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.

需要表征室外空气污染浓度与健康之间关联的程度和形状，以便估计拟议缓解策略对公共健康的益处。已经针对这种表征提出了专门的参数函数。然而，非参数样条模型在描述这些关联时提供了更大的灵活性、更少的偏差和预测能力，因此比相对简单的参数公式更受青睐。经常报告不受限制的样条表示，但许多不适合效益分析，因为它们不稳定的浓度响应行为，并且通常不以符合进行效益分析所需的要求的格式呈现。我们提出了一种方法，通过将样条预测及其在研究暴露范围内的不确定性转换为新的样条公式，该公式既单调增加又仅限于浓度，以适应适合公共卫生效益分析的浓度-反应关联的非参数样条表示-适合用于健康效益评估的响应模式。我们选择了加拿大和美国长期接触细颗粒物与死亡率之间关联的两个例子，我们建议，它们的样条拟合既不是单调递增的，也不适合进行效益分析。我们建议我们的模型适合进行效益分析，并针对加拿大和美国进行此类分析，将效益估计与传统模型进行比较。最后，我们提供有关如何报告样条拟合结果的指导，以便它们可以直接用于效益分析，或适合我们的新模型。