  Testing the association between a phenotype and many genetic variants from
case-control data is essential in genome-wide association study (GWAS). This is
a challenging task as many such variants are correlated or non-informative.
Similarities exist in testing the population difference between two groups of
high dimensional data with intractable full likelihood function. Testing may be
tackled by a maximum composite likelihood (MCL) not entailing the full
likelihood, but current MCL tests are subject to power loss for involving
non-informative or redundant sub-likelihoods. In this paper, we develop a
forward search and test method for simultaneous powerful group difference
testing and informative sub-likelihoods composition. Our method constructs a
sequence of Wald-type test statistics by including only informative
sub-likelihoods progressively so as to improve the test power under local
sparsity alternatives. Numerical studies show that it achieves considerable
improvement over the available tests as the modeling complexity grows. Our
method is further validated by testing the motivating GWAS data on breast
cancer with interesting results obtained.
