Meta‐Analysis Methods to Estimate the Shape and Uncertainty in the Association Between Long‐Term Exposure to Ambient Fine Particulate Matter and Cause‐Specific Mortality Over the Global Concentration Range

Estimates of excess mortality associated with exposure to ambient concentrations of fine particulate matter have been obtained from either a single cohort study or pooling information from a small number of studies. However, standard frequentist methods of pooling are known to underestimate statistical uncertainty in the true risk distribution when the number of studies pooled is small. Alternatively, Bayesian pooling methods using noninformative priors yield unrealistically large amounts of uncertainty in this case. We present a new hybrid frequentist‐bayesian framework for meta‐analysis that incorporates features of both frequentist and Bayesian approaches, yielding estimated uncertainty distributions that are more useful for burden estimation. We also present an example of mortality risk due to long‐term exposure to ambient fine particulate matter obtained from a small number of cohort studies conducted in the United States and Europe. We compare our new risk uncertainty distribution to that obtained by the integrated exposure‐response (IER) model used in the Global Burden of Disease 2010 project for which risk was modeled over the entire global concentration range. We suggest a method to incorporate our new risk uncertainty distribution based on the relatively low concentrations observed in the United States and western Europe into the IER model, thus extending risk estimation to the global concentration range.