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A Geometry-Based Multiple Testing Correction for Contingency Tables by Truncated Normal Distribution

Author

Listed:
  • Tapati Basak

    (Kyoto University)

  • Kazuhisa Nagashima

    (Kyoto University)

  • Satoshi Kajimoto

    (Kyoto University)

  • Takahisa Kawaguchi

    (Kyoto University)

  • Yasuharu Tabara

    (Kyoto University)

  • Fumihiko Matsuda

    (Kyoto University)

  • Ryo Yamada

    (Kyoto University)

Abstract

Inference procedure is a critical step of experimental researches to draw scientific conclusions especially in multiple testing. The false positive rate increases unless the unadjusted marginal p-values are corrected. Therefore, a multiple testing correction is necessary to adjust the p-values based on the number of tests to control type I error. We propose a multiple testing correction of MAX-test for a contingency table, where multiple χ2-tests are applied based on a truncated normal distribution (TND) estimation method by Botev. The table and tests are defined geometrically by contour hyperplanes in the degrees of freedom (df) dimensional space. A linear algebraic method called spherization transforms the shape of the space, defined by the contour hyperplanes of the distribution of tables sharing the same marginal counts. So, the stochastic distributions of these tables are transformed into a standard multivariate normal distribution in df-dimensional space. Geometrically, the p-value is defined by a convex polytope consisted of truncating hyperplanes of test’s contour lines in df-dimensional space. The TND approach of the Botev method was used to estimate the corrected p. Finally, the features of our approach were extracted using a real GWAS data.

Suggested Citation

  • Tapati Basak & Kazuhisa Nagashima & Satoshi Kajimoto & Takahisa Kawaguchi & Yasuharu Tabara & Fumihiko Matsuda & Ryo Yamada, 2020. "A Geometry-Based Multiple Testing Correction for Contingency Tables by Truncated Normal Distribution," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(1), pages 63-77, April.
  • Handle: RePEc:spr:stabio:v:12:y:2020:i:1:d:10.1007_s12561-020-09271-6
    DOI: 10.1007/s12561-020-09271-6
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    References listed on IDEAS

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    1. David Lamparter & Daniel Marbach & Rico Rueedi & Zoltán Kutalik & Sven Bergmann, 2016. "Fast and Rigorous Computation of Gene and Pathway Scores from SNP-Based Summary Statistics," PLOS Computational Biology, Public Library of Science, vol. 12(1), pages 1-20, January.
    2. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
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