proportional hazards assumption, that the hazard associated with a risk factor remains proportional over time, were investigated using Schoenfeld residuals as assessed by the Grambsch & Therneau test (Grambsch & Therneau, 1994). Identified violations were resolved by modeling age interactions with the pertinent variable. Age risk periods were chosen based on developmental cutoffs (e.g., menarche, entering middle or high school) and on examination of graphical representations of the data to observe failure rates to see where hazards diverged. Once violations were resolved, post hoc tests were conducted to ensure that the hazard ratios could not be equated across risk periods to provide additional confidence that the defined risk periods were distinct. Survival ties were handled by the Efron approximation (Efron, 1977). All analyses were adjusted for familial clustering via the Huber-White robust standard errors as implemented in Stata (StataCorp, 2015).
