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Sample size calculation for a regularized t-statistic in microarray experiments

Author

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  • Hirakawa, Akihiro
  • Hamada, Chikuma
  • Yoshimura, Isao

Abstract

The regularized t-statistic, wherein, a regularization term is added to the denominator in order to improve the identifiability of differentially expressed genes, outperforms an ordinary t-statistic. Most methods of sample size calculation in the literature, however, calculate the sample size based on the ordinary one. We derive an approximate formula for the distribution of regularized t-statistics and develop a formula of sample size calculation for regularized t-statistics. The sample size is determined based on sensitivity under certain conditions to maintain a certain false discovery rate using a mixture model. The usefulness of the proposed method is demonstrated by numerical studies that compare the sample sizes of regularized and ordinary t-statistics and simulation studies for examining the robustness of the proposed method based on real data.

Suggested Citation

  • Hirakawa, Akihiro & Hamada, Chikuma & Yoshimura, Isao, 2011. "Sample size calculation for a regularized t-statistic in microarray experiments," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 870-875, July.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:870-875
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    References listed on IDEAS

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    1. Jianhua Hu & Fred A. Wright, 2007. "Assessing Differential Gene Expression with Small Sample Sizes in Oligonucleotide Arrays Using a Mean-Variance Model," Biometrics, The International Biometric Society, vol. 63(1), pages 41-49, March.
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    3. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
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