在右設限資料下，進行K組母體中位數存活時間相等性的檢定時，Brookmeyer和Crowley (1982b) 提出的檢定統計量，需要K組母體分布之形狀相同或變異數相同，才能推導其在虛無假設成立的漸近抽樣分布。實際上，當K組母體中位數存活時間相同時，其母體分布的變異數未必全然相同，所以Rahbar et al. (2012) 提出之檢定統計量可克服此限制。然而，Rahbar et al. (2012) 的方法需使用自助法估計各組樣本中位數存活時間的變異數。當樣本數大時，以自助法估計之，可能會花費較多時間。因此，Tsai et al. (2014) 根據中位數存活時間的信賴區間長度，估計樣本中位數存活時間之變異數。賴 (2014) 則依據不同的方式推導中位數存活時間之信賴區間，以估計樣本中位數存活時間之變異數。因為Rahbar et al. (2012) 提出的檢定統計量，型I誤判機率會稍偏高，所以本論文沿用Rahbar et al. (2012) 的檢定統計量，再以Tsai et al. (2014) 及賴 (2014) 估計樣本中位數存活時間變異數的方法取代自助法。最後提出調整的檢定統計量，期望能藉此維持型I誤判機率。本論文以模擬來驗證調整統計量的準確性，模擬結果顯示調整統計量的型I誤判機率較Rahbar et al. (2012) 的方法接近名目型I誤判機率。

In clinical trials, researchers usually need to compare the treatment effects of several therapies, the results can be drawn by the K-sample median test. The asymptotic distribution of the test statistic proposed by Brookmeyer and Crowley was derived when the shapes of K populations are the same. To overcome this limitation, Rahbar et al. suggested a nonparametric test statistic which employed the Bootstrap method to estimate the asymptotic variance of the sample median. To provide an explicit formula for the asymptotic variance, Tsai et al. proposed a variance estimator based on the confidence interval for median. Lai further estimated the length of confidence interval for median by another . Because the type I error rates of the test statistic proposed by Rahbar et al. are slightly higher than the nominal level, their test is extended by replacing the bootstrapped variance with the length-based estimator. Simulation studies are conducted to evaluate the type I error rates and powers of the proposed tests. Generally, the proposed test statistics are recommended for the K-sample median test with the right-censored data.

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