Functional data modeling to measure exposure to ozone

One of the many challenges involved in environmental studies of pollutants on human health is how to measure the daily exposure to ozone. Despite hourly measures of ozone concentrations are available, studies on short-term effects of ozone and human health reduce the hourly measures to a single daily summary measure, such as daily average, daily maximum etc. This reduction leads to disregard the non-uniform temporal distribution of the pollutant, and can be an issue in modelling the association between short-term effects of ozone and human health outcome. We present alternative approach by treating all hourly measures of a day as one function. The functional form of ozone incorporates all hourly measures and aids to uncover important features of the daily patterns of ozone. To investigate the effect of the hourly records on health, we consider a functional generalized linear model (FGLM) in which the predictor is functional ozone and the response is daily hospital admissions. The model allows to estimate the effect of ozone as a function of daily hour that allows to examine the influence of the pollutant throughout the day. Thus, the portion of daily ozone function potentially linked to health can be recognized. We demonstrate the superiority of our approach over the classical models that use daily summary measures using out-of-sample predictive performance.