Concentration–Response Functions as an Essence of the Results from Lags

Among various aspects of environmental epidemiology, one is to assess the relationships between ambient air pollution and health outcomes. The goal of this work is to estimate the associations in the form of the parametric concentration–response functions (C-RF). Various forms of the C-RFs are proposed in this short-term health effect study. Emergency department (ED) visits for all respiratory health problems are analyzed as an illustrative example. A case-crossover (CC) technique is applied as a study design. Daily cases are organized as daily counts by the same day of the week in one common month. A conditional Poisson regression is used in the constructed statistical models. Temperature and relative humidity are included in the statistical models in the form of natural splines. Ground-level ozone concentration is considered an exposure. Ozone concentration values are transformed and submitted to the statistical models. The parameters of the transformation are determined by using the goodness of fit criterion. Counts of ED visits are analyzed in relation to a sequence of lagged exposure to ozone. The C-RF shapes are constructed for each individual lag. In a final step, the set of the estimated C-RF shapes is used to create a pooled C-RF shape. The results are positive and statistically significant for nine lagged exposures, from 0 to 8 days. The following relative risks (RR) were estimated from the constructed C-RFs at 30 ppb concentration of ozone: RR = 1.0531 (95% confidence interval: 1.0231, 1.0718), 1.0462 (1.0253, 1.0677), and 1.0387, (1.0240, 1.0531), realizing the CC method, CC method + transformation, and CC method + flexible transformation, respectively. The pooled C-RF shape gives a summary of the associations between ED visits for respiratory conditions and ambient ozone. The estimated shapes indicate lower air health effects than the standard CC methods. Among three considered statistical models, the CC method + flexible transformation is the most appropriate to use according to the goodness of fit criterion.