Bivariate traits association analysis using generalized estimating equations in family data.

Genome wide association study (GWAS) is becoming fundamental in the arduous task of deciphering the etiology of complex diseases. The majority of the statistical models used to address the genes-disease association consider a single response variable. However, it is common for certain diseases to have correlated phenotypes such as in cardiovascular diseases. Usually, GWAS typically sample unrelated individuals from a population and the shared familial risk factors are not investigated. In this paper, we propose to apply a bivariate model using family data that associates two phenotypes with a genetic region. Using generalized estimation equations (GEE), we model two phenotypes, either discrete, continuous or a mixture of them, as a function of genetic variables and other important covariates. We incorporate the kinship relationships into the working matrix extended to a bivariate analysis. The estimation method and the joint gene-set effect in both phenotypes are developed in this work. We also evaluate the proposed methodology with a simulation study and an application to real data.

Quantile modeling through multivariate log-normal/independent linear regression models with application to newborn data.

In this article, we propose and study the class of multivariate log-normal/independent distributions and linear regression models based on this class. The class of multivariate log-normal/independent distributions is very attractive for robust statistical modeling because it includes several heavy-tailed distributions suitable for modeling correlated multivariate positive data that are skewed and possibly heavy-tailed. Besides, expectation-maximization (EM)-type algorithms can be easily implemented for maximum likelihood estimation. We model the relationship between quantiles of the response variables and a set of explanatory variables, compute the maximum likelihood estimates of parameters through EM-type algorithms, and evaluate the model fitting based on Mahalanobis-type distances. The satisfactory performance of the quantile estimation is verified by simulation studies. An application to newborn data is presented and discussed.

An Efficient Test for Gene-Environment Interaction in Generalized Linear Mixed Models with Family Data.

Gene-environment (GE) interaction has important implications in the etiology of complex diseases that are caused by a combination of genetic factors and environment variables. Several authors have developed GE analysis in the context of independent subjects or longitudinal data using a gene-set. In this paper, we propose to analyze GE interaction for discrete and continuous phenotypes in family studies by incorporating the relatedness among the relatives for each family into a generalized linear mixed model (GLMM) and by using a gene-based variance component test. In addition, we deal with collinearity problems arising from linkage disequilibrium among single nucleotide polymorphisms (SNPs) by considering their coefficients as random effects under the null model estimation. We show that the best linear unbiased predictor (BLUP) of such random effects in the GLMM is equivalent to the ridge regression estimator. This equivalence provides a simple method to estimate the ridge penalty parameter in comparison to other computationally-demanding estimation approaches based on cross-validation schemes. We evaluated the proposed test using simulation studies and applied it to real data from the Baependi Heart Study consisting of 76 families. Using our approach, we identified an interaction between BMI and the Peroxisome Proliferator Activated Receptor Gamma (PPARG) gene associated with diabetes.