Monthly rural-urban scaling of road accidents in England, Wales and Scotland (2019-2023)

Road traffic accidents remain a major public health challenge worldwide, with urbanisation and population density identified as key factors influencing risk. This study analyses monthly accident data from 2009 to 2023 across 632 parliamentary constituencies in England, Wales, and Scotland, using an area-normalised approach based on population density. Segmented power law models consistently identified breakpoints separating sublinear rural from superlinear urban scaling behaviours. Seasonal variation in scaling exponents was pronounced in rural regions but less evident in urban ones. Fourier-based cross-spectral analysis of yearly cycles revealed systematic phase shifts: rural exponents lagged pre-exponential factors by 4.5 months, while urban exponents were 2.7 months out of phase, producing a 5.3 month shift between rural and urban exponents. These findings highlight the importance of pre-exponentials—defined as the expected density of accidents at unit population density—as comparable descaled metrics, revealing both long-term national declines and recurring seasonal peaks. Notably, the phase offsets suggest structurally distinct causes of rural and urban accident risk, with urban regions exhibiting increasing acceleration in accident scaling, potentially linked to growth in vehicle numbers, size, and weight. Residuals, modelled with the Type I Generalised Logistic Distribution (GLD), captured skewness and heterogeneity more effectively than normal assumptions. Geospatial mapping highlighted persistent urban hotspots alongside rural and coastal constituencies with systematically lower accident densities than predicted. Together, these findings advance understanding of how density and urbanisation shape accident risk and provide evidence to support more targeted road safety interventions and policy planning.