Testing for genetic association with constrained models using triads

It has been shown that it is preferable to use a robust model that incorporated constraints on the genotype relative risk rather than rely on a model that assumes the disease operates in a recessive or dominant fashion. Previous methods are applicable to case-control studies, but not to family based studies of case children along with their parents (triads). We show here how to implement analogous constraints while analyzing triad data. The likelihood, conditional on the parents genotype, is maximized over the appropriately constrained parameter space. The asymptotic distribution for the maximized likelihood ratio statistic is found and used to estimate the null distribution of the test statistics. The properties of several methods of testing for association are compared by simulation. The constrained method provides higher power across a wide range of genetic models with little cost when compared to methods that restrict to a dominant, recessive, or multiplicative model, or make no modeling restriction. The methods are applied to two SNPs on the methylenetetrahydrofolate reductase (MTHFR) gene with neural tube defect (NTD) triads.