A Simulation Study for Evaluation in Estimation of Fold Change from Gene Expression Data in Microarray Experiments

科學家可以利用高密度寡聚核苷酸晶片一次檢測成千上萬基因，是本世紀最受矚目的基因研究工具之一。Affymetrix高密度寡聚核苷酸晶片則是其中一種被廣泛使用的生物晶片產品。學者探測基因有無表現的方式是藉由觀察不同濃度的晶片下的基因相對表現量(fold change)，亦求晶片之間基因表現值的倍數關係。通常計算相對表現量的方法會將不同濃度晶片的基因表現量做對數轉換(底數為2)再進行相減；換言之，相對表現量先決條件是預設呈一對數常態分布並用最大概似估計法(MLE)估計。然而相對表現量在對數常態分布時應用最小變異不偏估計法(MVUE)較 MLE 具有不偏性和最小變異。為了觀測 MLE 和 MVUE 在估計相對表現量的優劣性，我們考慮不同重複晶片數、探針數和參數組合下執行一個生物晶片模擬研究。而產生基因表現量的模式是目前常用來分析Affymetrix高密度寡聚核苷酸晶片的表現量模型，有Robust multi-array average (RMA)和Based expression index (MBEI)中提出的PM/MM difference, PM-only和SUM模型。在模擬結果中發現 MLE 較 MVUE 具有不偏性，而 MVUE 較 MLE 具有較小變異。這樣的結果也間接說明由 RMA 和 MBEI 模型中產生出來的基因表現量並非呈一對數常態分布。High density oligonucleotide arrays allow scientists to monitor expression levels of thousands of genes simultaneously. Currently Affymetrix high-density oligonucleotide array is one of the most frequently employed array products. Scientists use the expression data of genes from microarray experiments to estimate relative change in expression levels between two conditions. Fold change, defined as the ratio of mean expression level of a gene under one condition to that of the same gene under another condition. Current approach first is to take logarithmic transformation (based on 2) of the original expression data. Next the difference of the arithmetic means on the log-scale between the two conditions is computed. The current approach implicitly assumes that the expression levels follow the log-normal distribution and is the maximum likelihood estimate (MLE) of the fold change. However, MLE is a biased estimator of the fold change and minimum variance estimator (MVUE) of the fold change exists under the log-normal distribution. To investigate the bias and variability of the two estimators, a simulation study was conducted under of various combinations of the number of assays, variability, and number of probe cells. In simulation study, the data were generated by the four methods proposed for the expression levels by Affymetrix high-density oligonucleotide array. They are robust multi-array average (RMA) and PM/MM difference, PM-only and SUM model of based expression index (MBEI). Simulation results show that the bias of MLE is smaller than that of MVUE and the mean square error of MLE is greater than the mean square error of MVUE. The simulation findings are not in agreement of the theoretical results. This suggests that the data generated by RMA, and MBEI do not follow a log-normal distribution.Contents Chapter 1 Introduction…………..…………………………….…………1 Chapter 2 Affymetrix high-density oligonucleotide array…….....………5 2.1 Model Based Expression Index (MBEI)……….....……….…........6 2.1.1 PM/MM Model…….….......……………………………….6 2.1.2 PM-only Model…...……...………………………………...7 2.1.3 SUM Model…….……….....…......……………………..…8 2.2 Robust Multi-Array Average (RMA)…….…..…………......…….9 2.3 Hess’s Model……………………….…….…..……………10 2.4 Fold Change……………....…..….………………..……….12 Chapter 3 Estimation of Fold Change……………………..…………...13 3.1 Maximum Likelihood Estimator (MLE)…………………………13 3.2 Minimum Variance Unbiased Estimator (MVUE)………………...14 Chapter 4 Simulation Studies………………….….....…..…………..…16 4.1 Simulated Data for Normal……..………………………………16 4.2 Simulated Data for RMA…………….…………………………17 4.3 Simulated Data for MBEI…………….…………………..…….18 4.3.1 PM/MM.…………..……………………………………..18 4.3.2 PM Only………………...……………………………….18 4.3.3 SUM............………………...…………………………..19 4.4 Procedures……..……………..………………………………20 4.5 Results….…………………………….……………………..22 4.5.1 The Descriptive Statistics…………………………..……...24 4.5.2 Test for normal……………...……...……………..……...27 4.6 An example………………………..……………….………...27 Chapter 5 Summary and Discussion……………..…...………...………..29 References………………….………..…………..……………………....31 Appendix A………………...…………………….………………………33 Appendix B: SAS Program…..…………….….....………....……………81 Appendix C: Real Data………………..........……….….......……………8