Forecasting the daily demand for emergency medical ambulances in England and Wales: a benchmark model and external validation

Abstract

BACKGROUND: We aimed to select and externally validate a benchmark method for emergency ambulance services to use to forecast the daily number of calls that result in the dispatch of one or more ambulances. METHODS: The study was conducted using standard methods known to the UK's NHS to aid implementation in practice. We selected our benchmark model from a naive benchmark and 14 standard forecasting methods. Mean absolute scaled error and 80 and 95% prediction interval coverage over a 84 day horizon were evaluated using time series cross validation across eight time series from the South West of England. External validation was conducted by time series cross validation across 13 time series from London, Yorkshire and Welsh Ambulance Services. RESULTS: A model combining a simple average of Facebook's prophet and regression with ARIMA errors (1, 1, 3)(1, 0, 1, 7) was selected. Benchmark MASE, 80 and 95% prediction intervals were 0.68 (95% CI 0.67 - 0.69), 0.847 (95% CI 0.843 - 0.851), and 0.965 (95% CI 0.949 - 0.977), respectively. Performance in the validation set was within expected ranges for MASE, 0.73 (95% CI 0.72 - 0.74) 80% coverage (0.833; 95% CI 0.828-0.838), and 95% coverage (0.965; 95% CI 0.963-0.967). CONCLUSIONS: We provide a robust externally validated benchmark for future ambulance demand forecasting studies to improve on. Our benchmark forecasting model is high quality and usable by ambulance services. We provide a simple python framework to aid its implementation in practice. The results of this study were implemented in the South West of England.