# A Risk Assessment for Ozone Regulation Based on Statistical Rollback
## 1 Introduction  
Regulating high ozone levels is essential as exposure to ozone can affect the risk of respiratory diseases or related deaths. Tropospheric ozone, also known as ground-level ozone, is one of the main harmful air pollutants that can cause adverse health effects. Many areas in the United States have been observed to exceed the current ozone National Ambient Air Quality Standards (NAAQS). Elevated ozone concentrations have also been a growing concern for rapidly developing nations where emissions of ozone precursors have been risen from expanding transportation networks [1]. Recently, U.S. EPA promulgated a new ozone NAAQS as 0.070 ppm (parts per million) and this change has prompted studies on the effects of the new ozone standard [2, 3, 4]. To investigate how different ozone NAAQS affect public health and welfare can be of great interest in epidemiologic studies, toxicological studies, or controlled human exposure studies. Based on the reviews of the air quality criteria for ozone (O\({}_{3}\)) and related photochemical oxidants and the NAAQS for O\({}_{3}\), a modification in the current ozone regulatory standards provides the required protection for public health and welfare (see also [5, 6]). [PERSON] et al. [7, 8] disapproved of the EPA's scientific reviews reporting that designations based on air quality data from 2006 to 2008 would be effective in air quality data to take effect in 2010 for the 2007 8-h ozone standard. Therefore, it would be interesting to investigate whether the current regulations are sufficiently stringent to prevent respiratory-related mortality or not.  
To assess how changes in the ozone regulations affect mortality, ground-level ozone must be adjusted by strengthening the air quality standards. Although rollback functions, namely, air quality adjustment procedures proposed by the EPA [9], can be useful for adjusting the ozone process, it cannot introduce sufficient variability in the rollback adjustment as the adjustment is deterministic and the EPA regulatory standards are based on the average of three consecutive years' AQI values. Thus, we consider a parametric rollback approach with quantile matching method to allow for uncertainty in the rollback procedureTo conduct the risk assessment, we consider hierarchical Bayesian models that provide uncertainty quantification for relevant parameters to predict the potential effects of different regulatory ozone standards. We also describe some variations in the results under different modeling assumptions. We analyze databases from the National Morbidity, Mortality, and Air Pollution Study [10] that is designed to study the public health effects of air pollutants. The Health Effects Institutes began this study with researchers from Johns Hopkins and Harvard University in 1996. The NMMAPS database contains 108 U.S. urban areas from 1987 to 2000 where one can build a multisite time-series model of ozone and mortality simultaneously with meteorology information such as temperature or dew point and air pollution (O\({}_{3}\), PM\({}_{10}\), SO\({}_{2}\), NO\({}_{2}\), and CO) (see also [11]).  
The focus of this paper is on statistical approaches to describe how the new ozone regulations affect mortality. We shall describe our results that mortality decreases as limits of acceptable ozone level get lower through the statistical rollback approach.