IMPROVED ESTIMATION OF COVARIANCE MATRIX IN HOTELLING’S T2 FOR MICROARRAY DATA

Suryaefiza Karjanto,Norazan Mohamed Ramli,Nor Azura Md Ghani

doi:10.22159/ijpps.2016v8s2.15215

Suryaefiza Karjanto, Norazan Mohamed Ramli + Show 1 more

Open Access

https://doi.org/10.22159/ijpps.2016v8s2.15215

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Abstract

The relationship between genes in gene set analysis in microarray data is analyzed using Hotelling’s T2 but the test cannot be applied when the number of samples is larger than the number of variables which is uncommon in the microarray. Thus, in this study, we proposed shrinkage approaches to estimating the covariance matrix in Hotelling’s T2 particularly to cater high dimensionality problem in microarray data. Three shrinkage covariance methods were proposed in this study and are referred as Shrink A, Shrink B and Shrink C. The analysis of the three proposed shrinkage methods was compared with the Regularized Covariance Matrix Approach and Kong’s Principal Component Analysis. The performances of the proposed methods were assessed using several cases of simulated data sets. In many cases, the Shrink A method performed the best, followed by the Shrink C and RCMAT methods. In contrast, both the Shrink B and KPCA methods showed relatively poor results. The study contributes to an establishment of modified multivariate approach to differential gene expression analysis and expected to be applied in other areas with similar data characteristics.

Highlights

A single microarray slide may contain thousands of spots and each spots signifying a single gene and all of them representing the entire set of genes of an organism [1]
For 0.5 separations, about 40 percent probability of Shrink B p-values being smaller 3.16 times than the corresponding Regularized Covariance Matrix Approach Testing (RCMAT) p-values and being smaller 3.16 times than the corresponding Kong’s Principal Component Analysis (KPCA) p-values are shown in fig. 3 and fig. 4 respectively
1.0 corresponding RCMAT p-values and KPCA p-values for a separation of one along the minor axis as depicted in fig. 11 and fig. 12 respectively

Summary

Introduction

A single microarray slide may contain thousands of spots and each spots signifying a single gene and all of them representing the entire set of genes of an organism [1]. The widespread of microarray technology was largely due to its ability to give the quick results, relatively easy to use and precisely perform simultaneous analysis of thousands of genes in a massively parallel manner to researchers in one experiment, providing valuable knowledge on gene interaction and function [2]. Wide applications of this technology have been implemented in various fields such as: Gene expression profiling. Gene expression profiling is the measurement of the expression (activity) of thousands of genes to create an overall picture of cellular function. The information obtained from microarray gene expression profiling will probably improve our basic understanding about certain diseases or how specific drugs work in cells [3]. Microarray technology provides a tremendous platform for the study of the effect of toxins on the cells and they are passing on to the offspring [4]

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