臺灣博碩士論文加值系統

現時狀態數據(current status data) 發生在發病時間(failure time) 無法直接被觀測時，其中所能得到的資訊是檢測時間(monitoring time) 及發病時間發生於檢測時間之前或後。關於此類數據可利用 Sun and Kalbfleisch (1993) 提出的檢定法，檢定群組之間發病的存活函數是否相同。若分別在 proportional hazards、additive hazards 和 accelerated life time 三種常見的半參數模型下，以分數檢定法(score test) 檢定之，恰好都 Sun and Kalbfleisch (1993) 提出的檢定法之一權重形式。本篇論文中，我們證明在給定比 Sun and Kalbfleisch (1993) 更寬的條件，這三個檢定統計量在虛無假設下的極限分佈，仍然是常態分佈。最後我們利用統計模擬來呈現此四個檢定統計量在特定模型及有限樣本下的比較結果。

Current status data arise when the failure time of interest is unable to observe. The observation consists only of a monitoring time and knowledge of whether the failure time occurred before or after the monitoring time. For testing the equality of the survival functions of the failure time among different groups, a test statistic provided by Sun and Kalbfleisch (1993) can be applied. Coincidentally, the score test statistics under proportional hazards model, additive hazards model and accelerated life time model, respectively, are the weighted version of the test statistic given by them. In this paper, we show that under the regular condition given by Sun and Kalbfleisch (1993), these three score test statistics have asymptotically normal distribution. A series of simulation studies are presented to evaluate the finite sample performance of these four test statistics (Poisson process, proportional hazards model, additive hazards model, accelerated life time model) under difference models.

List of Tables ii
中文摘要 iii
英文摘要 iv
1 Introduction 1
2 The three semi-parametric models 3
2.1 Proportional hazards model . . . . . . . . . . . . . 4
2.2 Additive hazards model . . . . . . . . . . . . . . . 4
2.3 Accelerated life time model . . . . . . . . . . . . 5
3 Asymptotic result of the test statistics 7
4 Simulation studies 9
5 An example 12
6 Discussion 14
Appendix 15
References 18

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