(CASAC) Peer Review of EPA's Integrated Science Assessment

confidence limits for the ED50 in this case) The Linn et al. data also indicate a slightlygreater amount of interindividual variability than those of Horstman—a geometricstandard deviation of 2.85 with 90% confidence limits of 2.10-5.75. Together, if weassume a lognormal distribution of individual thresholds as before, the central estimate ofinterindividual variability and the central estimate of the ED50 from the Linn et al datawould indicate that 95% of exercising asthmatics should have this response at between104 and 3250 ppb. Unfortunately, there is reason to doubt that the distribution isperfectly lognormal—a goodness of fit test indicates a barely statistically significantdeparture of the data from expectations from a lognormal model at P < .05.There are a couple of ways to combine these data for an aggregate analysis. One simpleway that I did was to add the Horstman observations where they would fall in thehistogram-like data from the Linn et al. papers. When this is done, the ED50 indicatedby the combined data is just under 700 ppb and the geometric standard deviation forinterindividual variability is 2.52 with 90% confidence limits of 2.01-3.83. The revisedcentral estimate ED50, combined with the central estimate of the geometric standarddeviation would indicate that 90% of exercising asthmatics should respond between 150and 320 ppb. Again, however, the combined data depart from expectations of alognormal distribution model at a P level of slightly less than 0.02. In further explorationof the combined data (including experiments of other research groups) I wouldrecommend an attempt to fit a mixture of two lognormal distributions. I could notattempt this in this analysis, however because a mixture of two lognormals involvesestimation of 5 parameters (two means, two standard deviations and a parameter tomeasure the fraction of the population that belongs to each component distribution) andthe Linn et al. data are aggregated only into 4 ranges. There is likely to be an infinitenumber of perfect-fit solutions when one uses only 4 data points to estimate 5 parameters.If it is of interest to EPA staff, I will provide the Excel spreadsheet showing thesecalculations.ReferencesHaas, C. N. "Dose Response Analysis Using Spreadsheets" Risk Analysis 14:1097-1100(1994).Hattis, D., Russ, A., Goble, R., Banati, P., and Chu, M. “Human InterindividualVariability in Susceptibility to Airborne Particles,” Risk Analysis, Vol. 21(4), pp. 585-599 (2001).16