摘 要 在基因微陣列(DNA microarrays)的技術中，可同時得到數以千筆的資料，為了找出具有顯著差異的基因，一般會考慮控制整體誤差率(familywise error rate,FWE) 的多重比較方法(multiple comparison procedures,MCP)。但當基因數或假設檢定個數過多時，其檢定會產生不易拒絕虛無假設的結果，使得結論過於保守。為解決此一問題，Benjamini & Hochberg(1995)建議採用控制錯誤發現率(false discovery rate,FDR)的方法來替代整體誤差率FWE。且Tusher et al.(2001)在DNA微陣列顯著分析(significance analysis of microarrays,SAM)的文章中提出利用排列分佈(permutations)估計錯誤發現率FDR的方法。本篇論文將介紹Tusher et al.(2001)所提出的SAM估計錯誤發現率FDR的方法，且提出一修正SAM方法：SAMM。另外介紹兩種控制顯著水準的統計方法：SAME和SAMT(t檢定)。透過電腦模擬驗證四種方法其錯誤發現率FDR的表現。 / Abstract DNA microarray technology provides tools enable to simultaneously study thousands of genes. A conservative multiple comparison procedure (MCP) controlling the familywise type I error rate (FWE) is considered. However, the conservativeness of a MCP becomes more and more severe as the number of comparisons (genes) increases. Instead of FWE, another error rate, the false discovery rate (FDR), is suggested. Tusher et al.(2001) proposed a statistical procedure, the Significance Analysis of Microarrays (SAM), to analyze a microarray data set. In which, the conclusion is drawn at a specific threshold and the false discovery rate (FDR) of the conclusion is estimated by permutations. In this paper, inspired by the SAM, three other methods are proposed. The performances of these methods are investigated and compared through simulations.

在DNA微陣列基因的實驗中資料包括數千個cDNA 序列，為了要篩選出有差異表現基因，同時針對大量基因個數作假設檢定。若無適當地調整個別檢定問題中的誤差率，則將會膨脹整體的誤差率。在多重假設檢定中為了讓整體誤差率(familywise error rate, FWE)控制在設定水準下，必須調整個別假設檢定之個別型一誤差率CWE的檢定準則，此為多重比較方法(multiple comparison procedures：MCP)。然而當多重比較的個數增加時，控制整體誤差率FWE之傳統的多重比較方法會是過於嚴格的標準，不容易推翻虛無假設，使得檢定的結果太過保守。為了解決此現象，Benjamini and Hochberg(1995) 建議另一種錯誤率：錯誤發現率(false discovery rate：FDR)。錯誤發現率定義為在被拒絕之虛無假設中錯誤拒絕的比例之期望值。而Benjamini and Hochberg(1995)也在文中提出一個得以控制錯誤發現率的多重比較方法，稱為BH方法。本篇論文將詳盡地介紹CWE、FWE和FDR三種誤差率，並提出－修正BH的方法，稱為BH( )。我們將透過電腦模擬驗證出新的修正BH方法之表現比原BH方法有較高的檢定力，且從實例的結果中發現BH( )比原BH方法能檢測出更多的顯著個數。 關鍵字：個別型一誤差率(CWE)；整體誤差率(FWE)；多重比較方法(MCP)； 錯誤發現率(FDR)。 / cDNA microarray technology provides tools to study thousands of genes simultaneously. Since a large number of genes are compared, using a conventional significant test leads to the increase of the type I error rate. To avoid the inflation, the adjustment for multiplicity should be considered and a multiple comparison procedure (MCP) that controls the familywise error rate (FWE) is recommended. However, the conservativeness of a MCP that controls FWE becomes more and more severe as the number of comparisons (genes) increases. Instead of FWE, Benjamini and Hochberg (1995) recommended to control the expected proportion of falsely rejecting hypotheses—the false discovery rate (FDR)—and developed a MCP, which has its FDR under control. In this paper, the error rates CWE, FWE and FDR are fully introduced. A new MCP with FDR controlled is developed and its performance is investigated through intensive simulations. KEY WORDS：Comparison-wise error rate (CWE)；Familywise error rate (FWE)；Multiple comparison procedure (MCP)；False discovery rate (FDR).