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Abstract:
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Analyses of the relationship between pollution and morbidity over time generally rely on Poisson regression models with smooth functions of time to account for unobserved time-varying confounders. We propose an approach here, based on making data-based choice of bases for the smooth function, as an alternative to the usual spline bases. In particular, we illustrate the strategy using a set of trigonometric bases chosen according to the spectral density of the data. In a simulation study, we find that the performance of our method, as measured by the Mean Squared Error of the parameter of interest, is less sensitive than regression splines to the number of basis functions chosen and the extent to which the confounded and confounding variable vary quickly or slowly with time. We apply our model in an analysis of daily time-series asthma-prescription data over four summers in Chicago.
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