Modelling seasonal and spatio-temporal variation in respiratory prescribing: the example of respiratory prescribing

Many measures of chronic diseases including respiratory disease exhibit seasonal variation together with residual correlation between consecutive time-periods and neighbouring areas. We demonstrate a modern strategy for modelling data that exhibit both seasonal trend and spatio-temporal correlation, through an application to respiratory prescribing. We analysed 55 months (2002-2006) of prescribing data, in the northeast of England, UK. We estimated the seasonal pattern of prescribing by fitting a dynamic harmonic regression (DHR) model to salbutamol prescribing in relation to temperature. We compared the output of DHR models to static sinusoidal regression models. We used the DHR fitted values as an offset in mixed-effects models that aimed to account for the remaining spatio-temporal variation in prescribing rates. As diagnostic checks, we assessed spatial and temporal correlation separately and jointly. Our application of a DHR model resulted in a better fit to the seasonal variation of prescribing, than was obtained with a static model. After adjusting the final model for the fitted values from the DHR model, we did not detect any remaining spatio-temporal correlation in the model’s residuals. Using a DHR model and temperature data to account for the periodicity of prescribing proved an efficient way to capture its seasonal variation. The diagnostic procedures indicated that there was no need to model any remaining correlation explicitly.This work was supported by the Colt Foundation, the UK Medical Research Council (grants MR/K020919/1 and G0800270), British Heart Foundation (grant SP/09/002), and the National Institute for Health Research (Cambridge Biomedical Research Center)