in either parent; (ii) graphed cumulative failure rates using the Kaplan-Meier survival function. Third, we estimated Cox proportional hazards regression models predicting age at first use of alcohol, cigarettes, cannabis, and age at sexual initiation from parental AUD (modeled with 3 dummy variables representing AUD in one parent, both parents, or possible AUD in one parent) and parental separation, before and after adjustment for control variables. Observations were censored at first use of substance or first sex; subjects who had not yet used substances or had sex were censored at their most recent age. Fourth, we performed post-hoc Wald chi-square tests to compare the relative strength of association with each outcome of parental separation with AUD in one parent and AUDs both parents. Significance for p-values was adjusted for multiple testing (p=.05/2 tests =.025). Tests of proportional hazards, i.e. the assumption that the risk associated with different levels of a variable remain proportional over time, were computed using Schoenfeld residuals (51). Where such variations in risk were found for parental AUDs and parental separation, interactions with age that correspond to key developmental periods were created and entered into the model (i.e., early childhood [12 and younger], puberty [13–15], early adolescence
