臺灣博碩士論文加值系統

囊狀性纖維化是一種少見且具有地區性的遺傳疾病, 其中以肺部和消化系統所受的影響最為嚴重, 而在此篇論文主要是在討論肺部的囊狀纖維化。在1994年rhDNase(pulmozyme) 獲FDA 核准上市, 且列為囊狀纖維化患者的治療藥物。其中我們感興趣的是rhDNase 對於囊狀纖維化患者療效和肺活量對此疾病的影響, 本篇研究的資料來自於研究脫氧核醣核酸酶團隊(ThePulmozyme Study Group) , 分析方法主要使用了邊際模型(marginal model): AG model 、PWP model 、WLW model 和脆弱模型(frailty model) 。由邊際模型和脆弱模型可以得到相同的結論, rhDNase能降低囊狀纖維化患者的
復發風險和肺活量增加可以改善囊狀纖維化患者的復發風險。

Cystic fibrosis (CF) is a rare and regional genetic disease mainly developing in lungs and digestive system. In this study, we focused on lung cystic fibrosis. In
1994, rhDNase (pulmozyme) was listed and approved by FDA as a therapeutic drug for patients with cystic fibrosis. We are interested in the effect of rhDNase therapy
and the impact of pulmonary forced expiratory volume (FEV). We applied various main stream statistical methods to analyze this recurrent event data obtained
from pulmozyme study group. These statistical methods include marginal models(AG model,PWP model and WLW model) and frailty model. The results derived from different
methods are consistent which suggest that rhDNase can reduce recurrent hazard for Cystic fibrosis patients and forced expiratory volume increasing could improve reccrrent
hazard for Cystic fibrosis patients.

摘要. . . . . . . . . .i
Abstract . . . . . . . ii
致謝詞. . . . . . . . .iii
目錄. . . . . . . . . .iv
圖目錄. . . . . . . ...vi
表目錄. . . . . . . . .vii
第一章緒論. . . . . . . .1
1.1 囊狀纖維化. . . . . 1
1.2 研究方法文獻回顧. . . 5
1.2.1 邊際模型. . . . . . .6
1.2.2 脆弱模型. . . . . . 7
1.3 研究目標. . . . . . . .9
第二章統計方法. . . . . . 10
2.1 符號定義和基本假設. . 10
2.2 邊際模型(Marginal Model) . . . . 11
2.2.1 AG邊際模型. . . . . . . . . . .15
2.2.2 PWP邊際模型. . . . . . . ......16
2.2.3 WLW邊際模型. . . . . . . . . . 17
2.2.4 三個邊際模型比較. . . . . . . 18
2.3 邊際模型參數估計. . . . . . . . .20
2.3.1 夾擠估計量(Sandwich Variance Estimators) . .....21
2.4 脆弱模型(Frailty Model) . . . . . . . . . . . ....23
2.5 脆弱模型參數估計. . . . . . . . . . .25
2.5.1 懲罰函數(Penalized Likelihood Approach)
–PPL 演算法. . . . . . . . . . . . . . 26
第三章實例分析. . . . . . . . . . . . . 29
3.1 資料說明. . . . . . . . . . . . . . 29
3.2 敘述性資料分析. . . . . . . . . . . 30
3.3 無母數方法分析. . . . . . . . . . . 32
3.3.1 Kaplan-Meier 估計量. . . . . . . .32
3.3.2 無母數假設檢定. . . . . . . . . . 33
3.4 模型估計. . . . . . . . . . . . . . 35
3.4.1 邊際模型(Marginal Model) . . . . .35
3.4.2 脆弱模型( Frailty Model) . . . . 39
第四章結果與結論. . . . . . . . . . . . 43
參考文獻. . . . . . . . . . . . . . . . . . . 45

[1] 林建甫(2008) 。存活分析。台北市: 雙葉書局。
[2] Andersen, P. K. and Gill, R. D. (1982). Cox''sregression model for counting processes: A large sample study. Annals of Statistics, 10,1100-1120.
[3] Cook, R. J. and Lawless, J. F. (2006). The statistical analysis of recurrent events. Springer, New York.
[4] Cox, D. R. (1972). Regression models and life-tables (with discussion).Journal of the Royal Statistical Society, B 34, 187-200.
[5] Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of chronic disease
incidence. Biometrika, 65, 141-151.
[6] Crowder, M. (1989). A multivariate distribution with Weibull connections.Journal of the Royal Statistical Social, B 51, 93-107.
[7] Fuchs, H. J., Borowitz, D. S., Christiansen, D. H., Morris, E. M.,Nash, M. L., Ramsey, B. W., Rosenstein, B. J., Smith, A. L., and Wohl, M. E. (1994) Effect of aerosolized recombinant human DNase on exacerbations of respiratory symptoms and on pulmonary function
in patients with cystic fibrosis. The Pulmozyme Study Goup.
New England Journal Medicine, 331, 637-642.
[8] Guo, G. and Rodriguez, G. (1992). Estimating a multivariate proportional hazards model for clustered data using the em algorithm.with an application to child survival in guatemala. Journal of American
Statistical Association, 87, 969-976.
[9] Hougaard, P.(1986a). Survival models for heterogeneous populations derived frim stable distributions. Biometrics, 73, 671-678.
[10] Hougaard, P. (1986b). A class of multivariate failure time distributions.Biometrics, 73, 387-396.
[11] Huber, P. J. (1967). The behaviour of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 221-233.
[12] Klein, J. P. (1992). Semiparametirc estimation of random effects using the cox model based on the em algorithm. Biometrics, 48,798-806.
[13] Kaplan, E. L. and Meier, P. (1958). Non-parameteric estimation from incomplete observtion. Journal of American Statistical Association,
53, 457-481.
[14] Lin, D. Y. and Wei, L. J. (1989). The robust inference for the cox proportional hazard model. Journal of the American Statistical Association, 84, 1074-1078.
[15] Lin, D. Y. (1994). Cox regression analysis of multivariate failure time data: the marginal approach. Statistics in Medicine, 13, 2233-2247.
[16] Liang, K. Y., Self, S. G., Bandeen-Roche, K. J., and Zeger, S. L.(1995). Some recent developments for regression analysis of multivariate failure time data. Lifetime Data Analysis, 1, 403-415.
[17] MaGilchrist, C. A. and Aisbtt, C. W. (1991). Regression with frailty in survival analysis. Biometrics, 47, 461-466.
[18] Oakes, D. (1992). Frailty models for multiple event times. Survival analysis: state of the art, 371-379.
[19] Prentice, P. L., Williams, B. J., and Peterson, A. V. (1981). On the regression analysis of multivariate failure time data. Biometrika, 68,373-379.
[20] Rubin, D. B. (1976) Inference and Missing Data. Biometrika, 63, 581-592.
[21] Therneau, T. M. and Grambush, P. M.(2000). Modeling survival data: extending the Cox model. Springer, New York.
[22] Vaupel, J. W., Manton, K. G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439-454.
[23] Wei, L. J., Lin, D. Y., and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of American Statistical ssociation, 84, 1065-1073.
[24] Yashin, A. I., Vaupel, J. W., and Iachine, I. A. (1995). Correlated individual frailty: An advantageous approach to survival analysis of bivariate data. Mathematical Population Studies, 5(2), 145-159.