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.

Integrated Uncertainty Analysis for Ambient Pollutant Health Risk Assessment: A Case Study of Ozone Mortality Risk.

The U.S. Environmental Protection Agency (EPA) uses health risk assessment to help inform its decisions in setting national ambient air quality standards (NAAQS). EPA's standard approach is to make epidemiologically-based risk estimates based on a single statistical model selected from the scientific literature, called the "core" model. The uncertainty presented for "core" risk estimates reflects only the statistical uncertainty associated with that one model's concentration-response function parameter estimate(s). However, epidemiologically-based risk estimates are also subject to "model uncertainty," which is a lack of knowledge about which of many plausible model specifications and data sets best reflects the true relationship between health and ambient pollutant concentrations. In 2002, a National Academies of Sciences (NAS) committee recommended that model uncertainty be integrated into EPA's standard risk analysis approach. This article discusses how model uncertainty can be taken into account with an integrated uncertainty analysis (IUA) of health risk estimates. It provides an illustrative numerical example based on risk of premature death from respiratory mortality due to long-term exposures to ambient ozone, which is a health risk considered in the 2015 ozone NAAQS decision. This example demonstrates that use of IUA to quantitatively incorporate key model uncertainties into risk estimates produces a substantially altered understanding of the potential public health gain of a NAAQS policy decision, and that IUA can also produce more helpful insights to guide that decision, such as evidence of decreasing incremental health gains from progressive tightening of a NAAQS.

Uncertainty in the estimated risk of lung function decrements owing to ozone exposure.

In the most recent Health Risk and Exposure Assessment (HREA) for Ozone, the US Environmental Protection Agency (EPA) used an exposure-response function estimated on clinical data to calculate the risk of lung function decrements in a series of population-level simulations. These risk estimates are subject to both statistical uncertainty (which arises because the exposure-response function was estimated on a sample of clinical observations) and model uncertainty (which arises because there are different plausible ways to model the relationship between ozone exposure and lung function decrement). In this paper, we describe and apply an approach that allows us to estimate the statistical uncertainty present in these risk estimates. In the example we consider, statistical uncertainty produces 95% confidence intervals on the risk estimates that in some cases include zero, suggesting that in these cases we cannot exclude the possibility of no health risk to lung function owing to ozone exposure. Model uncertainty is also apparent, with a plausible alternative model specification leading to a substantially different distribution of risk.

Do local landmark bridges increase the suicide rate? An alternative test of the likely effect of means restriction at suicide-jumping sites.

A number of recent studies have examined the effect of installing physical barriers or otherwise restricting access to public sites that are frequently used for suicides by jumping. While these studies demonstrate that barriers lead to a reduction in the number of suicides by jumping at the site where they are installed, thus far no study has found a statistically significant reduction in the local suicide rate attributable to a barrier. All previous studies are case studies of particular sites, and thus have limited statistical power and ability to control for confounding factors, which may obscure the true relationship between barriers and the suicide rate. This study addresses these concerns by examining the relationship between large, well-known bridges ("local landmark" bridges) of the type that are often used as suicide-jumping sites and the local suicide rate, an approach that yields many more cases for analysis. If barriers at suicide-jumping sites decrease the local suicide rate, then this implies that the presence of an unsecured suicide-jumping site will lead to a higher local suicide rate in comparison to areas without such a site. The relationship between suicides and local landmark bridges is examined across 3116 US counties or county equivalents with negative binomial regression models. I found that while exposure to local landmark bridges was associated with an increased number of suicides by jumping, no positive relationship between these bridges and the overall number of suicides was detected. It may be impossible to conclusively determine if barriers at suicide-jumping sites reduce the local suicide rate with currently available data. However, the method introduced in this paper offers the possibility that better data, or an improved understanding of which potential jumping sites attract suicidal individuals, may eventually allow researchers to determine if means restriction at suicide-jumping sites reduces total suicides.