A genetic bivariate model assessed the relationship between brain structure and number of cigarette pack-years, treating both measures as continuous variables. Shared environmental effects were non-significant in univariate analyses of brain structure (Kremen et al. 2010; Eyler et al. 2011; Eyler et al. 2012). Similarly, there were no significant differences between a full model and submodels for which shared environmental effects on brain structure as well as the shared environmental covariance shared between brain structure and cigarette pack-years were removed. Therefore, bivariate models decomposed the covariance between brain structure and cigarette pack-years into genetic and unique environmental variance while estimating the contribution of shared environmental influences for cigarette pack-years (Figure 1).
