雙染色點印微陣列A-最適設計之研究 - 使用技術性重複之實驗

Abstract

雙染色點印微陣列是一個可以用來同時檢測成千上萬個基因之表現量的生物技術，其常被用來探討不同領域的科學問題。現今有許多研究致力於發展微陣列實驗資料的資料轉換以及統計分析方法，然而與實驗設計相關的議題似乎較少被討論。在雙染色微陣列實驗中，合適的設計能幫助我們經由實驗得到所感興趣問題的答案，而高效能的設計更能夠確保實驗結果盡可能的精確。因此在雙染色微陣列實驗中，實驗設計亦扮演相當重要的角色。 在本文中，我們主要討論對照-處理實驗(control-test experiments)及比較實驗(comparative experiments)這兩種較常見的雙染色微陣列實驗，而主要關切的實驗設計議題包括：決定哪個mRNA樣本該被染上何種螢光染劑；決定哪兩個mRNA樣本應該被置於同一片晶片上做競爭雜合(competitive hybridization)。在與微陣列實驗設計相關的研究中，大部分被用來建構設計的模式其誤差項均被假設為不相關的(uncorrelated)隨機變數，然而這似乎與某些實際的情況相違背，例如當實驗中若使用所謂的技術性重複(technical replication)時，不同晶片的實驗結果間就可能會產生相關(correlation)。因此我們將Chai and Liao在2005年提出的整體正規化模式(global normalization model)作了些微的修正，使其能夠考慮因技術性重複所產生的相關。並針對對照-處理及比較實驗這兩種不同型態的實驗， 提出兩個演譯法有系統地產生A-最適設計(A-optimal designs)或高效能的設計。由結果發現，我們所得到的設計均對因使用技術性重複所產生的相關具有相當高的穩健性(robustness)。換句話說，在給定不同的相關係數值之下，藉由我們所提供的演譯法產生的設計均為相同的設計。我們將這些設計整理成表格以提供生物學家實際進行雙染色微陣列實驗時參考使用，並對一些設計的性質及具備特殊型態的設計作討論。

The two-color spotted microarray is a highly effective biotechnology to measure the expression levels of many thousands of genes simultaneously, and it has been commonly used to address various scientific questions in different fields. To date, there are a lot of research works devoted to developing methods of data transformation and data analysis for two-color microarray experiments. However, design issues seem to be relatively unexplored. An appropriate design may guarantee that all the scientific questions of interest are answerable. Also, an efficient design ensures the experimental results as precise as possible subject to scientific and practical constraints. Hence, the statistical design also plays an important role in a two-color microarray study. In the present study, we focus on two major types of experiments in two-color microarray studies: control-test experiments and comparative experiments. We consider the design issues that how to determine which mRNA samples are to be labeled with which fluorescent dye; which mRNA samples are to be hybridized together on the same slide. In the current design framework concerning two-color microarray experiments, random errors are usually assumed to be uncorrelated random variables in the statistical models used to construct designs, but it is often more reasonable to acknowledge that there could be some correlation structure among the random errors. Particularly, when the technical replicates are used in the experiments. The global normalization model proposed by Chai and Liao (2005) is slightly modified to incorporate the possible correlation due to technical replication. Two heuristic algorithms are thus developed to generate A-optimal or highly efficient designs based on the proposed model for the two types of experiments. Fortunately, resulting designs generated from these algorithms are shown to be robust against the correlation due to technique replication. The resulting designs tabularized in the appendix can be immediately used by biologists for conducting two-color microarray experiments. Moreover, some statistical properties and designs with special patterns are also reported.