Revising the National Ambient Air Quality Standards: The integration of science and policy

Under the Clean Air Act, Congress granted discretionary decision making authority to the Administrator of the Environmental Protection Agency (EPA). This discretionary authority involves setting standards to protect the public's health with an "adequate margin of safety" based on current scientific knowledge. The Administrator of the EPA is usually not a scientist, and for the National Ambient Air Quality Standard (NAAQS) for particulate matter (PM), the Administrator faced the task of revising a standard when several scientific factors were ambiguous. These factors included: (1) no identifiable threshold below which health effects are not manifested, (2) no biological basis to explain the reported associations between particulate matter and adverse health effects, and (3) no consensus among the members of the Clean Air Scientific Advisory Committee (CASAC) as to what an appropriate PM indicator, averaging period, or value would be for the revised standard. ^ This project recommends and demonstrates a tool, integrated assessment (IA), to aid the Administrator in making a public health policy decision in the face of ambiguous scientific factors. IA is an interdisciplinary approach to decision making that has been used to deal with complex issues involving many uncertainties, particularly climate change analyses. Two IA approaches are presented; a rough set analysis by which the expertise of CASAC members can be better utilized, and a flag model for incorporating the views of stakeholders into the standard setting process. ^ The rough set analysis can describe minimal and maximal conditions about the current science pertaining to PM and health effects. Similarly, a flag model can evaluate agreement or lack of agreement by various stakeholder groups to the proposed standard in the PM review process. ^ The use of these IA tools will enable the Administrator to (1) complete the NAAQS review in a manner that is in closer compliance with the Clean Air Act, (2) expand the input from CASAC, (3) take into consideration the views of the stakeholders, and (4) retain discretionary decision making authority. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^