對於區間刪減數據的研究中，Sun 在1996，2001，2004年提出以 log-rank 為基礎而延伸的檢定，來判斷多個樣本的母群體是否來自同樣的分佈。Chang 則在2004年驗證這三個檢定統計量在乘以校正因子之後，都是接近自由度(p-1)的卡方分佈，而這些校正因子是經由重複模擬所得到。在這篇論文中，我們用不同的方式處理這個問題，也就是提供拔靴法於這些檢定統計量，來估計一筆給定區間刪減數據的校正因子。模擬的結果顯示除了1996年的統計量以外，拔靴法的效果都不錯。而經由卡方適合度檢定，我們發現 Sun 在1996年所提出的統計量，即便乘以校正因子之後，仍然不是卡方分佈，亦即其與任何卡方分佈都有顯著的差異。

Comparison of two or more failure time distributions based on interval-censored data is tested by extension of log-rank test proposed by Sun (1996, 2001, 2004). Furthermore, Chang (2004) verified that the proposed test statistics are approximately chi-cquare with degrees of freedom p-1 after constants factor adjustment which can be obtained from simulations. In this paper we approach in a different way to estimate the adjustment factor of a given interval-censored data by applying the bootstrap technique to the test statistics. Simulation results indicate that the bootstrap technique performs well on those test statistics except the one proposed in 1996. By using chi-square goodness of fit test, we found that Sun's test in 1996 is significantly far from any chi-square.

1 Introduction
2 Turnbull's algorithm
3 Review of three log-rank type tests
3.1 Estimate covariance matrix by Fisher information matrix under logistic model
3.2 Apply resampling technique to estimate covariance matrix
3.3 Adjust the numbers of failures and risks and estimate covariance matrix with multiple imputation
4 Introduction of bootstrap
5 Simulation study
5.1 Simulation procedure
5.2 Simulation results of c*U1
5.3 Simulation results of c*U2
5.4 Simulation results of c*U3
5.5 Chi-square goodness of fit test
6 Conclusion
References

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