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

Studying the association between a phenotype and a number of genetic variants from case-control data is an important goal in many genetic studies. Association analysis is often carried out by testing the null hypothesis that two groups of multi-dimensional data are generated by the same population. Testing based on genotype data is a challenging task as the full likelihood of the data is usually intractable. This difficulty may be tackled by composite likelihood (MCL) tests which do not entail the full likelihood. But currently available MCL tests are subject to severe power loss for involving non-informative or redundant sub-likelihoods. To reduce the power loss, a forward search and test method for simultaneous powerful group difference testing and informative sub-likelihoods composition is developed. The new 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 it achieves considerable improvement over the available tests as the modeling complexity grows. The new method is illustrated through an analysis of genotype data from a case-control study on breast cancer.