[Back to Results | New Search]

Student Number 942205009 Author Xin-ru Kao(高欣如) Author's Email Address No Public. Statistics This thesis had been viewed 1951 times. Download 3028 times. Department Graduate Institute of Statistics Year 2008 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title Discussion on Cox Proportional Hazards Assumption and Application of Extended Hazard Model Date of Defense 2009-05-25 Page Count 50 Keyword Cox proportional hazards model Extended hazard model Longitudinal data Proportional hazards assumption Schoenfeld residual Abstract The Cox proportional hazards model has been widely used to describe the relationship between survival information and covariates. The validity to apply the Cox model for data is usually based on checking the proportional hazards assumption. It’s an interesting problem to investigate whether checking this assumption is sufficient as an evidence to fit data with the Cox model. On the other hand, when proportional hazards assumption fails, the Accelerated Failure Time (AFT) model is a popular alternative to the Cox model. However, when data include time-dependent covariates there are no convenient tools to check if AFT is appropriate for the data. An general class model termed “extended hazard model”, which contains the Cox and AFT models as its special case may be helpful to study the above problems. Because under the nested structure, we may test the fit of Cox and AFT models for data. Finally, we demonstrate the new model through a case study of Taiwanese HIV/AIDS cohort data. Table of Content 摘要 i

Abstract ii

誌謝辭 iii

目錄 v

圖目錄 vii

表目錄 viii

第一章緒論 1

1.1 研究背景及動機. . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 本文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

第二章統計方法 10

2.1 線性混合隨機效應模型. . . . . . . . . . . . . . . . . . . . . 11

2.2 Cox 比例風險模型. . . . . . . . . . . . . . . . . . . . . . . 12

2.3 加速失敗時間模型. . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 擴充風險模型. . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Schoenfeld 殘差. . . . . . . . . . . . . . . . . . . . . . . . 16

第三章統計模擬 19

3.1 模擬方法. . . . . . . . . . . . . . . . . . . . . . . . . . . .20

3.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . .23

第四章實例研究 25

4.1 台灣愛滋病病患資料與背景. . . . . . . . . . . . . . . . . . . 26

4.2 實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . . .29

第五章結論與討論 34

參考文獻 36Reference [1] Andersen, P.K. (1982). “Testing Goodness-of-Fit of Cox’s Regression and Life Model.” Biometrics, 38, 67-77.

[2] Breslow, N.E., Edler, L. and Berger, J. (1984). “A two-sample censored data rank test for acceleration.” Biometrics, 40, 1049-1062.

[3] Chen, Y.Q. and Jewell, N.P. (2001). “On a general class of semiparametric hazards regression models.” Biometrika B, 88, 687-702.

[4] Ciampi, A. and Etezadi-Amoli, J. (1985). “A general model for testing the proportional hazards and the accelerated failure time hypothesis in the analysis of censored survival data with covariate.” Communications

in Statistics, 14, 651-667.

[5] Cox, D.R. (1972). “Regression models and life-tables (with Discussion).” Journal of the Royal Statistical Society, Series B 34, 187-220.

[6] Cox, D.R. (1979). “A Note on the Graphical Analysis of Survival Data.” Biometrics, 66, 188-190.

[7] Cox, D.R. and Snell, E.J. (1968). “A General Definition of Residuals.” Journal of the Royal Statistical Society, Ser. B 30, 248-275.

[8] Chen, Y.Q. and Jewell, N.P. (2001). “On a general class of semiparametric hazards regression models.” Biometrika, 88, 687-702.

[9] Egger, M., Hirschel, B., Francioli, P. et al. (1997). “Impact of new antiretroviral combination therapies in HIV infected patients in Switzerland: prospective multicentre study.” Swiss HIV Cohort Study BMJ, 315(7117),

1194-9.

[10] Etezadi-Amoli, J. and Ciampi, A. (1987). “Extended hazard regression for censored survival data with covariates: A spline approximation for the baseline hazard function.” Biometrics, 43, 191-192.

[11] Grambsch, P.M. and Therneau, T.M. (1994). “Proportional hazards tests and diagnostics based on weighted residuals.” Biometrics, 81, 515-526.

[12] Gulick, R.M., Meibohm, A., Havlir, D., et al (2003). “Six-year follow-up of HIV-1-infected adults in a clinical trial of antiretroviral therapy with indinavir, zidovudine, and lamivudine.” AIDS, 17, 2345-2349.

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

[14] Kaufmann, G.R., Perrink, L., Pantaleo, G., et al. (2003). “CD4 Tlymphocyte recovery in individuals with advanced HIV-1 infection receiving potent antiretroviral therapy for 4 years: the Swiss HIV Cohort Study.” Arch. Intern. Med., 163, 2187-2195.

[15] Kay, R. (1977). “Proportional Hazards Regression Models and the Analysis of Censored Survival Data.” Applied Statistics, 26, 227-237.

[16] Laird, N.M. and Ware, J.H. (1982). “Random-effects models for longitudinal data.” Biometrics, 38, 963-974.

[17] Lagakos, S.W. (1981). “The Graphical Evaluation of Explanatory Variables in Proportional Hazards Regression Models.”, Biometrika, 68, 93-98.

[18] Louis, T.A. (1991). “Nonparametric analysis of an accelerated failure time model.” Biometrika, 68, 381-390.

[19] Lucas, C.M., Chaisson, R.E. and Moore, R.D. (1999) “Highly active antiretroviral therapy in a large urban clinic: risk factors for virologic failure and adverse drug reactions.” Ann Intern Med, 131, 81-87.

[20] Miller, R.G. (1981). Survival Analysis. Wiley: New York.

[21] Moreau, T., O’Quigley, J. and Mesbah, M. (1985). “A Global Goodnessof-Fit Statistic for the Proportional Hazards Model.” Applied Statistics, 34, 212-218.

[22] O’Quigley, J. and Pessione, F. (1989). “Score Tests for Homogeneity of Regression Effect in the Proportional Hazards Model.” Biometrics, 45, 135-145.

[23] Palella, F.J., Delaney, K.M., Moorman, A.C., et al. (1998). “Declining morbidity and mortality among patients with advanced human immunod-eficiency virus infection. HIV Outpatient Study Investigators.” N Engl J Med., 338(13), 853-860.

[24] Pawitan, Y. and Self, S. (1993). “Modeling disease marker process in AIDS.” Journal of the American Statistical Association, 88, 719-726.

[25] Schoenfeld, D. (1980). “Chi-Squared Goodness-of-Fit Tests for the Proportional Hazards Regression Models.” Biometrika, 67, 145-153.

[26] Schoenfeld, D.A. (1982). “Partial residuals for the proportional hazards regression model.” Biometrika, 69, 239-241.

[27] Therneau, T.M. and Grambsch, P.M. (2000). Modeling Survival Data: Extending the Cox Model. Springer-Verlag.

[28] Tseng, Y.K., Hsieh, F. and Wang, J.L. (2005). “Joint modeling of accelerated failure time and longitudinal data.” Biometrika, 92, 587-603.

[29] 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.

[30] Tsiatis, A.A. and Davidian, M. (2001). “A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error.” Biometrika, 88, 446-458.

[31] Wang, Y. and Taylor, J.M.G. (2001). “Jointly Modeling Longitudinal and Event Time Data With Application to Acquired Immunodeficiency Syndrome.” J. Am. Statist. Assoc., 96, 895-905.

[32] Wulfsohn, M.S. and Tsiatis, A.A. (1997). “A Joint Model for Survival and Longitudinal Data Measured with Error.” Biometrics, 53, 330-339.

[33] Zeng, D. and Cai, J. (2005). “Asymptotic Results for Maximum Likelihood Estimators in Joint Analysis of Repeated Measurements and Survival Time.” The annals of Statistics, 33(5), 2132-2163.Advisor Yi-kuan Tseng(曾議寬)

Files approve immediately

942205009.pdf Date of Submission 2009-06-25

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.