, Wang CC, Wang CH, Tseng YK and Chang YJ. (2015).Joint model of multiple longitudinal measures and a binary outcomean application to predict orthostatic hypertension for subacute strokepatients. Biometrical Journal, 57, 662-675.Laird, N. M. and Ware, J. H. (1982). Random-effect models for longi-tudinal data. Biometrics, 38, 963-974.Lin, J. Y. (2016). An AIDS case study in Taiwan - Using the jointmodel to explore the relationship between the survival time of AIDSpatients and related biomarkers.Lindstrom, M. J. and Bates, D. M. (1988). Newton-Raphsom andEM algorithm for linear mixed effects models for repeated-measuresdata. Journal of the American Statistical Association, 83, 1004-1022.Prentice, R. L. (1982). Covariate measurement errors and parameterestimation in a failure time regression model, Biometrika, 69, 331-342.Tsiatis, A. A., DeGruttola, V., and Wulfsohn, M. S. (1995). Mod-eling the relationship of survival to longitudinal data measured with43error. Applications to survival and CD4 counts in patients with AIDS.Journal of the American Statistical Association, 90, 27-37.Tseng, Y. K., Hsieh F., and Wang. J. L. (2005). Joint modelingof accelerated failure time and longitudinal data. Biometrika, 92, 587-603.Tseng, Y. K., Su, Y. R., Mao, M., and Wang, J. L. (2015). An ex-tended hazard model with longitudinal covariates. Biometrika, 102,135-150Weng, X. Y. (2013). An AIDS case study in Taiwan - The relationshipbetween the survival time of AIDS patients and their CD4 count andviral load using joint model to explore.Wulfsohn, M. S. and Tsiatis, A. A. (1997). A joint model for survivaland longitudinal data measured with error. Biometircs, 53, 330-339.Yang, Y. F. (2012). Joint model of longitudinal and survival data- New approach and numerical improvement.44Zeng D. and Cai J. (2005). Asymptotic Results for Maximum Like-lihood Estimators in Joint Analysis of Repeated Measurements andSurvival Time. The Annals of Statistics, 33, 2132-2163.
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 1 聯合長期追蹤與存活資料分析－肝硬化病患之實例研究 2 聯合模型之參數估計─軟體MATLAB套件JointModel與軟體R套件JM之比較 3 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 4 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 5 以聯合模型探討地中海果蠅繁殖力與老化之關係 6 對於右設限存活模型預測精準度的估計 7 加速失敗與長期追蹤聯合模型分析– 肝硬化之實例研究 8 條件評估法中處理「不知道」回應之研究

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 1 Joint modeling of parametric additive-multiplicative hazards model and longitudinal data 2 台灣愛滋病實例研究－以聯合模型探討愛滋病患存活時間與相關生物指標之關係 3 客家戲曲中的人物塑造 -以榮興客家採茶劇團之《大隘風雲》為例 4 具有光子循環之角度多工白光雷射照明之研究 5 應用高壓蒸氣技術製備抗菌輕質材料及其 特性評估研究 6 基於生物特徵的異常行為識別系統在真實車輛的可應用性研究 7 Model-base Time dependent AUC and Predictive Accuracy 8 Investigating the Growth Mechanism of Bacterial Flagella by Real-time Fluorescent Imaging 9 原子層沉積成長氧化物薄膜應用於氧化鋅奈米柱陣列電容器 10 耐延遲網路下地理路由及最佳化儲存空間管理機制 11 線上行為與學習成效關聯-以中央大學 Maple TA 與 LMS 為例 12 以氫氧化鉀蝕刻製程製作掘入式增強型氮化鋁銦/氮化鎵異質結構場效電晶體 13 超薄層異質通道場效電晶體及單石三維靜態隨機存取記憶體考慮負交疊設計之研究 14 快速退火影響石墨烯晶粒尺寸之研究 15 直接監控石墨烯成長之研究

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