Designing health impact functions to assess marginal changes in outdoor fine particulate matter

Estimating health benefits from improvements in ambient air quality requires the characterization of the magnitude and shape of the association between marginal changes in exposure and marginal changes in risk, and its uncertainty. Several attempts have been made to do this, each requiring different assumptions. These include the Log-Linear(LL), IntegratedExposure-Response(IER), and GlobalExposureMortalityModel(GEMM). In this paper we develop an improved relative risk model suitable for use in health benefits analysis that incorporates features of existing models while addressing limitations in each model. We model the derivative of the relative risk function within a meta-analytic framework; a quantity directly applicable to benefits analysis, incorporating a Fusion of algebraic functions used in previous models. We assume a constant derivative in concentration over low exposures, like the LL model, a declining derivative over moderate exposures observed in cohort studies, and a derivative declining as the inverse of concentration over high global exposures in a similar manner to the GEMM. The model properties are illustrated with examples of fitting it to data for the six specific causes of death previously examined by the GlobalBurdenofDisease program with ambient fine particulate matter (PM_2.5). In a test case analysis assuming a 1% (benefits analysis) or 100% (burden analysis), reduction in country-specific fine particulate matter concentrations, corresponding estimated global attributable deaths using the Fusion model were found to lie between those of the IER and LL models, with the GEMM estimates similar to those based on the LL model.