(3.236.6.6) 您好!臺灣時間:2021/04/22 19:06
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:盧韋誠
研究生(外文):Wei-Cheng Lu
論文名稱:長期追蹤及存活資料下潛藏因子結合模型
論文名稱(外文):A More Flexible Joint Latent Model for Longitudinal and Failure Time Data
指導教授:江金倉江金倉引用關係
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:29
中文關鍵詞:存活時間長期追蹤資料基底展式潛藏因子變異係數模型
外文關鍵詞:basis expansionfailure timelatent variablelongitudinal measurementsvarying-coefficient
相關次數:
  • 被引用被引用:0
  • 點閱點閱:101
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本論文主要針對時間函數之反應值及存活時間建立一合理且具解釋性的變異係數潛藏因子模型。
藉由更廣泛之非參數化潛藏因子模式,反應值內部相關,反應值與存活時間之相關及觀測個體在此兩隨機變數之非齊一性質被建立。
在長期追蹤及存活資料結構下,我們利用參數函數之基底展式估計值做為參數函數之估計。
在此,我們更進一步推導所提出估計函數之大樣本性質,並借助模擬樣本檢視估計式之有限樣本性質。
最後,我們將討論衍生之有趣研究主題及所提出模式延伸之可行性。
In this thesis, a more flexible and easily explained joint latent varying-coefficient model
is used to model the relationship between time-dependent responses and a failure time.
Here, the dependence mechanism within time-dependent responses, between time-dependent responses
and a failure time, and the heterogeneity among different subjects on
time-dependent responses and failure times are established
through a non-parametric latent process.
Based on the longitudinally measured responses and survival time data, we mainly propose an estimation
procedure for the time-dependent parameter functions. In our estimation approach, the parameter functions are
first approximated via the corresponding basis function expansions.
Trough the estimates of parameters in the basis function expansions,
the estimated parameter functions are then obtained.
Moreover, the asymptotic risks
of the estimated functions are developed in this study. A Monte-Carlo simulation is conducted to examine the
finite sample properties of the proposed estimated functions. Finally, some additional topics of interest
are considered and a possible extension of our proposed model to more complicated joint processes is discussed.
Table of Contents ------------------- ii
List of Tables ---------------------- iii
List of Figures --------------------- iv
Acknowledgements -------------------- v
Abstract ---------------------------- vi
摘要 -------------------------------- vii
1 Introduction -------------------------------------------------- 1
2 Joint Latent Model and Estimation Procedure ------------------- 4
2.1 Model ------------------------------------------------------- 4
2.2 Estimation -------------------------------------------------- 6
3 Asymptotic Properties ----------------------------------------- 9
4 Numerical Study ----------------------------------------------- 18
5 Further Study ------------------------------------------------- 25
Bibliography ---------------------------------------------------- 27
[1] Cai, Z. and Sun, Y. (2003). Local linear estimation for time-dependent coefficients
in Cox’s regression models. Scandinavian Journal of Statistics. 30, 93-111.

[2] Casella, G. and Robert, C. P. (1996). Rao-Blackwellisation of sampling schemes.
Biometrika. 83, 81-94.

[3] Chiang, C. T., Rice, J. A., andWu, C. O. (2000). Smoothing spline estimation for
varying coefficient models with repeatedly measured dependent variable. Journal
of the American Statistical Association. 96, 605-619.

[4] Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood
from incomplete observations. Journal of the Royal Statistical Society. B39,
1-38.

[5] Fan, J. Q. and Zhang, J. T. (2000). Functional linear models for longitudinal
data. Journal of the Royal Statistical Society. B62, 303-322.

[6] Gray, R. J. (1992). Flexible methods for analyzing survival data using splines,
with applications to breast cancer prognosis. Journal of the American Statistical
Association. 87, 942-951.

[7] H¨ammerlin, G. and Hoffmann, K. (1991). Numerical Mathematics. Springer-
Verlag, New York.

[8] Henderson, R., Diggle, P., and Dobson, A. (2000). Joint modeling of longitudinal
measurements and event time data. Biostatistics. 4, 465-480.

[9] Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L. P. (1998). Nonparametric
smoothing estimates of time-varying coefficient models with longitudinal data.
Biometrika. 85, 809-822.

[10] Huang J. Z., Wu C. O., and Zhuo L. (2002). Varying-coefficient models and basis
function approximations for the analysis of repeated measurements. Biometrika.
89, 111-128.

[11] Martinussen, T. and Scheike, T. H. (2002). A flexible additive multiplicative
hazard model. Biometrika. 89, 283-298.

[12] Murphy, S. and Sen, P. (1991). Time-dependent coefficients in a Cox-type regression
model. Stochastic Processes an Their Applications. 39, 153-180.

[13] Tian, L., Zucker, D., and Wei, L. J. (2005). On the Cox model with time-varying
regression coefficients. Journal of the American Statistical Association. 100, 172-
183.

[14] Tsiatis, A. A., DeGruttola, V., and Wulfsohn, M. S. (1995). Modeling the relationship
of survival to longitudinal data measured with error. Applications to
survival and CD4 counts in patients with AIDS. Journal of the American Statistical
Association. 90, 27-37.

[15] Winnett, A. and Sasieni, P. (2003). Iterated residuals and time-varying covariate
effect in Cox regression. Journal of the Royal Statistical Society. B62, 473-488.

[16] Wu, C. O., Chiang, C. T., and Hoover, D. R. (1998). Asymptotic confidence
regions for kernel smoothing of a varying coefficient model with longitudinal
data. Journal of the American Statistical Association. 93, 1388-1402.

[17] Wu, C. F. J. (1983). On the convergence of the EM algorithm. The Annals of
Statistics. 11, 95-103.

[18] Wulfsohn, M. S. and Tsiatis, A. A. (1997). A joint model for survival and longitudinal
data measured with error. Biometrics. 53, 330-339.

[19] Zuuker D. M. and Karr A. F. (1990). Nonparametric survival analysis with timedependent
cvariates: a penalized partial likelihood approach. The Annals of
Statistics. 18, 329-353.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔