A powerful method to test associations between ordinal traits and genotypes

The methods commonly used to test the associations between ordinal phenotypes and genotypes often treat either the ordinal phenotype or the genotype as continuous variables. To address limitations of these approaches, we propose a model where both the ordinal phenotype and the genotype are viewed as manifestations of an underlying multivariate normal random variable. The proposed method allows modeling the ordinal phenotype, the genotype and covariates jointly. We employ the generalized estimating equation technique and M-estimation theory to estimate the model parameters and deduce the corresponding asymptotic distribution. Numerical simulations and real data applications are also conducted to compare the performance of the proposed method with those of methods based on the logit and probit models. Even though there may be potential limitations in Type I error rate control for our method, the gains in power can prove its practical value in case of exactly ordinal phenotypes.