We first modeled the age trends in mean depressive symptoms and prevalence of daily smoking, marijuana use, and regular HED, using a separate intercept-only TVEM for each. These models were estimated separately for males and females. To examine the age-varying associations between substance use behaviors and depressive symptoms, we implemented TVEM in which daily smoking, marijuana use, and regular HED predicted depressive symptoms. We first estimated the independent age-varying association with depressive symptoms for each substance use behavior. We also estimated the adjusted age-varying associations using all three substance use behaviors as simultaneous predictors. To determine whether gender modified these complex associations between substance use behaviors and depressive symptoms at any point across the age span, all analyses were stratified by gender. In all models, we controlled for race (White, Black, other) and Hispanic ethnicity by specifying these as time-invariant covariates. All analyses were conducted in SAS 9.3 and TVEM was implemented using the SAS macros %normal_TVEM and %logistic_TVEM; these macros are available for download at methodology.psu.edu (Li et al., 2014). All TVEM models used the p-spline estimation method.
