The proportional hazards assumption was tested with the Grambsch and Therneau test of the Schoenfeld residuals (39). Violations were observed for the variables representing CSA in all models, co-twin early use in Model 2 for alcohol, cigarettes, and cannabis, and co-twin early use by zygosity in Model 2 for cigarettes. Violations indicated that the association of these variables with risk for initiation of substance use varied by period of risk (i.e., age), so hazard ratios were reported by risk period. Division of the risk period was based on the distribution of age at first use for each of the three substances. For alcohol, the 4 categories were 5–9, 10–14, 15–19, and ≥20 years; for cigarettes: 4–9, 10–14, 15–19, and ≥20 years; and for cannabis: 5–13, 14–17, 18–21, and ≥22 years.
