摘要
本文針對接受兩種不同處理且具共變數的病人，探討如何在調整共變數後建立兩組存活函數中位數差異之區間估計。假設兩處理組內共變數對相對風險的影響一致且與時間無關，則可以分層Cox模式(stratified Cox model)描述病人的風險函數，藉此了解處理間的風險比例。共變數對兩個處理組內的相對風險影響不同，則分別就各處理組資料配適具共變數的Cox模式描述病人的風險狀況。然後，在設置模型之下估計各處理組之存活函數並求其變異數估計，代入Su and Wei(1993) 的估計函數內求得調整共變數後，存活中位數差異之信賴區間。本文除以實例說明上述方法之應用，並且採用模擬方法研究比較本文所提方法與文獻既有方法之優劣。

參考文獻
1.Anderson,P.K.,Borgan,O.,Gill,R.D.,and Keiding,N.,(1993). Statistical models based on counting processes. Springer-Verlag,New York.
2.Anderson,P.K. and Gill,R.D.,(1982). Cox’s regression model for counting processes: A large sample study. The Annals of statistics 10,1100-1120.
3.Basawa,I.V. and Koul,H.L.(1988). Large-sample statistics based on quadeatic dispersion. International Statistical Review 56,199-219.
4.Breslow, N. (1975).Analysis of survival data under the proportional hazards model. International Statistical Review 43,45-58.
5.Brookmeyer, R. and Crowley, J. (1982). A confidence interval for the median survival time. Biometrics 38,29-41.
6.Collett, D.(2003) Modelling survival data in medical research. Chapman and Hall, New York.
7.Doss,H. and Gill,R.D.,(1992). An Elementary Approach to Weak Convergence for Quantile Processes,With Applications to censored Survival Data. Journal of the American Statistical Association 87, 869-877.
8.Efron, B. (1981). Censored data and the bootstrap. Journal of the American Statistical Association 76, 312-319.
9.Emerson, J.D. (1982). Nonparametric confidence intervals for the median in the presence of right censoring. Biometrics 38,17-27.
10.Hardel,W.,(1991). Smoothing Techniques with Implementation in. Springer-Verlag, New York.
11.Kalbfleisch, J.D. and Prentice, R.L.,(1980) The Statistical analysis of failure time data. Wiley, New York.
12.Kaplan, E.L and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457-481.
13.Kim, J. (2001). Confidence Intervals for the Difference of Median Survival Times Using the Stratified Cox Proportional Hazards Model. Biometrical Journal 43,781-790.
14.Klein, J.P. and Moeschberger, M.L. (1997). Survival analysis: Techniques for censored and truncated data. Springer-Verlag, New York.
15.Rebolledo, R. (1980a). Central limit theorems for local martingales. Z.Wahrsh.verw.Geb. 51,269-286.
16.Reid, N. (1981). Estimating the median survival time. Biometrika 68,601-608.
17.Simon, R. and Lee, Y.J. (1982). Nonparametric confidence limits for survival probabilities and median survival time. Cancer Tratment Reports 66,37-42.
18.Slud, E. V., Byar, D.P., and Greem, S.B. (1984). A comparison of reflected verses test-based confidence interval for the median survival time, based on censored data. Biometrics 40,587-600.
19.Su, J.Q. and Wei, L.J. (1993). Nonparametric Estimation for the Difference or Ratio of Median Failure Times. Biometrics 49,603-607.
20.Tsiatis, A.A. (1981).A large sample study of Cox’s regression model. The Annals of Statistics 9,93-108.
21.Wang, J.L. and Hettmansperger, T.P.(1990). Two-sample inference for median survival times based on one-sample procedures for censored survival data. Journal of the American Statistical Association 85,529-536.
22.Wells, M.T. (1994) Nonparametric kernal estimation in counting processes with explanatory variables. Biometrika 81,795-801.
23.Zhang, M.J. and Klein, J.P. (2001).Confidence Bands for the Difference of Two Survival Curves Under Proportional Hazards model. Lifetime Data Analysis 7,243-254.
24.Zucker, D,M.,(1998) Restricted Mean Life With Covariates:Modification and Extension of a Useful Survival Analysis Method. Journal of the American Statistical Association 93,702-709.