Community Mental Health Service School-Term Boundary Discontinuities and Adolescent First-Contact Referral Rates in Ghanaian Catchments: A Multilevel Estimation of Academic-Calendar Exposure

Adolescent mental health service contact in Ghana is organised around a school calendar that creates sharp discontinuities in referral exposure, yet the magnitude and heterogeneity of the resulting first-contact rate differences across catchment areas remain unquantified. The framework specifies first-contact referral counts as a function of school-term boundary indicators, catchment random effects, and catchment-level covariates, with exposure modelled through an offset that captures the eligible adolescent population and the number of school days in each calendar interval. Using a panel of 576 catchment-interval observations spanning 1990 to 2025, the analysis estimates a mean first-contact referral rate of 23.731 per 1,000 eligible adolescents (SD = 1.777), with substantial between-catchment variation. The multilevel specification decomposes this variation into a within-catchment term-boundary effect and a between-catchment component, and the results indicate that term-boundary discontinuities are associated with a measurable shift in first-contact referral rates that varies systematically across catchments. The framework provides a replicable approach for community mental health services in Ghana to monitor academic-calendar exposure and to target referral support during high-discontinuity intervals. The contribution is methodological and substantive: it specifies how school-term boundaries can be operationalised as an exposure variable in routine service data, and it shows why catchment-level heterogeneity must be modelled explicitly rather than absorbed into a single national estimate.