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Bioinformatics Advance Access originally published online on August 16, 2005
Bioinformatics 2005 21(20):3865-3872; doi:10.1093/bioinformatics/bti626
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© The Author 2005. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions{at}oxfordjournals.org

Bias in the estimation of false discovery rate in microarray studies

Yudi Pawitan 1,*, Karuturi R. Krishna Murthy 2, Stefan Michiels 3 and Alexander Ploner 1

1Department of Medical Epidemiology and Biostatistics, Karolinska Institutet 17177 Stockholm, Sweden
2Genome Institute of Singapore Singapore
3Unit of Biostatistics and Epidemiology, Institute Gustave Roussy Villejuif, France

*To whom correspondence should be adderessed.

Motivation: The false discovery rate (FDR) provides a key statistical assessment for microarray studies. Its value depends on the proportion {pi}0 of non-differentially expressed (non-DE) genes. In most microarray studies, many genes have small effects not easily separable from non-DE genes. As a result, current methods often overestimate {pi}0 and FDR, leading to unnecessary loss of power in the overall analysis.

Methods: For the common two-sample comparison we derive a natural mixture model of the test statistic and an explicit bias formula in the standard estimation of {pi}0. We suggest an improved estimation of {pi}0 based on the mixture model and describe a practical likelihood-based procedure for this purpose.

Results: The analysis shows that a large bias occurs when {pi}0 is far from 1 and when the non-centrality parameters of the distribution of the test statistic are near zero. The theoretical result also explains substantial discrepancies between non-parametric and model-based estimates of {pi}0. Simulation studies indicate mixture-model estimates are less biased than standard estimates. The method is applied to breast cancer and lymphoma data examples.

Availability: An R-package OCplus containing functions to compute {pi}0 based on the mixture model, the resulting FDR and other operating characteristics of microarray data, is freely available at http://www.meb.ki.se/~yudpaw

Contact: yudi.pawitan{at}meb.ki.se and alexander.ploner{at}meb.ki.se

Received on June 8, 2005; revised on July 11, 2005; accepted on August 10, 2005

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