Model misspecification, measurement error, and apparent supralinearity in the concentration-response relationship between PM2.5 and mortality.

A growing number of studies have produced results that suggest the shape of the concentration-response (C-R) relationship between PM2.5 exposure and mortality is "supralinear" such that incremental risk is higher at the lowest exposure levels than at the highest exposure levels. If the C-R function is in fact supralinear, then there may be significant health benefits associated with reductions in PM2.5 below the current US National Ambient Air Quality Standards (NAAQS), as each incremental tightening of the PM2.5 NAAQS would be expected to produce ever-greater reductions in mortality risk. In this paper we undertake a series of tests with simulated cohort data to examine whether there are alternative explanations for apparent supralinearity in PM2.5 C-R functions. Our results show that a linear C-R function for PM2.5 can falsely appear to be supralinear in a statistical estimation process for a variety of reasons, such as spatial variation in the composition of total PM2.5 mass, the presence of confounders that are correlated with PM2.5 exposure, and some types of measurement error in estimates of PM2.5 exposure. To the best of our knowledge, this is the first simulation-based study to examine alternative explanations for apparent supralinearity in C-R functions.

A simulation-based assessment of the ability to detect thresholds in chronic risk concentration-response functions in the presence of exposure measurement error.

An important question when setting appropriate air quality standards for fine particulate matter (PM2.5) is whether there exists a "threshold" in the concentration-response (C-R) function, such that PM2.5 levels below this threshold are not expected to produce adverse health effects. We hypothesize that measurement error may affect the recognition of a threshold in long-term cohort epidemiological studies. This study conducts what is, to the best of our knowledge, the first simulation of the effects of measurement error on the statistical models commonly employed in long-term cohort studies. We test the degree to which classical-type measurement error, such as differences between the true population-weighted exposure level to a pollutant and the observed measures of that pollutant, affects the ability to statistically detect a C-R threshold. The results demonstrate that measurement error can obscure the existence of a threshold in a cohort study's C-R function for health risks from chronic exposures. With increased measurement error the ability to statistically detect a C-R threshold decreases, and both the estimated location of the C-R threshold and the estimated hazard ratio associated with PM2.5 are attenuated. This result has clear implications for determining appropriate air quality standards for pollutants.