Using meta-smoothing to estimate dose-response trends across multiple studies, with application to air pollution and daily death.

Air pollution has been associated with daily mortality in numerous studies over the last decade. Although considerable attention has focused on issues of potential confounding in these associations, little has been done to address the question of what the shape of the dose-response relation looks like. The question of whether a threshold exists for these relations is of particular concern, with regard to both this application and many other epidemiologic questions. Nonparametric smoothing is widely used to control for the potentially nonlinear relations between covariates and daily deaths but has been little used to model the air pollution associations. Because sampling variability, among other factors, can introduce considerable noise into the estimates of linear dose-response curves, quantitative summaries have been widely used to come up with best linear fits. The same ability of meta-analytic techniques to average out noise applies to nonparametric smooth estimates in individual cities. We have developed a method of applying these techniques to combining nonparametric smooths. Using simulation studies, we show that this method can detect threshold and other nonlinear relations in epidemiologic studies, and we then apply it to analyze the association between PM10 and daily deaths in ten U.S. cities. We find that the association appears linear down to the lowest levels observed in the study. This method is generally applicable in settings where data from multiple studies can be combined.