劉仁沛臺灣大學：農藝學研究所邱詩婷Chiu, Shih-TingShih-TingChiu2007-11-282018-07-112007-11-282018-07-112007http://ntur.lib.ntu.edu.tw//handle/246246/59172傳統的假設檢定法利用檢定兩組樣本差異是否等於零來鑑定基因是否有顯著表現，但卻沒有考慮到具有生物意義的倍數變化量，然而在生物領域中基因表現的倍數變化超過某些定值即認定該基因是有表現的。相較於傳統的假設檢定法，2006年由戴家彥碩士論文提出一個區間假設的雙單尾檢定法，此方法不僅能考慮到生物意義亦能更準確地鑑別出有顯著表現的基因。在此我們將進一步將區間假設的雙單尾檢定法推展到無母數領域，以區間假設為基礎，應用多變量排列作出可以偵測基因表現值最小變化量的非介量檢定方法，探討其決策程序、整體型一錯誤、平均檢定力以及型一誤差。 模擬結果顯示在足夠的陣列重複數之下，區間假設檢定方法相較於其它傳統假設檢定方法，不僅整體與平均型一錯誤較低，檢定力亦比傳統的單尾檢定方法來得好，而非介量的多元排列檢定法能進ㄧ步改善這種區間假設檢定。The traditional hypothesis for identification of differentially expressed genes fails to take the biological meaning fold changes into consideration. However, a gene is differentially expressed if its fold change exceeds a threshold value in biological field. Compared with the traditional hypothesis of equality, the two one-sided tests procedure based on interval hypothesis（Liu, et al, 2007）not only consider the minimal biologically meaningful expression but truly identify the differentially expressed genes. To continue the research, we will apply multivariate permutation test to the interval hypothesis. Based on this proposed method, we conduct a simulation study to investigate its power, overall type I error and average type I error when the normal assumption of expression levels is in doubt. The simulation results indicate that because of lower overall type I error and average type I error and higher average power, the interval hypothesis works better than the traditional hypothesis of equality when there are enough replicates in array. And the multivariate permutation test which is a non-parametric approach could improve the ability of identifying gene expression with interval hypothesis.論文口試委員審定書 I 謝辭 II 摘要 III ABSTRACT IV CONTENTS V LIST OF FIGURES VII LIST OF TABLES VIII CHAPTER 1 INTRODUCTION 1 CHAPTER 2 CURRENT METHODS 3 2.1 THE TRADITIONAL AND THE INTERVAL HYPOTHESIS 3 2.1.1 The Traditional Hypothesis of Equality 3 2.1.2 The Interval Hypothesis 4 2.2 THE CURRENT PROCEDURES WITH THE TRADITIONAL HYPOTHESIS 5 2.2.1 Unpaired Two-sample t-test 5 2.2.2 Unpaired Two-sample t-test with Bonferroni Adjustment 6 2.2.3 The Fixed Fold-change Rule 6 2.2.4 Combination of the Unpaired Two-sample t-test and Fold-changes Rule 7 2.3 THE TWO ONE-SIDED TESTS PROCEDURE BASED ON INTERVAL HYPOTHESIS 7 CHAPTER 3 MULTIVARIATE PERMUTATION METHOD 9 3.1 PERMUTATION TEST 9 3.1.1 Permutation t-test 9 3.1.2 Multivariate Permutation Test 10 3.2 INTERVAL HYPOTHESIS BASED ON MULTIVARIATE PERMUTATION TEST 12 CHAPTER 4 SIMULATION 15 4.1 STATISTICAL MODELS TO GENERATING MICROARRAY EXPERIMENT DATA 15 4.1.1 Statistical Models for Generating Background-subtracted Raw Intensity Data 15 4.1.2 Statistical Models for Normalized Log-transformed Data 17 4.2 THE EMPIRICAL OVERALL AND AVERAGE TYPE I ERROR AND AVERAGE POWER 18 4.3 SIMULATION PROCEDURE 22 4.3.1 Multivariate Permutation Process 23 4.3.2 Parameter Combinations 25 4.4 SIMULATION RESULTS 26 4.4.1 Comparison between Different Size of Arrays 26 4.4.2 Results by Different Methods 27 4.4.3 Result from Different Settings of Multiplicative and Additive Error 28 4.4.4 Compare the Result from Four Different Models 28 CHAPTER 5 EXAMPLE 31 CHAPTER 6 DISCUSSION AND CONCLUSION 38677903 bytesapplication/pdfen-US倍數變化區間假設檢定雙單尾檢定法多元排列檢定法整體型一錯誤平均型一錯誤檢定力Fold changeInterval hypothesisTwo one-sided testsMultivariate permutationPowerOverall and Average Type I errorthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59172/1/ntu-96-R94621204-1.pdf