Comparison of alternative modelling techniques in estimating short-term effect of air pollution with application to...

In 2002, serious criticism was raised about the use of standard statistical software (Splus, SAS, Stata) to fit Generalized Additive Models (GAM) to epidemiological time series data. This criticism concerns convergence problems of the backfitting algorithm and inappropriate use of a linear approximation in estimating standard errors of estimates for parametric terms, such as the effect of air pollution. Here we analysed the association between PM10 and Mortality/Hospital Admissions in the Italian Meta-analysis of Short-term effects of Air pollutants (MISA) using two alternative approaches that are not affected by the same drawbacks: GAM with penalized regression spline fitted by the direct method in R (GAM-R) software and Generalized Linear Models with natural cubic spline (GLM+NS). A sensitivity analysis is also provided varying number of degrees of freedom for the seasonality spline and modality of adjustment for confounding effect of temperature. Published theoretical results and a simulation study are provided in order to explain discrepancies between GLM+NS and GAM-R estimates. We conclude that in general the fully parametric GLM+NS approach retains better statistical properties than GAM-R that could bring to biased air pollution effect estimates unless a certain degree of under-smoothing for seasonality spline is settled.