TY - JOUR
T1 - Modeling Liquid Association
AU - Ho, Yen Yi
AU - Parmigiani, Giovanni
AU - Louis, Thomas A.
AU - Cope, Leslie M.
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
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
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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
SN - 0006-341X
VL - 67
SP - 133
EP - 141
JO - Biometrics
JF - Biometrics
IS - 1
ER -