區間設限資料經常出現於週期性追蹤的臨床實驗研究上，真正的失效或發作時間只能被觀察到落於某一區間之中。在這篇論文中，針對比較兩組區間設限數據的樣本，我們提出一個加權的Wilcoxon型秩檢定方法，利用Fay (1999)所提出的數據產生模型，在虛無假設下，我們可推導出檢定統計量的期望值及變異數，透過電腦模擬可知，我們所提出的檢定方法比Mantel (1967)及Peto and Peto (1972)兩個Wilcoxon型檢定方法更具檢定力。最後將此檢定方法應用在愛滋病的研究例子上。

Interval-censored (IC) failure time data are often observed in medical follow-up studies and clinical trials where subjects can only be followed periodically and the failure time can only be known to lie in an interval. In this paper, we propose a weighted Wilcoxon-type rank test for the problem of comparing two IC samples. Under a very general sampling technique developed by Fay (1999), the mean and variance of the test statistic under the null hypothesis can be derived. Through simulation studies, we ‾nd that the performance of the proposed test is better than
that of the two existing Wilcoxon-type rank tests proposed by Mantel (1967) and Peto and Peto (1972). The proposed test is illustrated by means of an example involving patients in AIDS cohort studies.

Abstract i
1 Introduction 1
2 Data treatment 4
2.1 Assumptions and notation 4
2.2 Turnbull's algorithm 4
2.3 IC data generation 5
3 Wilcoxon-type rank tests 13
3.1 Review of the Wilcoxon rank test for exact data 13
3.2 Reviews of the Wilcoxon-type rank test for IC data 16
3.2.1 Mantel's test 16
3.2.1 Peto and Peto's test 20
3.3 Weighted rank test 23
4 Simulation studies 33
4.1 Case of exponential distribution 33
4.2 Case of lognormal distribution 34
4.3 Simulation result 34
5 An application to AIDS cohort study 41
References 42

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