Forecasting Australian Mental Health Service Demand with Distribution-Free Prediction Intervals: A Time-Series Analysis of MBS and PBS Data, 2014–2024

Version 2 (corrected, June 2026): This version reconciles the conformal coverage summary table (Table 4) to the committed analysis output, seeds the EnbPI residual bootstrap (random seed 42) so the deposited interval values are a single reproducible realisation, and corrects figure-caption numbering. No conclusions are affected. Background: Australia's mental health system has undergone repeated structural disruption since 2020, yet demand forecasting with calibrated uncertainty remains absent from policy planning. We applied changepoint detection, interrupted time-series (ITS) analysis, and conformal prediction to generate distribution-free forecasts for mental health service indicators. Methods: We analysed 40 quarters (2014–2024) of national Medicare Benefits Schedule (MBS) psychological services and Pharmaceutical Benefits Scheme (PBS) mental health prescribing data from the Australian Institute of Health and Welfare (AIHW), covering 12 indicator series across 6 MBS provider types and 6 PBS medication classes. Changepoints were detected using Pruned Exact Linear Time (PELT) and Bayesian Online Changepoint Detection (BOCPD). Segmented regression with Newey–West standard errors quantified policy effects at three intervention points: COVID-19 onset (Q1 2020), Better Access session reduction (Q1 2023), and 60-day dispensing reform (Q4 2023). Base forecasts from ARIMA, exponential smoothing (ETS), and Prophet were wrapped with Adaptive Conformal Inference (ACI) and Ensemble Batch Prediction Intervals (EnbPI) at 90% and 95% nominal coverage. PHN-level geographic equity was assessed as a secondary analysis. This study was pre-registered on the Open Science Framework (doi:10.17605/OSF.IO/QPZAJ). Results: ACI achieved near-nominal holdout coverage (90% nominal: 7 of 12 series fully covered, 5 at 75%; 95% nominal: 10 of 12 fully covered) with narrower intervals than EnbPI. The Better Access session reduction produced significant level reductions in MBS services of −15.4 per 1,000 for all providers (p < 0.001), −4.0 for clinical psychologists (p = 0.001), −4.7 for other psychologists (p < 0.001), and −4.6 for GPs (p = 0.048), corresponding to declines of 14.7–17.1%. COVID-19 onset produced heterogeneous effects, including accelerated psychostimulant dispensing growth (+1.21 per 1,000 per quarter, p < 0.001). Geographic analysis across 31 Primary Health Networks (PHNs) revealed stable structural inequality (Gini coefficient 0.107–0.113 over 10 years), with persistently low-access regions including Northern Territory (−56.3% below national mean) and Western Sydney (−41.5%). Conclusions: ACI conformal prediction provides calibrated uncertainty quantification for health service demand forecasting under non-stationarity introduced by policy interventions. The Better Access session reduction produced the largest measurable service disruption in the study period. Geographic prescribing inequity is structural and stable. These forecasts with distribution-free prediction intervals can support workforce planning and resource allocation for Australian mental health services.