A Robust Statistical Method for Detecting Differentially Expressed Genes


DNA microarray technology allows researchers to monitor the expressions of thousands of genes under different conditions, and to measure the levels of thousands of different DNA molecules at a given point in the life of an organism, tissue or cell. A wide variety of different diseases that are characterised by unregulated gene expression, DNA replication, cell division and cell death, can be detected early using microarrays. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The detection of differential gene expression under two different conditions is very important in biological studies, and allows us to identify experimental variables that affect different biological processes. Most of the tests available in the literature are based on the assumption of normal distribution. However, the assumption of normality may not be true in real-life data, particularly with respect to microarray data.

A test is proposed for the identification of differentially expressed genes in replicated microarray experiments conducted under two different conditions. The proposed test does not assume the distribution of the parent population; thus, the proposed test is strictly nonparametric in nature. We calculate the p-value and the asymptotic power function of the proposed test statistic. The proposed test statistic is compared with some of its competitors under normal, gamma and exponential population setup using the Monte Carlo simulation technique. The application of the proposed test statistic is presented using microarray data. The proposed test is robust and highly efficient when populations are non-normal.

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Author would like to thank Prof. PK Sen, University of North Carolina, Chapel Hill; Prof. Z Govindarajulu, University of Kentucky; and the referee for giving their valuable feedback.

This work is not supported by any research grant, and there is no conflict of interest.

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Corresponding author

Correspondence to Dr Sunil Mathur.



Appendix I

The algorithm for calculating the p-value.

Step-1 Generate random sample X from the population 1 under the null hypothesis.

Step-2 Generate random sample Y from the population 2 under the null hypothesis.

Step-3 Calculate sample X.

Step-4 Calculate sample Y.

Step-5 Calculate the test statistic Q.

Step-6 Repeat the process for N = 10,000 times.

Step-7 Find n1, the number of times Q exceeded 0.

Step-8 p-value = n1/N.

Appendix II

Critical value of Q for the right-tail test at 5% level of significance for the sample sizes (m, n) using the re-sampling scheme (table AI).

Table A1

Critical value (CV) of the proposed test statistic Q for the one-tail test at 5% level of significance for the sample sizes (m, n)

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Mathur, S. A Robust Statistical Method for Detecting Differentially Expressed Genes. Appl-Bioinformatics 4, 247–251 (2005). https://doi.org/10.2165/00822942-200504040-00004

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  • Microarray Data
  • Normal Mixture
  • Gene AC002378
  • Monte Carlo Simulation Technique
  • Nominal Significance Level