Analyses were performed in STATA version 12 (StataCorp, 2011), with the Huber-White robust variance estimator used to compute standard errors and confidence intervals adjusted for non-independence of twin-family data. Time-to-event data were analyzed using survival analysis to assess likelihood as well as timing of onset. Cox proportional hazards (PH) regression was conducted predicting onset of substance involvement from parental separation and parent and cotwin substance dependence. Parent and cotwin alcohol and cannabis dependence were initially modeled separately, with post-hoc tests for equality. Where no significant differences were observed, twin alcohol and cannabis dependence were examined as a combined phenotype, that is, either alcohol or cannabis dependence. Parental separation was modeled as a time-varying covariate to ensure onset prior to or during the same year as initiation. Offspring from intact families were right-censored at age at last interview if younger than 18 years. In the case of parental death, intact families were right-censored at offspring age when their parent(s) died. Post-hoc tests of interactions between parental separation and parental substance dependence were also conducted. The Efron approximation (Efron, 1977) was used
