Seasonal confounding in air pollution and health time-series studies: effect on air pollution effect estimates.

A major statistical challenge in air pollution and health time-series studies is to adequately control for confounding effects of time-varying covariates. Daily health outcome counts are most commonly analysed by Poisson regression models, adjusted for overdispersion, with air pollution levels included as a linear predictor and smooth functions for calendar time and weather variables to adjust for time-varying confounders. Various smoothers have been used so far, but the optimal strategy for choosing smoothers and their degree of smoothing remains controversial. In this work, we evaluate the performance of various smoothers with different criteria for choosing the degree of smoothing in terms of bias and efficiency of the air pollution effect estimate in a simulation study. The evaluated approaches were also applied to real mortality data from 22 European cities. The simulation study imitated a multi-city study. Data were generated from a fully parametric model. Model selection methods which optimize prediction may lead to increased biases in the air pollution effect estimate. Minimization of the absolute value of the sum of the partial autocorrelation function of the model's residuals (PACF), as a criterion to choose the degree of smoothness, gave the smallest biases. The penalized splines (PS) method with a large number of effective dfs (e.g. 8-12 per year) could be used as the basic, relatively conservative, analysis whereas the PS and natural splines in combination with PACF could be applied to provide a reasonable range of the effect estimate.