An algorithm for learning maximum entropy probability models of disease risk that efficiently searches and sparingly encodes multilocus genomic interactions

Motivation: In both genome-wide association studies (GWAS) and pathway analysis, the modest sample size relative to the number of genetic markers presents formidable computational, statistical and methodological challenges for accurately identifying markers/ interactions and for building phenotype-predictive models. Results: We address these objectives via maximum entropy conditional probability modeling (MECPM), coupled with a novel model structure search. Unlike neural networks and support vector machines (SVMs), MECPM makes explicit and is determined by the interactions that confer phenotype-predictive power. Our method identifies both a marker subset and the multiple k-way interactions between these markers. Additional key aspects are: (i) evaluation of a select subset of up to five-way interactions while retaining relatively low complexity; (ii) flexible single nucleotide polymorphism (SNP) coding (dominant, recessive) within each interaction; (iii) no mathematical interaction form assumed; (iv) model structure and order selection based on the Bayesian Information Criterion, which fairly compares interactions at different orders and automatically sets the experiment-wide significance level; (v) MECPM directly yields a phenotype-predictive model. MECPM was compared with a panel of methods on datasets with up to 1000 SNPs and up to eight embedded penetrance function (i.e. ground-truth) interactions, including a five-way, involving less than 20 SNPs. MECPM achieved improved sensitivity and specificity for detecting both ground-truth markers and interactions, compared with previous methods.