Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health

Generalized additive models (GAMs) have become the standard tool for the analysis of short-term effects of air pollution on human health. Usually, the confounding effect of seasonality and long-term trend is described by flexible parametric or non-parametric functions of calendar time. Two different modeling strategies, i.e. GAM with penalized regression splines and GAM with regression splines, were compared by means of a simulation study, addressing attention to the inference on air pollutant effect. Simulation results indicated that GAM with regression splines provides negligibly biased estimates of air pollutant effect and it is robust to misspecification of the degrees of freedom of the spline. GAM with penalized regression splines requires a certain amount of undersmoothing in order to reduce the bias of the estimates and to improve the coverage of confidence intervals. These findings agree with asymptotic results developed in the context of partially splined models.