One of the Goals of the CDEPAT report was to provide dose-response information for various biological effects associated with acute exposure to chemical agents under investigation. Specifically, estimates of the proportion of individuals at risk as a function of exposure were based on log-probit analysis. In this chapter, the subcommittee evaluates this procedure for deriving human-toxicity estimates.
Log-probit analysis assumes that the density distribution among individuals exposed at the exposures that produce a specified biological effect (for example, death or some incapacitating condition) can be described by a lognormal distribution. In other words, it assumes that the distribution of the log-exposure that produces an effect among individuals is normal. The lognormal distribution is a common and generally accepted approach for describing biological effects. Other statistical distributions could be selected and used, but many notable differences would likely not be observed because of the small numbers of exposure groups and individuals or animals
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--> 8— Evaluation of the Risk-Estimation Procedures Used in the CDEPAT Report One of the Goals of the CDEPAT report was to provide dose-response information for various biological effects associated with acute exposure to chemical agents under investigation. Specifically, estimates of the proportion of individuals at risk as a function of exposure were based on log-probit analysis. In this chapter, the subcommittee evaluates this procedure for deriving human-toxicity estimates. Use of Log-Probit Analysis Log-probit analysis assumes that the density distribution among individuals exposed at the exposures that produce a specified biological effect (for example, death or some incapacitating condition) can be described by a lognormal distribution. In other words, it assumes that the distribution of the log-exposure that produces an effect among individuals is normal. The lognormal distribution is a common and generally accepted approach for describing biological effects. Other statistical distributions could be selected and used, but many notable differences would likely not be observed because of the small numbers of exposure groups and individuals or animals
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--> generally used per exposure. Thus, the subcommittee accepts the log-probit analysis approach as reasonable for these types of data. Use of the ECt50 The ECt50, expressed as milligrams per cubic meter times exposure duration, is the effective vapor exposure at which 50% of the individuals exhibit a specified biological effect. The ECt50 is the concentration that causes an effect in 50% of the population (that is, the median exposure of the distribution). The ECtx is the exposure causes an effect in x% of the population, a percentage obtained by integrating the lognormal density distribution until the cumulative distribution is x%. The ECt50 is the median of the Iognormal distribution. Integrating the area under the lognormal density distribution up to a specified log-exposure gives the cumulative lognormal distribution (that is, the proportion of individuals that show an effect at or below that exposure). The standard deviation (SD) of the lognormal distribution is the reciprocal of the slope of the probit log-exposure response line. The probit log-exposure response line is obtained by converting the percentage of responders to a probit for each exposure group. For a lognormal distribution, this provides a straight-line relationship between probits and log-exposure that can be estimated by weighted linear-regression techniques. This line provides point (best) estimates of risk as a function of log-exposure to be used in risk-benefit decisions. For example, a slope of 5 indicates that a reduction of exposure by a factor of 10 (log 10 = 1 unit on a log-exposure scale) corresponds to a shift of 5 SDs. If ECt50 = 100 mg-min/m3, 50% of the individuals would exhibit the specified biological effect at that dose. At ECt 50 ÷ 10 = 100 ÷ 10 = 10 mg-min/m3, the proportion of individuals responding at 5 SDs below the mean of a lognormal distribution is 3 × 10-7. At ECt50 ÷ 2 = 100 ÷ 2 = 50 mg-min/m3, the log-exposure is log(50) = 1.70. With a probit slope of 5, the SD of log-exposure is 1 ÷ 5 = 0.20. Thus, ECt50 ÷ 2 is (log100 -log50) ÷ 0.20 = (2.00-1.70) ÷ 0.20 = 1.5 SDs below the mean, at which exposure 6.7% of the population of individuals are expected to respond. Therefore, a reduction in the exposure by a factor of 2 changes the risk from 50% to 6.7%. Similarly, an increase in the exposure by a factor of 2 to 2ECt50 = 200 mg-min/m3 increases the risk from 50% to 93.3%. With an uncertainty of a factor of 2 in the ECt50, the risk could vary from 6.7% to 93.3%.
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--> The above example demonstrates an inherent uncertainty in risk estimates for steep dose-response lines. In the CDEPAT report, the confidence limits on the ECt50s were often a factor of 2 (that is, ECt50 ÷ 2 to 2ECt50). For the above example, the estimated ECt50 could be 1.5 SDs above the true mean rather than at the geometric mean of the lognormal distribution. A log-exposure reduction of 1.645 SDs below the mean provides an estimate of the ECt5 (exposure corresponding to a 5% risk). If the estimated mean is actually 1.5 SDs above the true mean, the estimated exposure is 1.500-1.645 = -0.145 SDs from the true geometric mean. That exposure has a risk of 44.2% rather than the expected risk of 5%. The above example is illustrated in Figure 8-1. Suppose the ECt50 is estimated to be 60 mg-min/m3 and the estimate of the slope (percentage responding plotted on a probit scale vs. log-dose) is 5, as represented by the solid line in Figure 8-1. The ECt05 is estimated to be 28 mg-min/m3. Suppose, in fact, that the true ECt50 is lower by a factor of 2 and is 30 mg-min/m3. That discrepancy between the estimated and true value would not be uncommon for the available data. Assuming the same slope (or same SD), the true dose-response relationship is represented by the dashed line. Note that the true proportion of individuals affected at the estimated ECt50 is not 50% but 94%. Further, the true proportion of responders at the estimated ECt05 is 44% rather than 5%. Hence, small differences in exposure can result in large differences in the proportion of individuals affected. This is due to the steep dose-response lines for these agents. The above example does not take into account the uncertainty in the estimate of the slope. The slope is likely to be overestimated. The slope based on a homogenous group of inbred animals is likely to be steeper than the slope based on a group of heterogeneous individuals under battlefield conditions. Apart from that likelihood, the slope is expected to be overestimated 50% of the time because of random statistical variation. For the above example, suppose the ECt50 is estimated without error but the slope estimate is 7 rather than the true value of 5. Instead of the correct value of the ECt5 being 47 mg-min/m3, the estimate is 58 mg-min/m3 with a risk of 12% rather than 5%. Note that a relatively small change in concentration (47 mg-min/m3 to 58 mg-min/m3) results in a considerable change in risk (5% to 12%). With some human data available, exposure estimates of the ECt50 are probably within a factor of 2 of the true value. With this uncertainty and the steep dose-response curves observed, the true risk at the estimated ECt5 for humans can vary from nearly 1% to nearly 99%. The true risk at the
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--> Figure 8-1 Probit log-exposure (slope = 5). Estimated exposure response, solid line; true dose response, broken line. (a) True percent at estimated ECt50 is 94%. (b) True percent at estimated ECt5 is 44%. estimated ECt5 could vary from less than 1% to nearly 50%. With only sparse animal data, the uncertainty of exposure estimates might be as much
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--> as a factor of 10. Typically, uncertainty factors of 10 are used when extrapolating from animal-toxicity data to humans. The uncertainty of exposure and risk estimates should be estimated for critical biological effects. Use of Confidence Limits A shortcoming of the CDEPAT report is the failure to calculate confidence limits for the different exposures, such as ECt5 and ECt16. Point (best) estimates are needed to provide the best risk-benefit trade-offs, but the uncertainty of these estimates should be considered. Confidence intervals can be obtained for individual probit dose-response lines. The calculation of uncertainty becomes more complex when an average probit line is based on two or more sets of toxicity data. In that case, a central line might be chosen, as was done by CDEPAT for some of the estimates. If human data are not available, the line for the species most like humans may be selected. Various lines may be given more weight according to the quantity and quality of the data.