應用新的無母數檢定法檢測結腸癌病患之存活時間

在過去評估臨床的實驗中，不管是檢定二樣本的成對t檢定或是多樣本的變異數分析，其基本假設為：樣本的分布均需為常態和變異數均需為同質（homoscedasticity）。而採用無母數統計檢定的明顯優勢在於：在檢定之前，無需耗費太多的精力檢查分組資料是否來自常態，然而，當分組的特性具有異質性（heteroscedasticity）（變異數不等），在現存的無母數檢定中，並無法針對此情況而直接做檢定（Tomarken & Serlin, 1986;Oshima & Algina, 1992; Vargha & Delaney, 1998）。我們將提出克服上述問題之新檢定；其原理在於應用快速傅利葉轉換的參數具有漸近常態（asymptotic normal）的特性，最後此新檢定將被用模擬的方法（Rubinstein, 1981），來比較不同分組（階段、位置等）結腸癌病患的存活月。相較於Kruskal-Wallis檢定，對於異質性樣本的實驗，新檢定法確實擁有較準確的檢定力。最終，我們將舉北部某醫學中心的大腸直腸肛門外科的真實資料來檢定病患腫瘤分組的存活差異。

關鍵字

結腸癌； Kruskal-Wallis檢定；傅利葉參數；異質性

並列摘要

For data analysis in clinical trials, for examples, the evaluation of preclinical studies and clinical dose-finding trials, the statistical methods are always needed. Analysis of variance (ANOVA) remains a popular statistical technique. To use ANOVA appropriately, researchers must assume that the distributions of the measure for each sample are normal and have equal variance (homoscedasticity). If these conditions are not meet, non-parametric methods are often used to test the equality of treatments. However, non-parametric methods can be unreliable for the heteroscedasticity of variances across the different sample (Tomarken & Serlin, 1986; Oshima & Algina, 1992; Vargha & Delaney, 1998). In this paper, we propose a new test; the empirical distribution of Fourier coefficients is utilized and tests whether the medians of survival years are consistent with tumor location or stage. We study the asymptotic reference distribution of the test statistic analytically. Utilizing the simulation technique (Rubinstein, 1981), we show that the proposed test is a significant improvement over the original Kruskal-Wallis test and is consistently more powerful, regardless of unequal variance. Finally, we apply our test to actual data to compare the effect of tumor location or stage used on colon cancer resuscitation.