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Testing the association between a phenotype and many genetic variants fromcase-control data is essential in genome-wide association study (GWAS). This isa challenging task as many such variants are correlated or non-informative.Similarities exist in testing the population difference between two groups ofhigh dimensional data with intractable full likelihood function. Testing may betackled by a maximum composite likelihood (MCL) not entailing the fulllikelihood, but current MCL tests are subject to power loss for involvingnon-informative or redundant sub-likelihoods. In this paper, we develop aforward search and test method for simultaneous powerful group differencetesting and informative sub-likelihoods composition. Our method constructs asequence of Wald-type test statistics by including only informativesub-likelihoods progressively so as to improve the test power under localsparsity alternatives. Numerical studies show that it achieves considerableimprovement over the available tests as the modeling complexity grows. Ourmethod is further validated by testing the motivating GWAS data on breastcancer with interesting results obtained.

Parsimonious and powerful composite likelihood testing for group difference and genotype-phenotype association