# 臺灣博碩士論文加值系統

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 在這篇文章，我們提議兩個簡單的迭代法去估計Cox比例危險模型的參數：β及基線存活函數，並且應用在麻薩諸塞州健康防治中心研究（MHCPS）（Chappell, 1991）且資料為左截斷和區間刪減資料。我們發現，在估計β及基線存活函數的方法中，Kaplan and Meier迭代法總是比Empirical迭代法的來的較好。而且在檢定兩個族群的存活函數相等與否，Kaplan 和 Meier迭代法總是比Empirical迭代法有較佳的鑑別力。我們也定義了一個距離測度D，而且分別對上述兩種迭代法，來比較經由β和D的表現孰優孰劣。
 In this paper we propose two simple algorithms to estimate parameters β and baseline survival function in Cox proportional hazard model with application to Massachusetts Health Care Panel Study (MHCPS) (Chappell, 1991) data which is a left truncated and interval censored data. We find that, in the estimation of β and baseline survival function, Kaplan and Meier algorithm is uniformly better than the Empirical algorithm. Also, Kaplan and Meier algorithm is uniformly more powerful than the Empirical algorithm in testing whether two groups of survival functions are the same. We also define a distance measure D and compare the performance of these two algorithms through β and D.
 1. Introduction...12. Data in the Massachusetts Health Care Panel Study...33. The estimation methods for baseline survival function and the parameter...53.1. Empirical algorithm for survival function estimation...53.2. Kaplan and Meier algorithm for the survival function estimation...73.3. The estimation of parameter β...94. Simulation...104.1. Simulation method for producing data...104.2. Modification for the survival function estimation...124.3. Simulation result for Weibull (10,75)...134.4. Simulation result for Exponential (0.085)...164.5. Distance Comparison between Survival function estimates of Kaplan and Meier algorithm and Empirical algorithm ...194.6. The comparison of the estimator of β obtained by using Kaplan and Meier algorithm and Empirical algorithm...215. Power Comparison of the estimation of the estimator of β using Kaplan and Meier algorithm and Empirical algorithm...226. Power Comparison between using the estimator of β and the distance D...277. Application to MHCPS...298. Reference...32
 [1] Chappell, R. (1991). Sampling design of multiwave studies with an application to the Massachusetts Health Care Panel Study. Statistics in Medicine 10, 1945-1958.[2] Pan, W. and Chappell, R. (1998a). Estimating survival curves with left-truncated and interval-censored data under monotone hazards. Biometrics 54, 1053-1060.[3] Pan, W. and Chappell, R. (2002). Estimation in the Cox Proportional Hazards Model with Left-Truncated and Interval-Censored Data. Biometrics 58, 64-70.[4] Satten, G. A. (1996). Rank-based inference in the proportional hazards model for interval censored data. Biometrika 83, 355-370.[5] Sinha, D., Tanner, M. A., and Hall, W. J. (1994). Maximization of the marginal likelihood of grouped survival data. Biometrika 81, 53-60.[6] Sun, J. (1995). Empirical estimation of a distribution function with truncated and doubly interval-censored data and its application to AIDS studies. Biometrics 51, 1096-1104.[7] Turnbull, B. W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. J. Amer. Statist. Ass. 69, 169-173.[8] Turnbull, B. W. (1976). The empirical distribution function with arbitrarily group-ed censored and truncated data. Journal of the Royal Statistical Society, Series B 38, 290-295.
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 1 8.廖瑞堂、歐章煜，「崩坍地之調查要點及處理對策探討」，土木水利季刊，第十八卷，第二期，第25~41頁，（1991）。

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