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Permutation test for incomplete paired data with application to cDNA microarray data

Author

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  • Yu, Donghyeon
  • Lim, Johan
  • Liang, Feng
  • Kim, Kyunga
  • Kim, Byung Soo
  • Jang, Woncheol

Abstract

A paired data set is common in microarray experiments, where the data are often incompletely observed for some pairs due to various technical reasons. In microarray paired data sets, it is of main interest to detect differentially expressed genes, which are usually identified by testing the equality of means of expressions within a pair. While much attention has been paid to testing mean equality with incomplete paired data in previous literature, the existing methods commonly assume the normality of data or rely on the large sample theory. In this paper, we propose a new test based on permutations, which is free from the normality assumption and large sample theory. We consider permutation statistics with linear mixtures of paired and unpaired samples as test statistics, and propose a procedure to find the optimal mixture that minimizes the conditional variances of the test statistics, given the observations. Simulations are conducted for numerical power comparisons between the proposed permutation tests and other existing methods. We apply the proposed method to find differentially expressed genes for a colorectal cancer study.

Suggested Citation

  • Yu, Donghyeon & Lim, Johan & Liang, Feng & Kim, Kyunga & Kim, Byung Soo & Jang, Woncheol, 2012. "Permutation test for incomplete paired data with application to cDNA microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 510-521.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:510-521
    DOI: 10.1016/j.csda.2011.08.012
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    References listed on IDEAS

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    2. Klebanov Lev & Jordan Craig & Yakovlev Andrei, 2006. "A New Type of Stochastic Dependence Revealed in Gene Expression Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-24, March.
    3. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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    Cited by:

    1. Daniel Gaigall, 2020. "Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 437-465, May.

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