times used, especially when epidemiological evidence is lacking (EPA 1997). The first part is a primary analysis, which produces numerical estimates or projections of each health benefit in the form of a probability distribution. This analysis incorporates only one source of uncertainty: the random sampling error in the epidemiological study or studies that provide the estimated concentration-response function. The second part of the uncertainty assessment is an array of ancillary analyses in which many other sources of uncertainty are considered in several disparate ways.

Primary Uncertainty Analysis

The primary uncertainty analysis produces a numerical estimate of each health benefit EPA believes to be plausible for a particular regulatory action. Typically, the benefit is expressed as a number of deaths or cases of an adverse health event that will be avoided in the United States in a future year if some regulatory action is taken. The year chosen is often far into the future to allow for the action to be implemented, for the implementation to result in exposure reductions, and for the reduced exposures to result in health benefits. In the Tier 2 analysis, the chosen year was 2030.

EPA reports each numerical health benefit estimate in the form of a probability distribution and summarizes the distribution by reporting its mean and 5th and 95th percentiles. The distribution assigns a nonzero probability to every possible value including the null hypothesis of no benefit. The mean of the distribution is interpreted as the expected benefit based upon the analysis performed. The 5th and 95th percentiles are defined as a credible range within which the true benefit value will lie with a 90% probability (EPA 1999a, p. 3-26).

The solid line in Figure 5-1 shows the probability distribution from EPA’s primary analysis of avoided mortality for the proposed Tier 2 rule for the year 2030. The mean of the distribution (which is also the median and the 50th percentile) is 4,307 avoided deaths among persons 30 years of age and older. The 5th and 95th percentiles are 2,671 and 5,891 avoided deaths, respectively (EPA 1999a, p. 6-3).

The probability models in EPA’s primary analyses incorporate only one of the many sources of uncertainty in these analyses: the random sampling error in the estimated concentration-response function derived from either an epidemiological study or a meta-analytic or pooled aggregation of two or

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