Using the COGA data, we examined the association between the imputed PSI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{\hat{\mathrm \Psi }}}}_{\left( x \right)}$$\end{document}Ψ^x and both DSM-IV alcohol dependence and SXCT using generalized estimating equation (GEE) [24, 33]. Binomial (logit link function) and Poisson (log link function) were assumed to model DSM-IV AUD and SXCT, respectively. The pedigree matrix was constructed as a tiling of blocks along the diagonal; each block contained the correlation coefficients of individuals from an independent family. Equal coefficients were assumed for individuals in the same family; coefficients between individuals from different families were zero. Finally, the GEE regression was further adjusted with covariates of sex, 3 genotype arrays, 4 principal components related to population, and 3 birth cohorts.
