Mathur Sunil, Dolo Samuel
Department of Mathematics, University of Mississippi, MS, USA.
Stat Methods Med Res. 2008 Aug;17(4):405-19. doi: 10.1177/0962280206078643. Epub 2007 Aug 14.
DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions. The detection of differential gene expression under two different conditions is very important in microarray studies. Microarray experiments are multi-step procedures and each step is a potential source of variance. This makes the measurement of variability difficult because approach based on gene-by-gene estimation of variance will have few degrees of freedom. It is highly possible that the assumption of equal variance for all the expression levels may not hold. Also, the assumption of normality of gene expressions may not hold. Thus it is essential to have a statistical procedure which is not based on the normality assumption and also it can detect genes with differential variance efficiently. The detection of differential gene expression variance will allow us to identify experimental variables that affect different biological processes and accuracy of DNA microarray measurements.In this article, a new nonparametric test for scale is developed based on the arctangent of the ratio of two expression levels. Most of the tests available in literature require the assumption of normal distribution, which makes them inapplicable in many situations, and it is also hard to verify the suitability of the normal distribution assumption for the given data set. The proposed test does not require the assumption of the distribution for the underlying population and hence makes it more practical and widely applicable. The asymptotic relative efficiency is calculated under different distributions, which show that the proposed test is very powerful when the assumption of normality breaks down. Monte Carlo simulation studies are performed to compare the power of the proposed test with some of the existing procedures. It is found that the proposed test is more powerful than commonly used tests under almost all the distributions considered in the study. A microarray data is used to illustrate the working of the proposed test. Results indicate that the proposed test is very powerful in detecting the smallest change in differential expression variance with high degree of confidence than some of its competitors.
DNA微阵列技术使研究人员能够监测数千个基因在不同条件下的表达情况。在微阵列研究中，检测两种不同条件下的差异基因表达非常重要。微阵列实验是多步骤的过程，每个步骤都是潜在的变异来源。这使得变异性的测量变得困难，因为基于逐个基因估计方差的方法自由度很少。所有表达水平具有等方差的假设很可能不成立。此外，基因表达呈正态分布的假设也可能不成立。因此，必须有一个不基于正态性假设的统计程序，并且它能够有效地检测具有差异方差的基因。差异基因表达方差的检测将使我们能够识别影响不同生物过程的实验变量以及DNA微阵列测量的准确性。在本文中，基于两个表达水平之比的反正切开发了一种新的非参数尺度检验。文献中现有的大多数检验都需要正态分布假设，这使得它们在许多情况下不适用，而且也很难验证给定数据集是否适合正态分布假设。所提出的检验不需要对基础总体的分布进行假设，因此使其更具实用性和广泛适用性。在不同分布下计算了渐近相对效率，结果表明当正态性假设不成立时，所提出的检验非常有效。进行了蒙特卡罗模拟研究，以比较所提出的检验与一些现有程序的功效。结果发现，在所研究的几乎所有分布下，所提出的检验比常用检验更有效。使用一个微阵列数据来说明所提出检验的工作原理。结果表明，与一些竞争对手相比，所提出的检验能够非常有效地以高置信度检测差异表达方差的最小变化。
