A quadrivariate biometric model was constructed to decompose the genetic and environmental covariance between AUD and MDD into CON and SR (see Supplementary material for model-fitting results). An initial model included all three biometric factors (ACE), and a nested model fixed variance due to C at zero without a significant decrement in fit. Given the negligible influence of C, AE models were carried forward. We first fit an AE model in which SR was entered first, in order to derive genetic and environmental estimates specific to CON. Within this model, constraining parameters to be the same across men and women did not provide a significant decrement in fit, suggesting that there were no sex differences in the sources of covariation between MDD and AUD (see Supplementary material). The phenotypic correlation between MDD and AUD in the constrained model was 0.33, of which approximately two-thirds was explained by genetic influences [A = 0.63 (0.41–0.85)] and one-third was explained by unique environmental influences [E = 0.37 (0.15–0.59)].
