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

Tapati Basak, Kazuhisa Nagashima, Satoshi Kajimoto, Takahisa Kawaguchi, Yasuharu Tabara, Fumihiko Matsuda and Ryo Yamada ()
Additional contact information
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

Statistics in Biosciences, 2020, vol. 12, issue 1, No 4, 63-77

Abstract: 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.

Keywords: Contingency table; Convex polytope; MAX-test; Multiple testing; Type I error; Truncated normal distribution (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12561-020-09271-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stabio:v:12:y:2020:i:1:d:10.1007_s12561-020-09271-6

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/12561

DOI: 10.1007/s12561-020-09271-6

Access Statistics for this article

Statistics in Biosciences is currently edited by Hongyu Zhao and Xihong Lin

More articles in Statistics in Biosciences from Springer, International Chinese Statistical Association
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().