Logistic regression analysis of twin data: Estimation of parameters of the multifactorial liability-threshold model

We extend the DeFries-Fulker regression model for the analysis of quantitative twin data to cover binary traits and genetic dominance. In the proposed logistic regression model, the cotwin's trait status, C, is the response variable, while the proband's trait status, P, is a predictor variable coded as k (affected) and 0 (unaffected). Additive genetic effects are modeled by the predictor variable PR, which equals P for monozygotic (MZ) and P/2 for dizygotic (DZ) twins; and dominant genetic effects, by PD, which equals P for MZ and P/4 for DZ twins. By setting an appropriate scale for P (i.e., the value of k), the regression coefficients of P, PR, and PD are estimates of the proportions of variance in liability due to common family environment, additive genetic effects, and dominant genetic effects, respectively, for a multifactorial liability-threshold model. This model was applied to data on lifetime depression from the Virginia Twin Registry and produced results similar to those from structural equation modeling.