A staged Bayesian framework for longitudinal prediction of adolescent depression using add health data

Accurately predicting adolescent depression from longitudinal behavioral data requires methods that incorporate feedback between prior mental health and substance use while remaining reproducible and interpretable. The objective of this study is predictive rather than explanatory or causal.

Using Waves I-IV of the U.S. National Longitudinal Study of Adolescent to Adult Health (Add Health), we developed a novel staged Bayesian framework for longitudinal prediction: (Stage 1) multivariate logistic models with correlated random intercepts for depression, smoking, and alcohol use; (Stage 2) a composite substance-use indicator jointly modeled with depression; and (Stage 3) a temporal feedback model including lagged depression and lagged substance use. Posterior predictive checks and internal validation were used to assess model adequacy. Discrimination (area under the receiver operating characteristic curve [AUC]) and calibration (Brier score) were summarized across stages. The models are predictive rather than explanatory and are not intended to estimate causal effects.

Lagged depression (posterior mean = 0.98; 95% highest posterior density [HPD] interval: 0.45-1.52) and lagged substance use (posterior mean = 0.69; 95% HPD: 0.12-1.25) were associated with increased odds of future depression. Predictive performance improved from Stage 1 to Stage 3: AUC increased from 0.78 to 0.84, and Brier score decreased from 0.185 to 0.152. Posterior predictive checks supported model adequacy.

The staged Bayesian pipeline provides a generalizable template for longitudinal prediction with temporal feedback, improving discrimination and calibration while preserving interpretability.