Open Access Methodology article

Correction of unexpected distributions of P values from analysis of whole genome arrays by rectifying violation of statistical assumptions

Sheila J Barton1*, Sarah R Crozier1, Karen A Lillycrop34, Keith M Godfrey123 and Hazel M Inskip1

Author Affiliations

1 MRC Lifecourse Epidemiology Unit, University of Southampton, Southampton, UK

2 NIHR Southampton Biomedical Research Centre, University of Southampton and University Hospital Southampton NHS Foundation Trust, Southampton, UK

3 Human Development and Health Academic Unit, University of Southampton, Southampton, UK

4 School of Biological Sciences, University of Southampton, Southampton, UK

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BMC Genomics 2013, 14:161  doi:10.1186/1471-2164-14-161

Published: 11 March 2013

Abstract

Background

Statistical analysis of genome-wide microarrays can result in many thousands of identical statistical tests being performed as each probe is tested for an association with a phenotype of interest. If there were no association between any of the probes and the phenotype, the distribution of P values obtained from statistical tests would resemble a Uniform distribution. If a selection of probes were significantly associated with the phenotype we would expect to observe P values for these probes of less than the designated significance level, alpha, resulting in more P values of less than alpha than expected by chance.

Results

In data from a whole genome methylation promoter array we unexpectedly observed P value distributions where there were fewer P values less than alpha than would be expected by chance. Our data suggest that a possible reason for this is a violation of the statistical assumptions required for these tests arising from heteroskedasticity. A simple but statistically sound remedy (a heteroskedasticity–consistent covariance matrix estimator to calculate standard errors of regression coefficients that are robust to heteroskedasticity) rectified this violation and resulted in meaningful P value distributions.

Conclusions

The statistical analysis of ‘omics data requires careful handling, especially in the choice of statistical test. To obtain meaningful results it is essential that the assumptions behind these tests are carefully examined and any violations rectified where possible, or a more appropriate statistical test chosen.

Keywords:
P values; Distributions; Statistical analysis; Statistical assumptions; Whole genome methylation promoter arrays; Epigenome