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Introduction.  There are a few statistical approaches to estimate health impacts of the ambient air pollution concentrations. Air health effects are often studied in short-term exposure. In this context two main techniques are used; time-series and case-crossover (CC). This work focuses on the CC methodology. In the standard method risk is estimated using log-linear models. Aim.  This work proposes other types of the models. Material and methods.  The CC design is applied with various transformations of air pollution concentration. The mortality data are used for the period from 1987 to 2015 for Toronto, Canada. Daily concentration level of ambient ozone is considered as an exposure. The ozone concentration is transformed and used in the statistical models. The transformation is a product of two parts; a simple function such as logarithm and a logistic function as a weight. The transformed concentration is used in the CC statistical models. The models estimate the coefficient related to transformed concentration. It allows to construct the concentration-response function. The generated models are assessed using the Akaike information criterion (AIC). Results.  The relative risks (RR), reported at 75th percentile of the concentration (55 ppb) are different. The standard CC model gives RR=1.0195 with the 95% confidence interval (1.0035, 1.0358), whereas the model with the transformation gives better fit and estimates RR=1.0054 (1.0026, 1.0082). Conclusions.  The proposed methodology allows to construct an accurate approximation of the concentration-response functions. These functions provide adequate approximations and also identify a potential threshold.

The concentration-response functions for short-term exposure to ambient air pollution