Modeling Liquid Association

Yen Yi Ho, Giovanni Parmigiani, Thomas Louis, Leslie Cope

Research output: Contribution to journalArticle

Abstract

In 2002, Ker-Chau Li introduced the liquid association measure to characterize three-way interactions between genes, and developed a computationally efficient estimator that can be used to screen gene expression microarray data for such interactions. That study, and others published since then, have established the biological validity of the method, and clearly demonstrated it to be a useful tool for the analysis of genomic data sets. To build on this work, we have sought a parametric family of multivariate distributions with the flexibility to model the full range of trivariate dependencies encompassed by liquid association. Such a model could situate liquid association within a formal inferential theory. In this article, we describe such a family of distributions, a trivariate, conditional normal model having Gaussian univariate marginal distributions, and in fact including the trivariate Gaussian family as a special case. Perhaps the most interesting feature of the distribution is that the parameterization naturally parses the three-way dependence structure into a number of distinct, interpretable components. One of these components is very closely aligned to liquid association, and is developed as a measure we call modified liquid association. We develop two methods for estimating this quantity, and propose statistical tests for the existence of this type of dependence. We evaluate these inferential methods in a set of simulations and illustrate their use in the analysis of publicly available experimental data.

Original languageEnglish (US)
Pages (from-to)133-141
Number of pages9
JournalBiometrics
Volume67
Issue number1
DOIs
StatePublished - Mar 2011

Fingerprint

Trivariate
Association reactions
Liquid
liquids
Liquids
Modeling
Association Measure
Efficient Estimator
Statistical tests
Dependence Structure
Gene Expression
Multivariate Distribution
Gaussian Model
Microarrays
Statistical test
Marginal Distribution
Gene Expression Data
Parameterization
Microarray Data
Interaction

Keywords

  • Gene expression
  • Generalized estimating equations
  • Higher-order interaction
  • Liquid association
  • Non-Gaussian multivariate distribution

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Medicine(all)

Cite this

Modeling Liquid Association. / Ho, Yen Yi; Parmigiani, Giovanni; Louis, Thomas; Cope, Leslie.

In: Biometrics, Vol. 67, No. 1, 03.2011, p. 133-141.

Research output: Contribution to journalArticle

Ho, Yen Yi ; Parmigiani, Giovanni ; Louis, Thomas ; Cope, Leslie. / Modeling Liquid Association. In: Biometrics. 2011 ; Vol. 67, No. 1. pp. 133-141.
@article{4ce0fb6e2d6147889affa3e130d524a4,
title = "Modeling Liquid Association",
abstract = "In 2002, Ker-Chau Li introduced the liquid association measure to characterize three-way interactions between genes, and developed a computationally efficient estimator that can be used to screen gene expression microarray data for such interactions. That study, and others published since then, have established the biological validity of the method, and clearly demonstrated it to be a useful tool for the analysis of genomic data sets. To build on this work, we have sought a parametric family of multivariate distributions with the flexibility to model the full range of trivariate dependencies encompassed by liquid association. Such a model could situate liquid association within a formal inferential theory. In this article, we describe such a family of distributions, a trivariate, conditional normal model having Gaussian univariate marginal distributions, and in fact including the trivariate Gaussian family as a special case. Perhaps the most interesting feature of the distribution is that the parameterization naturally parses the three-way dependence structure into a number of distinct, interpretable components. One of these components is very closely aligned to liquid association, and is developed as a measure we call modified liquid association. We develop two methods for estimating this quantity, and propose statistical tests for the existence of this type of dependence. We evaluate these inferential methods in a set of simulations and illustrate their use in the analysis of publicly available experimental data.",
keywords = "Gene expression, Generalized estimating equations, Higher-order interaction, Liquid association, Non-Gaussian multivariate distribution",
author = "Ho, {Yen Yi} and Giovanni Parmigiani and Thomas Louis and Leslie Cope",
year = "2011",
month = "3",
doi = "10.1111/j.1541-0420.2010.01440.x",
language = "English (US)",
volume = "67",
pages = "133--141",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "1",

}

TY - JOUR

T1 - Modeling Liquid Association

AU - Ho, Yen Yi

AU - Parmigiani, Giovanni

AU - Louis, Thomas

AU - Cope, Leslie

PY - 2011/3

Y1 - 2011/3

N2 - In 2002, Ker-Chau Li introduced the liquid association measure to characterize three-way interactions between genes, and developed a computationally efficient estimator that can be used to screen gene expression microarray data for such interactions. That study, and others published since then, have established the biological validity of the method, and clearly demonstrated it to be a useful tool for the analysis of genomic data sets. To build on this work, we have sought a parametric family of multivariate distributions with the flexibility to model the full range of trivariate dependencies encompassed by liquid association. Such a model could situate liquid association within a formal inferential theory. In this article, we describe such a family of distributions, a trivariate, conditional normal model having Gaussian univariate marginal distributions, and in fact including the trivariate Gaussian family as a special case. Perhaps the most interesting feature of the distribution is that the parameterization naturally parses the three-way dependence structure into a number of distinct, interpretable components. One of these components is very closely aligned to liquid association, and is developed as a measure we call modified liquid association. We develop two methods for estimating this quantity, and propose statistical tests for the existence of this type of dependence. We evaluate these inferential methods in a set of simulations and illustrate their use in the analysis of publicly available experimental data.

AB - In 2002, Ker-Chau Li introduced the liquid association measure to characterize three-way interactions between genes, and developed a computationally efficient estimator that can be used to screen gene expression microarray data for such interactions. That study, and others published since then, have established the biological validity of the method, and clearly demonstrated it to be a useful tool for the analysis of genomic data sets. To build on this work, we have sought a parametric family of multivariate distributions with the flexibility to model the full range of trivariate dependencies encompassed by liquid association. Such a model could situate liquid association within a formal inferential theory. In this article, we describe such a family of distributions, a trivariate, conditional normal model having Gaussian univariate marginal distributions, and in fact including the trivariate Gaussian family as a special case. Perhaps the most interesting feature of the distribution is that the parameterization naturally parses the three-way dependence structure into a number of distinct, interpretable components. One of these components is very closely aligned to liquid association, and is developed as a measure we call modified liquid association. We develop two methods for estimating this quantity, and propose statistical tests for the existence of this type of dependence. We evaluate these inferential methods in a set of simulations and illustrate their use in the analysis of publicly available experimental data.

KW - Gene expression

KW - Generalized estimating equations

KW - Higher-order interaction

KW - Liquid association

KW - Non-Gaussian multivariate distribution

UR - http://www.scopus.com/inward/record.url?scp=79952602171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952602171&partnerID=8YFLogxK

U2 - 10.1111/j.1541-0420.2010.01440.x

DO - 10.1111/j.1541-0420.2010.01440.x

M3 - Article

C2 - 20528865

AN - SCOPUS:79952602171

VL - 67

SP - 133

EP - 141

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -