微陣列資料中，基因表現值的變異數與平均數呈現某種函數關係為眾所皆知的事實。對此種情形，學者建議透過變異數轉換穩定變異數以提高估計的有效性與檢定力。Chan 和 Lin (2007) 針對兩種顏色的微陣列資料提出無母數簡單函數轉換法以穩定變異數。然而，大多數的轉換法多為有母數轉換形式，且很少或未涉及多時期的 time-course 微陣列資料。
本論文探討多時期微陣列資料之變異數穩定轉換。我們推廣文獻上已有之Started Log (sLog)，Log-Linear Hybrid (Hyb)，Generalized Logarithm Transformation (glog) 和Spread-versus-level plot transformation (SVL) 之變異數轉換至多時期微陣列資料；同時提出以無母數簡單函數轉換法來處理多時期微陣列資料變異數不等的問題。由模擬結果和實際資料的分析，本論文所提出的無母數簡單函數轉換法有好的表現，並且在績效上可以和其他變異數穩定轉換法相提並論。

It is well known that, for microarray data, the variance of gene expression intensity is a function of its mean expression value. To improve the estimation efficiency and detection power, researchers try to stabilize the variance through variable transformation. However, most of the transformation is made parametrically, and none or very few focus on stabilizing the variance for multiple time-course microarray data. In this study, we utilize the nonparametric simple function transformation proposed by Chan and Lin (2007) to stabilize the variance of gene expression in a two-color array. We also extend it to stabilize the variance for time-course microarray data. The existing parametrical methods, such as Started Log (sLog), Log-Linear Hybrid (Hyb), Generalized Logarithm Transformation (glog) , and nonparametric Spread-versus-level plot transformation (SVL), are also extended to stabilize the variance for time-course microarray data. Simulation and real data results show that the performance of the proposed simple function method is comparable to other transformation methods.

Archer, K. J. et al. (2004) Graphical technique for identifying a monotonic variance stabilizing transformation for absolute gene intensity signals. BMC Bioinformatics,
5,60.
Chan, S. H. and Lin, Y. R. (2007) A Step function approach in stabilizing variance for microarray data. Master Thesis National Cheng Kung University.
Motakis, G. P. et al. (2006) Variance stabilization and normalization for one-color microarray data using a data-driven multiscale approach. Bioinformatics, 22, 2457-2553.
Rocke, D. M. and Durbin, B. P. (2001) A model for measurement error for gene expression arrays. Journal of Computational Biology, 8, 557-569.
Rocke, D. M. and Durbin, B. P. (2003) Approximate variance-stabilizing transformations for gene-expression microarray data. Bioinformatics, 19, 966-972.
Tukey, J. W. (1977) Exploratory Data Analysis. Addison-Wesley, Reading, MA.