Adapting non-parametric spline representations of outdoor air pollution health effects associations for use in public health benefits assessment

The magnitude and shape of the association between outdoor air pollution concentrations and health need to be characterized in order to estimate public health benefits from proposed mitigation strategies. Specialized parametric functions have been proposed for this characterization. However, non-parametric spline models offer more flexibility, less bias, and predictive power, in describing these associations and are thus preferred over relatively simple parametric formulations. Unrestricted spline representations are often reported but many are not suitable for benefits analysis due to their erratic concentration-response behavior and are usually not presented in a format consistent with the requirements necessary to conduct a benefits analysis. We propose a method to adapt non-parametric spline representations of concentration-response associations that are suitable for public health benefits analysis by transforming spline predictions and its uncertainty over the study exposure range to a new spline formulation that is both monotonically increasing and restricted to concentration-response patterns suitable for use in health benefits assessment. We selected two examples of the association between long-term exposure to fine particulate matter and mortality in Canada and the USA that displayed spline fits that were neither monotonically increasing nor suitable, we suggest, for benefits analysis. We suggest our model is suitable for benefits analysis and conduct such analyses for both Canada and the USA, comparing benefits estimates to traditional models. Finally, we provide guidance on how to report spline fitting results such they can be used either in benefits analysis directly, or to fit our new model.