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研究生:林韋智
研究生(外文):Wei-Chih Lin
論文名稱(外文):The joint model of multivariate longitudinal covariates and AFT model – A case study on Taiwanese AIDS cohort study
指導教授:曾議寬曾議寬引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:56
中文關鍵詞:聯合模型加速失敗時間模型核心平滑函數期望最大值演算法隨機效應模型
外文關鍵詞:Joint modelAFT modelKernel smooth densityEM algorithmRandom effect model
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  • 被引用被引用:0
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  • 下載下載:11
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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.
Contents
Chapter 1 Introduction 1
1.1 The background . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The aim of the study . . . . . . . . . . . . . . . . . . . . 6
Chapter 2 Statistical methods 10
2.1 The multivariate longitudinal model . . . . . . . . . . . 12
2.2 The accelerated failure time model . . . . . . . . . . . . 13
2.3 The joint model . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 The Expectation-Maximization Algorithm . . . . . . . . 17
Chapter 3 Simulation 25
Chapter 4 Data analysis for AIDS 29
4.1 Introduction of AIDS data . . . . . . . . . . . . . . . . . 29
4.2 Linear mixed effect model . . . . . . . . . . . . . . . . . 30
4.3 The joint model of multivariate longitudinal and survival
model . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 5 Discussion 37
APPENDIX 39
Reference 42
List of Figures
1 Figure 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Figure 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 33
List of Tables
1 Table 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2 Table 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Table 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
ii
4 Table 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5 Table 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6 Table 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7 Table 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8 Table 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
9 Table 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Reference
Brown, 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 the
Royal Statistical Society, Series B 34, 187-220.
Hsieh, F., Tseng, Y. K. and Wang, J. L. (2006). Joint Modeling of
Survival and Longitudinal Data: Likelihood Approch Revisited. Bio-
metrics, 62, 1037-1043.
42
Hwang YT, Wang CC, Wang CH, Tseng YK and Chang YJ. (2015).
Joint model of multiple longitudinal measures and a binary outcome
an application to predict orthostatic hypertension for subacute stroke
patients. 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 joint
model to explore the relationship between the survival time of AIDS
patients and related biomarkers.
Lindstrom, M. J. and Bates, D. M. (1988). Newton-Raphsom and
EM algorithm for linear mixed effects models for repeated-measures
data. Journal of the American Statistical Association, 83, 1004-1022.
Prentice, R. L. (1982). Covariate measurement errors and parameter
estimation 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 with
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error. 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 modeling
of 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,
135-150
Weng, X. Y. (2013). An AIDS case study in Taiwan - The relationship
between the survival time of AIDS patients and their CD4 count and
viral load using joint model to explore.
Wulfsohn, M. S. and Tsiatis, A. A. (1997). A joint model for survival
and 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.
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Zeng D. and Cai J. (2005). Asymptotic Results for Maximum Like-
lihood Estimators in Joint Analysis of Repeated Measurements and
Survival Time. The Annals of Statistics, 33, 2132-2163.
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