A critical assessment of shrinkage-based regression approaches for estimating the adverse health effects of multiple air pollutants

Most investigations of the adverse health effects of multiple air pollutants analyse the time series involved by simultaneously entering the multiple pollutants into a Poisson log-linear model. Concerns have been raised about this type of analysis, and it has been stated that new methodology or models should be developed for investigating the adverse health effects of multiple air pollutants. In this paper, we introduce the use of the lasso for this purpose and compare its statistical properties to those of ridge regression and the Poisson log-linear model. Ridge regression has been used in time series analyses on the adverse health effects of multiple air pollutants but its properties for this purpose have not been investigated. A series of simulation studies was used to compare the performance of the lasso, ridge regression, and the Poisson log-linear model. In these simulations, realistic mortality time series were generated with known air pollution mortality effects permitting the performance of the three models to be compared. Both the lasso and ridge regression produced more accurate estimates of the adverse health effects of the multiple air pollutants than those produced using the Poisson log-linear model. This increase in accuracy came at the expense of increased bias. Ridge regression produced more accurate estimates than the lasso, but the lasso produced more interpretable models. The lasso and ridge regression offer a flexible way of obtaining more accurate estimation of pollutant effects than that provided by the standard Poisson log-linear model.