本文針對具右設限的成對存活資料，檢定兩個存活時間邊際分配是否為相同的韋伯(Weibull)分配。Owen et al. (2000)與Caroni(2008)曾在相同的致病傾向參數(frailty parameter)下，針對獨立的服從韋伯分配之成對存活時間，研究兩個存活時間分配是否相等。本文則是針對服從二元韋伯分配的相關成對存活時間，分別根據成對存活時間及其比率建立模式，並且推導檢定相同韋伯邊際分配的概似比檢定方法。本文除採用模擬方法研究所提檢定方法的型I 誤差率及檢定力表現，也以實例說明所提檢定方法的應用。

In this article, we are concerned with testing for the equality of the two marginal weibull distributions for paired survival data that are subjected to random right-censorship. Owen et al. (2000) and Caroni (2008) have discussed the tests when the paired data are independently distributed to weibull distributions given the frailty parameter. This article constructs likelihood ratio tests based on the correlated paired data and the ratio of each pair, respectively, when bivariate weibull distributions are under consideration. The results of a simulation study are presented for the investigation of type I error rate and power of the proposed tests. Finally, the application of the tests is illustrated by using a real data set.

1. Batchelor, J. R. and Hackett, M. (1970). HLA matching in treatment of burned patients with skin allografts. Lancet 2, 581-583.
2. Caroni, C. (2008). Tests for censored paired data. Statistical Methodology.
3. Dabrowska, D.M. (1986). Rank tests for independence for bivariate censored data. The Annals of Statistics 14, 250-264.
4. Frees, E.W. and Valdez E.A. (1998). Understanding relationships using copulas.
North American Actuarial Journal 2, 1-25.
5. Gumbel, E.J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association 55, 698-707.
6. Hanagal, D.D. (2005). Bivariate Weibull regression model based on censored samples. Statistical Papers 47, 137-148.
7. Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika 73, 671-678.
8. Jones, M.P. and Yoo, B. (2005). Linear signed-rank tests for paired survival data subject to a common censoring time. Lifetime Data Analysis 11, 351-365.
9. Jung, S.H. (1999). Rank tests for matched survival data. Lifetime Data Analysis 5, 67-79.
10. Kendall, M.G. (1962). Rank correlation methods. Griffin, London.
11. Lee, L. (1979). Multivariate distributions having Weibull properties, Journal of Multivariate Analysis 9, 267-277.
12. Lu, J.C. and Bhattacharyya, G.K. (1990). Some new constructions of bivariate Weibull models. Annal of the Institute of Statistical Mathematics 42, 543-559.
13. Lu, J. C. and Bhattacharyya, G. K. (1991). Inference procedures for a bivariate exponential model of Gumbel. Statistics and Probability Letters 12, 37-50.
14. Lu, W. (2007). Tests of independence for censored bivariate failure time data. Lifetime Data Analysis 13, 75–90.
15. Mantel, N., and Byar, 0.P. (1974). Evaluation of response-time data involving transient states: An illustration using heart-transplant data. Journal of the American Statistical Association 69, 81-86.
16. Murray, S. (2001). Using weighted Kaplan-Meier statistics in nonparametric comparisons of paired censored survival outcomes. Biometrics 57, 361-368.
17. Nelsen, R. (1999). An introduction to copulas. Springer, New York.
18. O’Brien, P. C. and Fleming, T. R. (1987). A paired Prentice-Wilcoxon test for censored paired data. Biometrics 43, 169-180.
19. Owen, W. J., Sinha D. and Capozoli, M.H. (2000). A paired-data analysis for a lifetime distribution. The American Statistician 54, 252-256.
20. Woolson, R. F. and O’Gorman, T. W. (1992). A comparison of several tests for censored paired data. Statistics in Medicine 11, 193-208.
21. 楊政學. (2006). 成對右設限資料檢定之研究。國立中央大學統計研究所碩士論文。