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研究生：	林育如 Lin, Yu-Ju
論文名稱：	利用階梯函數變換以穩定微陣列資料之變異數轉換 A step function approach in stabilizing variance for microarray data
指導教授：	詹世煌 Chan, Shin-Huang
學位類別：	碩士 Master
系所名稱：	管理學院 - 統計學系 Department of Statistics
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	44
中文關鍵詞：	微陣列、無母數變異數穩定、階梯函數
外文關鍵詞：	microarray, nonparametric variance stabilization, step function
相關次數：	點閱：58 下載：1
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微陣列資料中基因的變異數通常會不一致，而與基因的平均數呈現某種函數關係。此種變異數的不穩定使得許多假設變異數為一致的統計方法不適於應用。針對微陣列資料，Durbin et al. (2002) 和 Inoue et al. (2004) 對單一顏色的基因表現值資料提出基因表現模型並推導出變異數與平均數的函數關係，進而求得使變異數穩定的變數變換。Rocke 和 Durbin (2001, 2004) 則針對兩種顏色的微陣列資料提出基因表現值的模型並發展出有母數變異數穩定轉換法。鑒於有母數變換不具穩健性，Chung (2006) 不透過任何基因表現值的模型，而從實際資料的變異數對平均數的散佈圖中以lowess法找出兩者的關係，再以指數函數在小區間上從事變數轉換，惟Chung 的方法在資料轉換後出現不合理的群聚現象。
在本研究中，我們探討對兩種顏色微陣列表現比之對數值的變異數穩定問題。首先以無母數lowess法得到估計之變異數函數，之後利用階梯函數的概念，估計區域性之變異數與平均數之間的函數關係，再以變異數穩定轉換的方式來轉換微陣列資料。結果發現本方法不僅改善了Chung 的無母數變異數穩定轉換法上的不連續現象，且在統計模擬或實例分析上，本方法明顯的比 Chung 的無母數法或有母數變異數穩定轉換有更好的成效。

For microarray data, the variances of genes are not constant, but function of mean expression level. As a result, it can not be analyzed by traditional statistical methods, which assume that the variance of noise is constant. Durbin et al. (2002) and Inoue et al. (2004) separately established the one-color gene expression models and derived the variance-stabilizing transformation functions based on the model they assumed. Rocke and Durbin (2001, 2004) considered two-color gene expression model and developed parametric variance-stabilizing transformation method. All of them took the parametric approach to stabilize the variance. Chung (2006), concerned about the robustness of parametric transformation approach, recommended a nonparametric variance-stabilizing transformation method. Chung (2006) investigated the scatter plot of variance versus mean and applied lowess method to estimate the variance function. He used exponential function to approximate the variance function in a small region, but the results are weird and unreasonable.
In this thesis, we transform the microarray data with a nonparametric approach. We estimate the relationship between variance and mean of gene expression by lowess regression, then locally take step function to approximate the lowess curve. We find that the nonparametric step function transformation method is able to solve the problem of intermittent pattern from Chung’s approach. Simulation study and real data analysis show that the performance of the suggested method is better than the parametric variance-stabilizing transformation method and Chung’s nonparametric approach in stabilizing variance.

Contents
CHAPTER 1 INTRODUCTION	1
CHAPTER 2 LITERATURE REVIEW	3
2.1 VARIANCE-STABILIZING TRANSFORMATION FOR ONE COLOR ARRAY	3
2.2 VARIANCE-STABILIZING TRANSFORMATION FOR TWO-COLOR ARRAY	6
2.3 THE SHORTCOMING OF MODEL APPROACH	8
CHAPTER 3 VARIANCE-STABILIZING TRANSFORMATION	9
3.1 NONPARAMETRIC TRANSFORMATION	9
3.2 NEW NONPARAMETRIC TRANSFORMATION - STEP FUNCTION	10
3.3 SIMPLE FUNCTION APPROACH	11
3.4 PERFORMANCE COMPARISONS	13
CHAPTER 4 SIMULATION STUDY	16
4.1 SIMULATION SETTING	16
4.2 SIMULATION RESULTS	17
CHAPTER 5 REAL EXAMPLES	22
5.1 SELF-HYBRIDIZATION	22
5.1.1 NCKU data	22
5.1.2 Data analysis	23
5.2 HYBRIDIZATION WITH CELL LINE TSGH	28
5.2.1 Asia data	28
5.2.2 Data analysis	28
CHAPTER 6 CONCLUSIONS	34
REFERENCE	35
APPENDIX	36

Table
TABLE 4 - 1 CV COMPARISONS FOR DIFFERENT TRANSFORMATION METHODS: N = 1,  	19
TABLE 4 - 2 THE CV COMPARISONS FOR DIFFERENT TRANSFORMATION METHODS: N = 500, REPLICATES = 3,  	20
TABLE 4 – 3 THE CV COMPARISONS FOR DIFFERENT TRANSFORMATION METHODS: N = 500, REPLICATES = 10,  	21

TABLE 5 - 1 CV VALUES FOR DIFFERENT TRANSFORMATION METHODS	27
TABLE 5 - 2 CV VALUES FOR DIFFERENT TRANSFORMATION METHODS	33

Figure
FIGURE 3 - 1 SCATTER PLOT OF MEAN AND VARIANCE WITH SUPERIMPOSED LOWESS CURVE FOR ORIGINAL DATA. THE CV IS 2.6591.	14
FIGURE 3 - 2 SCATTER PLOT OF MEAN AND VARIANCE WITH SUPERIMPOSED LOWESS CURVE FOR TRANSFORMED DATA (USING STEP FUNCTION). THE CV IS 1.9361.	15

FIGURE 4 - 1 SCATTER PLOTS OF MEAN VS. VARIANCE WITH LOWESS CURVES SUPERIMPOSED. ORIGINAL SIMULATED DATA HAVING A VARIANCE FUNCTION   AND VARIANCE-STABILIZING TRANSFORMED DATA.	18

FIGURE 5 - 1 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: WITHOUT TRANSFORMATION, F = 1/3	24
FIGURE 5 - 2 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: PARAMETRIC (EXPONENTIAL) TRANSFORMATION METHOD, F = 1/3	24
FIGURE 5 - 3 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: PARAMETRIC (QUADRATIC) TRANSFORMATION METHOD, F = 1/3	25
FIGURE 5 - 4 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC TRANSFORMATION METHOD, F = 1/3	25
FIGURE 5 - 5 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC STEP FUNCTION WITH MOVING AVERAGE, F = 1/3	26
FIGURE 5 - 6 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC STEP FUNCTION WITH SIMPLE FUNCTION, F = 1/3	26
FIGURE 5 - 7 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: THE GENERALIZED-LOG TRANSFORMATION, F = 1/3	27
FIGURE 5 - 8 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: WITHOUT TRANSFORMATION, F = 1/11.	29
FIGURE 5 - 9 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: PARAMETRIC (EXPONENTIAL) TRANSFORMATION METHOD, F = 1/11.	30
FIGURE 5 – 10 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: PARAMETRIC (QUADRATIC) TRANSFORMATION METHOD, F = 1/11.	30
FIGURE 5 – 11 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC TRANSFORMATION METHOD, F = 1/11.	31
FIGURE 5 – 12 SCATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC STEP FUNCTION WITH MOVING AVERAGE, F = 1/11.	31
FIGURE 5 – 13 SATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: NONPARAMETRIC STEP FUNCTION WITH SIMPLE FUNCTION, F = 1/11.	32
FIGURE 5 - 14 SATTER PLOT OF VARIANCE VS. MEAN WITH LOWESS CURVE SUPERIMPOSED: THE GENERALIZED-LOG TRANSFORMATION, F = 1/11.	32

Reference

Durbin, B. P., Hardin, J. S. Hawkins, D. M. and Rocke, D. M. (2002). A variance-stabilizing transformation for gene-expression microarray data. Bioinformatics, 18, 105-110.

Durbin, B. P. and Rocke, D. M. (2004). Variance-stabilizing transformations for two-color microarrays. Bioinformatics, 20, 660-667.

Inoue, M., Nishimura, S. I., Hori, G., Nakahara, H., Saito, M., Yoshihara, Y. and Amar, S. I. (2004). Improved parameter estimation for variance-stabilizing transformation of gene-expression microarray data. Journal of Bioinformatics and Computational Biology, 2, 669-679.

Rocke, D. M. and Durbin B. P. (2001). A model for measurement error for gene expression arrays. Journal of Computational Biology, 8, 557-569.

Chung, Xiang-Yu (2006). A nonparametric variance-stabilizing transformation method in cDNA microarray. National Cheng Kung University.

校內：2008-07-25公開
校外：2008-07-25公開

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