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Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis

Author

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  • Hwang J.T. Gene

    (Cornell University)

  • Liu Peng

    (Iowa State University)

Abstract

As a consequence of the "large p small n" characteristic for microarray data, hypothesis tests based on individual genes often result in low average power. There are several proposed tests that attempt to improve power. Among these, the FS test that was developed using the concept of James-Stein shrinkage to estimate the variances showed a striking average power improvement. In this paper, we establish a framework in which we model the key parameters with a distribution to find an optimal Bayes test which we call the MAP test (where MAP stands for Maximum Average Power). Under this framework, the FS test can be derived as an empirical Bayes test approximating the MAP test corresponding to modeling the variances. By modeling both the means and the variances with a distribution, a MAP statistic is derived which is optimal in terms of average power but is computationally intensive. An empirical Bayes test called the FSS test is derived as an approximation to the MAP tests and can be computed instantaneously. The FSS statistic shrinks both the means and the variances and has numerically identical average power to the MAP tests. Much numerical evidence is presented in this paper that shows that the proposed test performs uniformly better in average power than the other tests in the literature, including the classical F test, the FS test, the test of Wright and Simon, the moderated t-test, SAM, Efron's t test, the B-statistic and Storey's optimal discovery procedure. A theory is established which indicates that the proposed test is optimal in power when controlling the false discovery rate (FDR).

Suggested Citation

  • Hwang J.T. Gene & Liu Peng, 2010. "Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-35, October.
    • Handle: RePEc:bpj:sagmbi:v:9:y:2010:i:1:n:36
    DOI: 10.2202/1544-6115.1587
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    References listed on IDEAS

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    1. Herbert Pang & Tiejun Tong & Hongyu Zhao, 2009. "Shrinkage-based Diagonal Discriminant Analysis and Its Applications in High-Dimensional Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1021-1029, December.
    2. 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.
    3. John D. Storey, 2007. "The optimal discovery procedure: a new approach to simultaneous significance testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 347-368, June.
    4. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    5. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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    Cited by:

    1. Ji Tieming & Liu Peng & Nettleton Dan, 2012. "Borrowing Information Across Genes and Experiments for Improved Error Variance Estimation in Microarray Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-29, May.
    2. Bar Haim Y. & Booth James G. & Wells Martin T., 2012. "A Mixture-Model Approach for Parallel Testing for Unequal Variances," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(1), pages 1-21, January.
    3. Xiao Min & Chen Ting & Huang Kunpeng & Ming Ruixing, 2020. "Optimal Estimation for Power of Variance with Application to Gene-Set Testing," Journal of Systems Science and Information, De Gruyter, vol. 8(6), pages 549-564, December.
    4. Wang, Cheng & Tong, Tiejun & Cao, Longbing & Miao, Baiqi, 2014. "Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 222-232.
    5. Qiu Jing & Qi Yue & Cui Xiangqin, 2014. "Applying shrinkage variance estimators to the TOST test in high dimensional settings," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(3), pages 323-341, June.

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