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Technical Comments on the 

Primary National Ambient Air Quality Standard for Sulfur Dioxide. 

Proposed Rule 

Docket No. EPA-HQ-OAR-2007-0352 

by 

Edmund A.C. Crouch, Ph.D. 

and 

Laura C. Green, Ph.D., D.A.B.T. 

Cambridge Environmental Inc. 

Cambridge, Massachusetts 

February 8, 2010 (Docket No. EPA-HQ-OAR-2007-0352-1061.1) 

Corrected April 6, 2010 

Note: Correction of an error in one spreadsheet results in a minor change in the numbers 

calculated in this analysis, specifically inTable 4, Table 5 and Table 6. This update contains 

corrected entries and corrected embedded spreadsheets (“sRaw_analysis_final 2.xls” and 

“Exposure distributions 2.xls” have been corrected). The error was in “sRaw_analysis_final 

2.xls” at DR-Analysis!AG13:AJ35, where the formulae used the exposure concentrations in DRAnalysis!AG38:AJ38 in place of the correct ones at DR-Analysis!AG12:AJ12. In addition, the 

paragraphs on page 24 describing the factors by which the EPA analysis is in error have been 

corrected to show the full ranges. 
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Table of Contents 

1. Executive summary..................................................................................................................... 3 

2. Introduction................................................................................................................................. 4 

3. The independence assumption is untenable................................................................................ 5 

4. The Agency miscalculated the total number of effects............................................................... 7 

5. Failure to incorporate corrections and additional data.............................................................. 15 

6. Updated calculations................................................................................................................. 15 

6.1. Short-period constancy of E100 evaluations ....................................................................... 16 

6.2. Independence of E100 evaluations over long periods ......................................................... 17 

6.3. Evaluation of population E100 distribution......................................................................... 18 

7. Effect of the Final REA errors on estimation of population effects ......................................... 21 

8. The RIA substantially underestimates the uncertainty in hospital admissions due to SO2 ...... 25 

9. The RIA co-benefits assessment is based entirely on an incorrect assumption........................ 26 

10. Erratum ................................................................................................................................... 29 

11. Addendum............................................................................................................................... 29 

12. Acknowledgement .................................................................................................................. 30 

13. References............................................................................................................................... 30 

14. Appendix: Calculations........................................................................................................... 32 
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1. Executive summary 

The Proposed Rule relies heavily on the Final REA. However, the Final REA provides estimates 

of potential health effects that are completely unreliable and not scientifically based. In Section 

3 we show that the fundamental assumption used in the Final REA to evaluate experimental data 

is incorrect. Under that assumption, the probability for the patterns seen in the subset of 

experimental data used in the Final REA is less than 1 in 10,000,000, and considering all 

available experimental data the probability for the patterns is less than 2 in 1,000,000,000. Such 

probabilities are so low that the assumption must be rejected. Even were the assumptions of the 

Final REA correct, the Final REA adds up the numbers incorrectly. In Section 4 we demonstrate 

the resultant substantial errors, using more detailed information from the computer runs used in 

the Final REA. Section 5 points out that the Final REA failed to take account of known errors in 

data entry, and failed to incorporate all available data. In Section 6 we update our previous 

demonstration of calculations using a correct basic assumption about the experimental data. In 

Section 7 we provide a corrected accounting for the case of transient exercise-adjusted relative 

sRaw increments of 100%. The bottom lines for number of events with this end point, taking 

account of both the incorrect assumptions and incorrect summations of the Final REA, are (see 

Table 5 and Table 6): 

 Scenario 

 As Is CS 99/50 99/100 99/150 99/200 99/250 98/200

Greene County Logistic 

Final REA 12500 12700 12500 12500 12500 12600 12600 12600

Best estimate of corrected results 1 49 0.1 1 5 11 22 18 

Green County Probit 

Final REA 1600 1800 1600 1600 1600 1600 1700 1700 

Best estimate of corrected results 0.4 30 0.03 0.5 2 6 12 10 

St. Louis Logistic 

Final REA 65700 167200 65200 68600 76200 88000 103600 99700

Best estimate of corrected results 103 27867 47 458 1649 3968 7677 6721 

St Louis Probit 

Final REA 9000 93300 8600 11100 17000 26400 39200 36000

Best estimate of corrected results 25 21577 9 175 844 2381 5094 4376 

Our calculations indicate that the probit model is approximately twice as likely as the logistic, 

based solely on the experimental data. Finally, although the Proposed Rule takes no account of 

the RIA, we argue in Sections 8 and 9 that the RIA calculations are substantially overconfident 

or just plain wrong. 
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2. Introduction 

These comments are directed at the Proposed Rule for the Primary National Ambient Air Quality 

Standard for Sulfur Dioxide (“Proposed Rule”), insofar as that proposed rule relies on the “Risk 

and Exposure Assessment to Support the Review of the SO2 Primary National Ambient Air 

Quality Standards: Final Report” (EPA-452/R-09-007, July 2009, EPA-HQ-OAR-2007-0352-

0033), hereinafter “Final REA.” A second draft version of the REA was previously entered in 

the Docket as EPA-HQ-2007-0352-0016 (“Draft REA”). 

The Proposed Rule relies heavily on the Final REA, and in particular it relies to a large extent on 

the numerical estimates of the number and fraction of asthmatics who might suffer an event 

consisting of a measurable transient decrement in lung function due to SO2 exposure. For the 

reasons given here, the REA does not provide reliable or scientifically justifiable estimates for 

these numbers or fractions. Because of the errors that we have identified, the Final REA 

overestimates the numbers of such lung function decrements by about a factor varying from 5 to 

69,000, and hence also the fraction of asthmatics potentially experiencing such events by the 

same factor. 

We provided technical comments on the Draft REA and entered them in the Docket at EPA-HQOAR-2007-0352-0031.1, Attachment 1 (“Our Comments”). We specifically commented on, 

inter alia: 

• Errors in data entry, 

• Failure to incorporate all available data, 

• The independence assumption underlying EPA’s analysis of raw data on the effects of 

SO2 on sRaw, and 

• A miscalculation that we identified in EPA’s summing up of the total number of effects. 

and we provided corrected estimates for the total numbers of potential events where exercising 

asthmatic individuals might experience increments in exercise-corrected sRaw of more than 

100% (see Our Comments for definitions of terms). 

Since those original technical comments, new copies of some of the handwritten raw data have 

been entered in the Docket, including individual data on an additional experiment (Linn et al., 

1983). In another Docket, (EPA-HQ-ORD-2006-0260-0036 and 0036.1 through 0036.5), EPA 

has now substantially improved the data entry (minor remaining errors that we identified in a 

subset of these data are given in another entry in this docket), confirmed the data entry errors we 

previously pointed out, and entered some of the new individual data in machine readable form. 

The Final REA, however, does not respond in any meaningful way to Our Comments, which we 

therefore incorporate here by reference to apply to the Final REA and to the Proposed Rule 

which relies on the Final REA. We also here augment those comments and provide some 

stronger arguments, based on material available to EPA prior to the Draft REA and now in the 

Docket. We further provide some comments on the Regulatory Impact Assessment (“RIA”) 
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included in the Docket at EPA-HQ-OAR-2007-0352-0048 and 0048.1 through 0048.8), although 

we recognize that the RIA was not used in developing the Proposed Rule. 

3. The independence assumption is untenable 

In Our Comments (Section 3, “Theoretical considerations”) we pointed out that the 

independence assumption1

 that is the basis for the analysis methodology used in the Draft and 

Final REA (in Appendix C) denies the existence of individual exposure-response curves that 

apply across different exposures in the experiments evaluated. We subsequently, however, 

demonstrated consistent dose-response curves between the two rounds of the Linn et al. (1987) 

experiment. The independence assumption of the Final REA necessarily denies the validity of 

the dose-response curves published by Horstman et al. (1986)2 and featured prominently on the 

cover page of EPA’s 1986 Staff Paper (EPA 1986). It would also necessarily deny the validity 

of the published distribution of E100 values3

 that Horstman et al. (1986) derived from those doseresponse curves, which distribution is prominently displayed on the cover page of the EPA 1994 

Staff Paper (EPA, 1994). The approach we took for analysis of the experimental data in Our 

Comments corresponds closely with that published by Horstman et al. (1986); we just 

augmented the technical approach to provide uncertainty estimates also. These factors alone 

should be sufficient to reject the independence assumption. 

Quite independently, we may examine the data themselves to see whether they are consistent 

with an independence hypothesis. Consider the case where the same set of individuals 

(numbering N) is exposed at different times to two different concentrations of SO2, with R1

responding at one dose and R2 at the second dose, where R2 ≥ R1 (interchange the doses if 

necessary so that this is true).4 The responders at the second dose define a partition of the N

individuals into two groups of size R2 and N−R2. Now partition the responders to the first dose 

into s1 who also responded to the second and s2 who did not, with s1+s2=R1. Under the 

independence hypothesis, the proportion of responders to the first dose who fall into the 

responder/non-responder groups at the second dose should simply be in proportion to the 

numbers in those responder/non-responder groups at the second dose. The probability for any 

particular pattern for s1 & s2 can thus be simply obtained by a counting argument, and in 

particular, the probability for a contrast as extreme or more extreme than the observed s1/R2

versus s2/(N−R2) can be obtained by such a counting argument. Indeed, this is just the counting 

argument required for the Fisher Exact test.5

 Alternative hypotheses, such as the existence of 

individual dose-response relationships, lead to extreme contrasts. In that case a responder at one 

 

1

 REA, Appendix C, page 3-5, “... we assumed a single response probability (for a given definition of response) for 

all individuals and treated the repeated exposures for a single subject as independent exposures in the binomial 

distribution.” 

2

 We incorporated the data used by Horstman et al. (1986) in our analysis; they are primarily those from Roger et al.

(1985), but also include data at 2 ppm that were omitted in the latter paper. 

3

 See Our Comments for notation. The PC(SO2) values defined by Horstman et al. (1986) correspond to what we 

call E100, the exposure causing 100% increase in exercise-adjusted relative sRaw. 4

 The precise definition of “response” is not needed for this argument, which applies to any well-defined response. 5

 The contrasts to be examined are all those of n1/R2 versus n2/(N−R2) subject to R2≥n1≥s1, N−R2≥n2≥0 with fixed 

n1+n2=s1+s2=R1, R2, and N. 
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dose should also respond at a higher dose, so that the contrast observed should be extreme — all 

responders at one dose will also respond at the higher dose (although introduction of variability 

may reduce the contrast). 

As an example, compare the 0.4 ppm and 0.6 ppm doses in round 1 of Linn et al. (1987). There 

were 40 subjects tested, of whom 10 at 0.4 ppm and 14 at 0.6 ppm responded with exerciseadjusted relative sRaw increments greater than 100% (the “response”). Of the 10 at 0.4 ppm 

who responded, 9 also responded at 0.6 ppm. So the contrast here is 9/14 versus 1/26. The 

probability (under the independence hypothesis) for such a contrast or one even more extreme is 

6.26 × 10−5

 (there is only one more extreme contrast in this case, 10/14 versus 0/26). Thus, 

based solely on round 1 of the Linn et al. (1987) experiment, it is possible to reject the 

independence hypothesis with very high confidence. 

Applying the same analysis to all the dose-response experiments available gives the results 

shown in Table 1.6 Individual experiments (as reported in different papers) on different subjects 

are independent of one another; and under the independence hypothesis so are the repeated 

exposures (at different concentrations) on the same subjects within each experiment. The 

probabilities for all independent contrasts may thus be multiplied to obtain the overall probability 

(under the independence hypothesis) for patterns as extreme or more extreme than observed for 

all experiments combined. For those experiments included in the Final REA (“Omit L83 and 

L87 Round 2” in Table 1) this probability is 2.26 × 10−8. Incorporating all available experiments 

(“Overall” in Table 1), it is 1.12 × 10−12. The independence hypothesis is thus rejected with 

virtual certainty; the data themselves are not consistent with the independence hypothesis as used 

in the Draft REA and the Final REA. 

Analysis of the experiments as though the observations corresponded to “independent exposures 

in the binomial distribution” (Final REA, Appendix C, page 3-5) thus has to be rejected in favor 

of an analysis that can account for the non-independence. We demonstrated such an analysis in 

Our Comments (and update it in Section 6, below), where we showed that the result is a 

substantially steeper estimate for the slope of the resulting population distribution for E100 (the 

exposure causing 100% increment in exercise-corrected relative sRaw) than obtained in the Draft 

REA and Final REA. Similar results can be expected for other increments in sRaw, and in 

decrements in FEV1. 

 

6

 See sheet “Independence assumption” in workbook “Table 3-1 Analyses 2.xls” (see Section 14). 
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Table 1 Probabilities evaluated under the independence hypothesis for observed patterns of 

response in dose-response experiments (L = Linn et al., R = Roger et al., 85 = 1985 etc.). 

Experiment Contrast Probability 

L83 0.2 ppm vs. 0.4 ppm 1.00E+00a

L83 0.4 ppm vs. 0.6 ppm 4.74E-02 

R85 0.25 ppm vs. 0.5 ppm 1.00E+00a

R85 0.5 ppm vs. 1 ppm 4.07E-02 

L87 Round 1 0.2 ppm vs 0.4 ppm 5.77E-02 

L87 Round 1 0.4 ppm vs. 0.6 ppm 6.26E-05 

L88 0.3 ppm vs. 0.6 ppm 3.47E-01 

L90 0.3 ppm vs. 0.6 ppm 4.43E-01 

L87 Round 2 0.2 ppm vs. 0.4 ppm 2.56E-01 

L87 Round 2 0.4 ppm vs. 0.6 ppm 6.48E-03 

Overall 1.78E-12 

Omit L83 & L87 Round 2 2.26E-08 

a In the implementation of the Fisher Exact test used for these calculations 

any case with s1/R2 ≤ s2/(N−R2) was assigned probability 1. This results 

in a slight overestimate for the overall probability.

4. The Agency miscalculated the total number of effects 

We pointed out in Our Comments (Section 5.2, “Overcount due to inappropriate binning”) that if 

the distribution of exposure concentrations was close to lognormal, as appeared plausible from 

previous experience, from examination of distributions of actual SO2 measurements available to 

us, and from the information provided in the Draft REA, then the calculation method illustrated 

in Table 3-2 of Appendix C of both the Draft REA and the Final REA (and in Table 9-2 of the 

main text in both cases) results in a substantial overestimate of the numbers of events. We now 

demonstrate conclusively, using the more detailed results of the APEX calculations used in the 

Draft REA and Final REA, that such overcounts definitely occur.7

Section 8.8.3 of the Final REA describes the adjustments made to estimate and model air quality 

(SO2 concentrations) for the various alternative scenarios examined. The assumption made is 

that the time pattern of relative SO2 concentrations is invariant and corresponds to the modeling 

performed for the “As is” scenario, only the absolute concentration changing between scenarios. 

The APEX modeling was therefore performed only once (for each of the four areas included in 

the examples; Greene County is treated as a single area, St. Louis as three areas, with the three 

 

7

 The results described in this Section may be found in the workbook “Exposure distributions 2.xls” (see Section 

14). 
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area results combined to provide the values shown in the Final REA) to estimate exposures, and 

the different scenarios obtained by scaling the concentration in the resultant exposure 

distributions. In practice, this meant that to obtain fixed bin sizes of multiples of 50 ppb for the 

different scenarios (as was the aim), a larger set of bins was used in the single APEX modeling 

run — Table 8-14 of the Final REA shows the bin edge concentrations used to correspond to 

multiples of 50 ppb in all the examined scenarios. 

As a result, the APEX model8

 was actually run with more bin edges even than indicated in Table 

8-14 of the Final REA — for Greene County, APEX was run with bin edges of 0, 14.4, 16.2, 

18.9, 20.3, 23.6, 27, 28.8, 31.4, 32.4, 37.7, 40.5, 43.2, 47.2, 48.6, 50, 54, 56.6, 57.6, 60.8, 62.9, 

64.8, 70.8, 72, 75.5, 81, 86.4, 94.3, 97.2, 100, 100.8, 101.3, 108, 113.2, 113.4, 115.2, 117.9, 

121.5, 125.8, 129.6, 132.1, 135, 141.5, 141.8, 144, 145.8, 150, 150.9, 157.2, 158.3, 162, 165.1, 

169.8, 172.7, 178.2, 182.3, 187.1, 188.7, 189, 194.4, 200, 201.5, 202.5, 207.5, 210.6, 212.3, 

215.9, 216, 220.1, 222.8, 226.4, 226.8, 230.3, 235.8, 243, 245.3, 250, 251.6, 259.2, 259.4, 263.3, 

264.1, 270, 283, 283.5, 297, 300, 301.9, 303.8, 306.6, 314.4, 324, 330.2, 345.9, 350, 351, 353.8, 

364.5, 377.3, 378, 400, 405, 408.8, 424.5, 432, 440.2, 445.5, 450, 471.7, 486, 500, 503.1, 518.8, 

526.5, 550, 566, 567, 600, 607.5, 613.2, 648, 650, 660.3, 700, 707.5, 729, 750, 754.7, 800, 810, 

849, 891, 943.3, 972, 1037.7, 1053, 1132, 1134, 1215, 1226.3, 1296, 1320.7, 1415, and 1509.3 

ppb, while for St. Louis APEX was run with bin edges of 0, 8, 10.6, 12.7, 13.3, 15.8, 16, 17.7, 

21.1, 21.2, 24, 25.3, 26.5, 31.7, 31.8, 32, 35.3, 38, 39.8, 40, 42.2, 42.4, 47.5, 48, 50, 50.7, 53, 56, 

63.3, 63.6, 64, 66.3, 70.7, 72, 74.2, 76, 79.2, 79.5, 80, 84.4, 84.8, 88, 88.3, 88.7, 92.8, 95, 95.4, 

96, 100, 101.3, 104, 105.6, 106, 110.8, 112, 114, 116.6, 119.3, 120, 123.7, 126.7, 127.2, 128, 

132.5, 137.8, 139.3, 141.3, 142.5, 145.8, 147.8, 148.4, 150, 152, 158.3, 159, 164.7, 168.9, 169.6, 

172.3, 174.2, 176.7, 177.3, 185.5, 190, 194.3, 198.8, 200, 202.7, 205.8, 211.1, 212, 221.7, 229.7, 

232.2, 237.5, 238.5, 247.3, 250, 253.3, 265, 274.4, 282.7, 285, 291.5, 295.6, 300, 316.7, 318, 

337.8, 344.5, 348.3, 350, 371, 380, 397.5, 400, 411.7, 424, 443.3, 450, 475, 477, 500, 506.7, 530, 

550, 570, 583, 600, 633.3, 636, 650, 689, 696.7, 700, 742, 750, 760, 795, 800, 823.3, 848, 886.7, 

950, and 1013.3 ppb. These values may be confirmed in the control files for the APEX model 

runs (from which they were copied), and in the corresponding output files. 

It is therefore possible to use all these bins to calculate numbers of events in every scenario, 

rather than summing up the relevant bins to examine just bins corresponding to 50 ppb multiples 

in each particular scenario before calculating the numbers of events. We provide in this 

document the example that corresponds exactly to Table 3-2 of Appendix C of the Final REA 

(Table 9-2 of the main text).9

 Table 2 duplicates Table 9-2 of the Final REA, but with no 

 

8

 The APEX model and all input and output files were provided by EPA upon request. In our opinion these model 

files should have been provided either in the Docket or readily available on the EPA web site. The APEX model 

used is not that available on EPA’s web site, but is a modified version. We do not have the time or budget available 

for review of the model or its modifications. 

9

 This example calculation is in the worksheet “St. Louis” in workbook “Exposure distributions 2.xls.” The 

corresponding calculations for Table 4-1 of Appendix C of the Final REA are included in the workbook “Exposure 

distributions 2.xls” in worksheets “Greene” and “St. Louis” (see Section 7 for summary results, and Section 14 for 

the workbook). 
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rounding of the output of APEX10 and, as in Table 9-2 of the REA, summing results of APEX 

into the bins shown (50 ppb multiples) prior to calculating the number of events.11 Table 3 

shows exactly the same results, but maintaining all the bins calculated in APEX, as adjusted for 

this scenario (it is the 99/100 scenario for St. Louis; for this scenario the Final REA assumes that 

the ambient concentration would be 1.579 times that estimated for the “as is” scenario12). 

Table 2 Duplication of Table 9-2 of the Final REA, using exact output of the APEX model (no 

rounding). 

SO2 Exposure Bin (ppb) 

Lower 

Bound 

Upper 

Bound Midpoint 

Number of

Exposures

Probability of 

Response at Midpoint

SO2 Level 

Expected Number of

 Occurrences of Lung

 Function Response 

0 50 25 16519000 0.00406 67067.1 

50 100 75 136621 0.02334 3188.7 

100 150 125 15760 0.05162 813.5 

150 200 175 3825.5 0.08563 327.6 

200 250 225 1051.4 0.123 129.3 

250 300 275 413.8 0.1622 67.1 

300 350 325 175.97 0.2021 35.6 

350 400 375 83.54 0.2419 20.2 

400 450 425 30.622 0.2806 8.6 

450 500 475 23.024 0.3183 7.3 

500 550 525 7.549 0.3543 2.7 

550 600 575 0 0.3885 0.0 

600 650 625 0 0.4209 0.0 

650 700 675 7.595 0.4515 3.4 

700 750 725 0 0.466 0.0 

750 800 775 0 0.4938 0.0 

Total number of exposures 16677000 Expected number 

of occurrences 71671.2 

 

10 It is strictly incorrect to round the results from APEX, as was done in the Final REA, before doing subsequent 

calculations. However, the errors involved are small. 

11 The calculation of the number of events involves approximating the exposure for each bin as being the 

concentration at the center of the bin; this is where the problem arises. 

12 The concentration multipliers derived from Table 8-14 of the Final REA for the various scenarios are shown in 

worksheet “Factors” of workbook “Exposure distributions 2.xls” (see Section 14). 
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Table 3 Re-evaluation of Table 9-2 of the Final REA, using all available bins in the output of the 

APEX model (no rounding; the exposure range is truncated after the last non-zero number of 

exposures). 

SO2 Exposure Bin (ppb) 

Probability of 

Response at Midpoint

SO2 Level 

Expected Number of

Occurrences of Lung

Function Response 

Lower 

Bound 

Upper 

Bound Midpoint 

Number of

Exposures

 

0.0 12.6 6.3 13787600 0.0004446 6130.3 

12.6 16.7 14.7 1088100 0.001728 1879.8 

16.7 20.1 18.4 525300 0.002481 1303.4 

20.1 21.0 20.5 116100 0.002959 343.5 

21.0 24.9 23.0 346200 0.003545 1227.3 

24.9 25.3 25.1 20700 0.004087 84.6 

25.3 27.9 26.6 155000 0.004486 695.3 

27.9 33.3 30.6 208600 0.005622 1172.8 

33.3 33.5 33.4 4600 0.006456 29.7 

33.5 37.9 35.7 108400 0.007178 778.1 

37.9 39.9 38.9 37850 0.008246 312.1 

39.9 41.8 40.9 29060 0.008924 259.3 

41.8 50.1 45.9 91490 0.01074 983.1 

50.1 50.2 50.1 1340 0.01234 16.5 

50.2 50.5 50.4 2670 0.01244 33.2 

50.5 55.7 53.1 35560 0.01354 481.4 

55.7 60.0 57.9 21040 0.01550 326.2 

60.0 62.8 61.4 11480 0.01704 195.6 

62.8 63.2 63.0 1370 0.01774 24.3 

63.2 66.6 64.9 11540 0.01859 214.5 

66.6 66.9 66.8 980 0.01945 19.1 

66.9 75.0 71.0 20750 0.02141 444.2 

75.0 75.8 75.4 1830 0.02354 43.1 

75.8 78.9 77.4 5340 0.02452 130.9 

78.9 80.1 79.5 1770 0.02559 45.3 

80.1 83.7 81.9 5270 0.02679 141.2 

83.7 88.4 86.1 5360 0.02897 155.3 
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88.4 99.9 94.2 10321 0.03335 344.2 

99.9 100.4 100.2 291 0.03671 10.7 

100.4 101.1 100.7 369 0.03702 13.7 

101.1 104.7 102.9 2221 0.03824 84.9 

104.7 111.6 108.2 3388 0.04133 140.0 

111.6 113.7 112.7 868 0.04401 38.2 

113.7 117.2 115.4 1347 0.04568 61.5 

117.2 120.0 118.6 858 0.04761 40.8 

120.0 125.1 122.5 1610 0.05006 80.6 

125.1 125.5 125.3 123 0.05179 6.4 

125.5 126.3 125.9 244 0.05219 12.7 

126.3 133.3 129.8 1657 0.05466 90.6 

133.3 133.9 133.6 146 0.05710 8.3 

133.9 138.9 136.4 1028 0.05895 60.6 

138.9 139.4 139.2 62 0.06077 3.8 

139.4 140.1 139.7 106 0.06114 6.5 

140.1 146.5 143.3 1020 0.06350 64.8 

146.5 150.0 148.3 422 0.06684 28.2 

150.0 150.6 150.3 107 0.06824 7.3 

150.6 151.6 151.1 169 0.06878 11.6 

151.6 157.9 154.7 712 0.07127 50.7 

157.9 159.9 158.9 215 0.07416 15.9 

159.9 164.2 162.1 444 0.07637 33.9 

164.2 166.7 165.5 155 0.07876 12.2 

166.7 167.4 167.1 45 0.07987 3.6 

167.4 174.9 171.2 574 0.08279 47.5 

174.9 176.8 175.9 99.4 0.08619 8.6 

176.8 180.0 178.4 255.3 0.08802 22.5 

180.0 184.1 182.1 276.1 0.09066 25.0 

184.1 188.4 186.2 268.6 0.09372 25.2 

188.4 189.5 188.9 45.8 0.09570 4.4 

189.5 195.3 192.4 230.4 0.09827 22.6 

195.3 200.1 197.7 228.9 0.1022 23.4 

200.1 200.8 200.5 15.3 0.1043 1.6 

200.8 202.1 201.5 31.5 0.1050 3.3 
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202.1 209.2 205.7 208 0.1082 22.5 

209.2 217.6 213.4 213.5 0.1141 24.4 

217.6 220.0 218.8 38.7 0.1182 4.6 

220.0 223.1 221.5 91.5 0.1203 11.0 

223.1 225.0 224.1 15.5 0.1222 1.9 

225.0 230.2 227.6 144.9 0.1250 18.1 

230.2 233.4 231.8 76.5 0.1282 9.8 

233.4 234.3 233.8 23 0.1298 3.0 

234.3 236.8 235.6 38.7 0.1312 5.1 

236.8 240.0 238.4 38.5 0.1334 5.1 

240.0 250.0 245.0 115.8 0.1385 16.0 

250.0 251.1 250.5 0 0.1429 0.0 

251.1 260.1 255.6 99.1 0.1468 14.6 

260.1 266.7 263.4 61 0.1530 9.3 

266.7 267.8 267.2 23.6 0.1561 3.7 

267.8 272.1 269.9 46 0.1582 7.3 

272.1 275.1 273.6 54.17 0.1611 8.7 

275.1 279.0 277.0 23.08 0.1639 3.8 

279.0 280.0 279.5 0 0.1658 0.0 

280.0 292.9 286.4 91.37 0.1714 15.7 

292.9 300.0 296.5 15.48 0.1794 2.8 

300.0 306.8 303.4 30.36 0.1849 5.6 

306.8 313.9 310.3 46.33 0.1905 8.8 

313.9 315.8 314.8 7.5 0.1941 1.5 

315.8 320.1 317.9 0 0.1966 0.0 

320.1 325.0 322.5 15.44 0.2002 3.1 

325.0 333.3 329.1 30.29 0.2055 6.2 

333.3 334.7 334.0 0 0.2094 0.0 

334.7 350.1 342.4 46.05 0.2161 10.0 

350.1 362.7 356.4 15.14 0.2272 3.4 

362.7 366.6 364.7 7.55 0.2338 1.8 

366.6 375.0 370.8 23.02 0.2386 5.5 

375.0 376.6 375.8 7.59 0.2426 1.8 

376.6 390.5 383.5 7.54 0.2486 1.9 

390.5 394.7 392.6 22.7 0.2557 5.8 
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394.7 400.0 397.3 0 0.2594 0.0 

400.0 418.4 409.2 23.022 0.2686 6.2 

418.4 433.3 425.8 7.6 0.2814 2.1 

433.3 446.4 439.8 0 0.2921 0.0 

446.4 450.0 448.2 0 0.2984 0.0 

450.0 460.3 455.1 7.551 0.3036 2.3 

460.3 466.7 463.5 7.878 0.3098 2.4 

466.7 473.7 470.2 0 0.3148 0.0 

473.7 500.1 486.9 7.595 0.3270 2.5 

500.1 502.1 501.1 0 0.3373 0.0 

502.1 533.4 517.7 7.549 0.3492 2.6 

533.4 544.0 538.7 0 0.3638 0.0 

544.0 550.0 547.0 0 0.3695 0.0 

550.0 552.6 551.3 0 0.3725 0.0 

552.6 585.8 569.2 0 0.3846 0.0 

585.8 600.0 592.9 0 0.4002 0.0 

600.0 627.6 613.8 0 0.4137 0.0 

627.6 631.6 629.6 0 0.4237 0.0 

631.6 650.1 640.8 0 0.4306 0.0 

650.1 669.5 659.8 7.595 0.4422 3.4 

669.5 700.0 684.7 0 0.4570 0.0 

700.0 710.5 705.2 0 0.4688 0.0 

Total number of exposures 16677000 Expected number 

of occurrences 19150.2 

To obtain Table 3 we had to estimate the probability corresponding to each bin. We used a 

logistic curve that matched the values used in Table 2.13 That logistic has parameters 

β = −0.43724377, γ = −1.610183412 (using the notation of Appendix C of the Final REA, with 

concentrations expressed in ppm). 

 

13 See workbook “Fit_EPA_curves,” Section 14. Strictly, the probabilities may not be from a single logistic, since 

the values used in Table 3-2 of Appendix C of the Final REA are supposed to be the mean values from a probability 

distribution. However, the deviation from a single logistic are smaller than the uncertainties involved in estimating 

the mean values for Table 3-2 of Appendix C of the Final REA. As explained in Footnote 13 of Post and Mahoney 

(2009), the values shown in Table 3-2 differ slightly from those given in Table 4-1 of Appendix C of the Final REA 

because mean values were re-calculated after Table 3-2 was constructed, and the difference is supposedly due to the 

uncertainties of calculation. The major difference, however (although not mentioned in Post and Mahoney, 2009), 

arises because Table 4-1 uses the median estimate not the mean estimate. Nevertheless, all these differences are 

small compared with the errors we are pointing out. 
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As can be seen, the calculation in Table 2 yields an estimate (rounded) of 71,700 occurrences, in 

agreement with Table 9-2 of the Final REA, whereas the more accurate calculation of Table 3 

yields an estimate of 19,150 occurrences, a factor 3.74 difference. This was entirely to be 

expected based on the discussion in Our Comments. Examination of Table 2 and Table 3 shows 

that the overestimate in the former occurs because of the assignation of a concentration of 25 ppb 

to most of the exposures (those in the lowest bin, from 0 to 50 ppb), whereas in fact most of the 

exposures in the first 50 ppb bin are at concentrations much lower than 25 ppb. The same 

problem occurs with all the calculations of expected numbers of occurrences in the Final REA, 

and occurs even assuming everything else in the Final REA is correct (see Section 7 for the 

results of corresponding calculations for Table 4-1 of Appendix C of the Final REA). And the 

same problem can be expected to affect the calculations of other end points in the Final REA 

(200% increment in exercise-adjusted relative sRaw, and the FEV1-related end points). 

The most detailed results from APEX demonstrate that the number of exposures versus 

concentration follows a distribution that is almost exactly lognormal over the range that can be 

examined (Figure 1 shows the distribution for St. Louis; Greene County is shown in Figure 6). 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

234567

ln(concentration/ppb)

Normal ordinate

Figure 1 Cumulative distribution of number of exposures versus natural logarithm of 

concentration for St. Louis — APEX estimates. The dotted line is a lognormal distribution fitted 

to these results. 
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If this distribution continues to lower exposures, as we consider highly likely, then even the 

calculation shown in Table 3 slightly overestimates the number of events in the lowest bin — 

assuming a perfect lognormal distribution (a fit to this distribution gives it a median of 3.209 

ppb, and the distribution of logarithms of concentration has standard deviation 0.9693), the 

number of events is 17,400.14

5. Failure to incorporate corrections and additional data 

The Final REA failed to incorporate the data entry corrections that were pointed out in Our 

Comments and confirmed by subsequent EPA investigation (EPA-HQ-ORD-2006-0260-0036). 

The justification given in the Final REA (page 326-327), prior to a full investigation of the 

possible errors, was that the changes we indicated would only make small differences to the 

percentages of responders. No attempt was apparently made to estimate the effect on 

uncertainties or the effect on the estimates of numbers of occurrences expected, although this 

effect does indeed turn out to be small. 

Moreover, the Final REA (indeed, even the Draft REA) did not attempt to incorporate all the 

available data. The Draft REA omitted any consideration of round 2 of the Linn et al. (1987) 

experiments, even though those data were available at the time. Table 3-1 of Appendix C of the 

Draft REA and the Final REA contains 334 samples suitable for analysis with (for an exercisecorrected sRaw increment of 100%) 99 positive results. Round 2 of Linn et al. (1987) would 

have added another 120 samples with 27 positive results; a substantial addition if the 

independence assumption were correct. The Final REA also omitted to take account of the 

additional information available on the experiments of Linn et al. (1983) that became available 

between the Draft REA and Final REA, another 69 samples with 14 positive results. The Final 

REA thus omits about 36% of the samples and 29% of the positive results (for an exercisecorrected sRaw increment of 100%). 

These omissions do not substantially change the estimated results, but incorporating them is very 

simple, and would aid in reducing the substantial uncertainties that remain. 

6. Updated calculations 

The additional data entry by EPA (in EPA-HQ-ORD-2006-0260-0036 and 0036.1 through 

0036.5), and the additional data (in EPA-HQ-OAR-2007-0352-0038 and 0038.1 through 0038.8) 

allowed us to correct a few data entry errors of our own, fully include Round 2 of Linn et al. 

(1987), and include the Linn et al. (1983) experiment in the analysis reported in Our Comments. 

The following summarizes the results, which correct the errors in the Final REA identified in 

Our Comments and here. Notation and terminology corresponds to those defined in Our 

Comments — we examine only the case of exposures resulting in 100% increment in exercisecorrected relative sRaw (E100), since this is the most sensitive end point considered. The same 

considerations apply to all the other end points examined in the Final REA. 

 

14 See Section 11 for the formula required for this calculation. 
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6.1. Short-period constancy of E100 evaluations 

Figure 2 shows the comparison of E100 estimates for Round 1 and Round 2 of Linn et al. (1987), 

for all 40 subjects (previously we could include only 35 of them).15 This demonstrates the shortterm constancy of E100 estimates, as discussed in Our Comments, for all but one subject. The 

lack of constancy for one subject shows that even in the relatively short term subjects can 

change, as we previously demonstrated for longer periods (see also Section 6.2), but for any 

single experiment we still expect to be able to demonstrate individual dose-response curves (the 

measurements are clearly not independent as assumed in the Final REA). 

0.1

1

10

100

0.1 1 10 100

E100 (ppm) Round 1

E100 (ppm) Round 2

Figure 2 Comparison of E100 estimates in Round 1 and Round 2 of Linn et al. (1987). 

Confidence intervals are approximate ±1 standard deviation (estimated by a change of 0.5 in 

profile loglikelihood). 

 

15 The calculations for this Section are in workbook “Within study replicates 2.xls”, see Section 14. 
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6.2. Independence of E100 evaluations over long periods 

The additional data available allow adding (to the analysis we performed in Our Comments) 

another two subjects who took part in different experiments (Figure 3; only Round 1 of Linn et 

al., 1987 was included in these comparisons).16 There is no change in interpretation from Our 

Comments. Three subjects (# 297, # 608, and # 611) were each tested in three experiments (Linn 

et al., 1983; Linn et al., 1987; and Linn et al., 1988). For two of these subjects the estimated 

E100 was similar for all three experiments (#297: 0.40, 0.39, and 0.24 ppm; # 608: 0.57, 0.34, and 

0.60 ppm). However, subject 611 showed a response in Linn et al. (1983) with an E100 of about 

0.45 ppm, no response in Linn et al. (1987) Round 1 and Linn et al. (1988), and a small response 

(E100 estimate of 0.95 ppm) in Linn et al. (1987) Round 2. 

These results and those of Section 6.1 correspond with the discussion in Our Comments — in the 

short term, individuals demonstrate a consistent dose-response relationship; but their response 

may change over the longer term, or perhaps in response to external stimuli. Further, at any one 

time, not all asthmatics are hyperresponsive to exercise plus SO2. 

 

16 The calculations for this Section are in workbook “Between study replicates 2.xls,” see Section 14. 
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0.1

1

10

100

0.1 1 10 100

E100 (ppm) Study 1

E100 (ppm) Study 2

Figure 3 Comparison of E100 estimates between studies for 17 subjects. Confidence intervals are 

approximate ±1 standard deviation (estimated by a change of 0.5 in profile loglikelihood). 

6.3. Evaluation of population E100 distribution 

Figure 4 shows all available estimates for E100 (including subjects who did not respond at all) 

taking account of corrections and new data, with superposed maximum likelihood estimates for 

the distribution of E100 assuming probit or logistic distributions. The distributional estimates 

incorporate the additional individual data that do not define dose-response curves (see Our 

Comments for details of methods).17 Also shown are the distributions derived (incorrectly, see 

Section 3) in the Final REA and used for calculations of Table 4-1 and 4-2 of Appendix C to the 

REA. The inclusion on this plot of the non-responders is strictly incorrect; the distributions are 

for responding asthmatics and do not include the non-responders. As discussed in Our 

Comments, approximately 12.5% of asthmatics can be expected to not respond at any time,18

 

17 These calculations are all performed in workbook “sRaw_analysis_final 2.xls,” see Section 14. 18 The failure to account for non-response was another problem with the Draft REA identified in Our Comments. 

The same problem affects the Final REA. 
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although different individuals might be non-responders at different times. Figure 5 shows the 

same information as Figure 4, but omitting the non-responders. 

-3

-2

-1

0

1

2

3

0.01 0.1 1 10 100

E100 (ppm)

Normal ordinate

Data Probit_MLE Logistic_MLE EPA_Probit EPA_Logistic 

Figure 4 Individual E100 estimates with approximate ±1 standard deviation confidence intervals, 

with superposed maximum likelihood estimates for the distribution and the Final REA estimates 

for the distribution. 

The visual deviation of the fitted curves from the individual data points in Figure 4 and Figure 5 

is due to the uncertainties in the measurements. As explained in Our Comments, the fitted curve 

is expected to have a steeper slope than the measured points, particularly at the higher estimated 

E100 values where the uncertainties are largest. 

It is apparent from these graphs that the population curves used in the Final REA (EPA Probit, 

and EPA Logistic in Figure 4 and Figure 5) substantially overestimate the probability for 

response at low exposures. 
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-3

-2

-1

0

1

2

3

0.01 0.1 1 10 100

E100 (ppm)

Normal ordinate

Observed Logistic MLE Probit MLE EPA Logistic EPA Probit 

Figure 5 As for Figure 4, but omitting non-responders. 

We use the parameterization of the Final REA (Appendix C, equations 3.1 and 3.2), that is 

“exposure-response” functions (actually population distribution functions for E100) given by 

( ) ( ) ( )

( ) () ( ) ( ) ln( ) 2

1 Logistic: ; , 1 exp ln

1 Probit: ; , ln exp 2 2

P P

L L

L L

x

PP P P

y x

x

y x x t dt β λ

β γ β λ

βγ β λ

π

+

−∞

= + +

=Φ + = − ∫

where y is the fraction of the population with E100 less than concentration x (ppm). With this 

parameterization, our (maximum likelihood) estimates for the parameters are given in Table 4. 

The analysis method also provides some information on the relative likelihood of the probit 

versus the logistic distribution shape; and the probit is favored by a factor of about 1.9. 
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Table 4 Maximum likelihood estimates for population distribution functions for E100 for logistic 

and probit shapes. 

βL -2.22553

γL -3.37953

βP 1.242975

γP 1.931819

7. Effect of the Final REA errors on estimation of population effects 

In Our Comments and here, we have described multiple errors in the Draft REA that were 

continued into the Final REA. These errors have a substantial effect on the estimated number of 

lung function events. We have calculated corrected estimates for the numbers of events causing 

an increment in exercise-corrected relative sRaw of 100%,19 but the same substantial errors arise 

for all the other end-points. 

For Greene County, Table 5 shows these corrections. The first lines for each dose-response 

shape (“Table 4-1 in Appendix C of Final REA”) shows the entry in the Final REA. To 

demonstrate we know how those numbers were obtained, the second row shows a duplication of 

that calculation — the minor differences are due to the rounding of values in the Final REA and 

to our use of an exposure-response formula to estimate the probabilities in each bin (see Footnote 

13 — using the exact same probabilities as used in the Final REA reproduces Table 4-1 exactly). 

The lines “Full APEX table” corresponds to the recalculation described in Section 4 (compare 

with Table 2 and Table 3), making use of all the output from the APEX modeling. 

 

19 The calculations described in this Section are in workbook “Exposure distributions 2.xls,” see Section 14. 
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Table 5 Number of events (exercise-corrected relative sRaw increment of 100%) for Greene 

County, showing the effect of correcting errors in the Final REA. 

 Scenario 

 As Is CS 99/50 99/100 99/150 99/200 99/250 98/200

Logistic 

Table 4-1 in Appendix C of Final REA 12500 12700 12500 12500 12500 12600 12600 12600

Duplicating Table 4-1 calculation 12517 12769 12511 12518 12541 12578 12636 12615

Full APEX table 1689 12733 602 1857 3588 5723 8220 7326 

Lognormal shape 145 1082 52 160 308 490 701 626 

Correct E-R curve, full APEX table 2 139 0.2 3 10 27 57 45 

Correct E-R curve, lognormal 1 49 0.1 1 5 11 22 18 

 Probit 

Table 4-1 in Appendix C of Final REA 1600 1800 1600 1600 1600 1600 1700 1700 

Duplicating Table 4-1 calculation 1605 1798 1601 1606 1622 1650 1694 1678 

Full APEX table 19 1769 2 24 111 321 709 553 

Lognormal shape 9 243 1 11 33 70 124 104 

Correct E-R curve, full APEX table 0.1 24 0.001 0.1 1 3 8 6 

Correct E-R curve, lognormal 0.4 30 0.03 0.5 2 6 12 10 

The lines “Lognormal shape” give the exact values that would be obtained for a lognormal 

distribution of concentrations fitted to the APEX results for Greene County (with median 

concentration 0.4233 ppb, standard deviation of the logarithm of concentration of 1.2827).20

Figure 6 shows the APEX estimated cumulative distribution of exposures, and the lognormal 

approximation for Greene County. Considering the still-poor coverage of the range of 

concentrations obtained from the APEX output (the lowest non-zero bin edge concentration 

output from APEX was 14.4 ppb for Greene County in the “As Is” scenario, well above the 

median concentration of all exposures), we consider the estimate based on a lognormal 

approximation to the concentrations to be the best one currently available. 

The previous corrections show that the estimates for number of events in Greene County in the 

Final REA are considerably in error — so much so, indeed, that there is virtually no 

distinguishing any of the scenarios — even were the rest of the calculations of the Final REA to 

be correct. As described here and previously in Our Comments, however, the exposure-response 

(E-R) curves used in the Final REA are very much in error. The lines “Correct E-R curve” in 

Table 5 incorporate the corrected exposure-response curves described in Our Comments and 

 

20 The required calculation is described in Section 11. 
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updated in Section 6, including the estimate of only 87.5% of asthmatics being hyperresponsive 

to SO2 at any time. 

2

2.5

3

3.5

4

4.5

5

2 2.5 3 3.5 4 4.5 5

ln(concentration/ppb)

Normal ordinate

Figure 6 Cumulative distribution of number of exposures versus natural logarithm of 

concentration, for Greene county — APEX estimates. The dotted line is a lognormal distribution 

fitted to these results. 

The lines “Correct E-R curve, full APEX table” correspond to a calculation such as that shown in 

Table 3 using the full APEX results but with probabilities calculated using the correct E-R curve. 

The lines “Correct E-R curve, lognormal” correspond to the calculated result, assuming a 

lognormal distribution of concentrations as described above. Again, we believe that the last lines 

(assuming a lognormal distribution), correspond to the current best estimates.21 

For Greene County, if the E100 population distribution (the “exposure-response curve”) is 

assumed to be probit in shape, then the lognormal approximation actually gives slightly higher 

estimates for the total number of effects than using the full APEX table (compare the last two 

 

21 It would be very straightforward for EPA to run the APEX model and obtain adequate tabular coverage of 

concentrations. For the four areas involved each combined run takes approximately 180 processor-hours total, based 

on the log files of the runs used for the Final REA, but we did not have time or resources to make these runs 

ourselves (we would also have to perform multiple cross-checks for correctness of our computer runs that EPA 

presumably would not, having done this already). A slight modification of the program might be necessary to allow 

for more concentration bins (we have not checked the current maximum allowable number of bins), but this should 

be a minor modification if the program has been correctly written. Substantially increasing the number of bins 

might also slow the program noticeably if it has not been carefully designed. 
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lines of Table 5). In this case, either the APEX modeling did not involve sufficient samples to 

accurately capture the effect of very rare high concentrations, or the lognormal approximation is 

too far off for sufficiently high concentrations (there are too few APEX samples to evaluate 

which of these might be true). 

For the three counties of St. Louis included in the APEX modeling, the corresponding results are 

given in Table 6. While in this case the inaccurate results of the Final REA gave some 

discrimination between scenarios, they showed nowhere near the relative differences actually to 

be expected. Once again, we believe that the most accurate results currently available are given 

by the lines in Table 6 labeled “Correct E-R curve, lognormal”. 

As can be seen, even if everything else about the Final REA analysis were perfect (which it is 

not), the simple adding up of the results performed for Table 4-1 of Appendix C is incorrect by 

factors that range from about 12 to 241 for the logistic E100 distribution in Greene County 

(comparing the lines “Table 4-1 in Appendix C of Final REA” and “Lognormal shape”) and 1.1 

to 12 for St. Louis. For the probit shape, the corresponding factors of error are 7 to 1194 for 

Greene County and 1.1 to 18 for St. Louis. Taking account also of the errors in the derivation of 

the E100 distributions (“exposure-response curves”), the Final REA is in error by factors that for 

the logistic range from 260 to 90,940 in Greene County and 6 to 1,380 in St. Louis, while for the 

probit the range is 60 to 56,000 in Green County and 4.3 to 982 in St. Louis. 

All the estimates of total number of events in the Final REA are thus overestimates by very large 

factors, ranging from 60 to 90,940 in Greene County and 4.3 to 1,380 in St. Louis for events 

corresponding to increments in exercise-corrected relative sRaw of 100% or more. We have not 

calculated the similar errors for increments of 200% or in exercise-corrected relative sRaw, nor 

for the FEV1-related end points; however, the Final REA analysis is similarly flawed for those 

also, since the same erroneous assumptions are made and the same flawed methods are used in 

those analyses as in the sRaw analysis. The same errors also occur in the calculation of the 

number of asthmatics experiencing the “adverse” events (rather than the number of those events), 

although again we have not done the complete correct analysis. All the values in the Final REA 

that form the basis for the Proposed Rule are thus overestimates by substantial factors. 
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Table 6 Number of events (exercise-corrected relative sRaw increment of 100%) for St. Louis, 

showing the effect of correcting errors in the Final REA. 

 Scenario 

 As Is CS 99/50 99/100 99/150 99/200 99/250 98/200

Logistic 

Table 4-1 in Appendix C of Final REA 65700 167200 65200 68600 76200 88000 103600 99700

Duplicating Table 4-1 calculation 65842 166637 65304 68728 76334 88087 103613 99733

Full APEX table 8753 160138 5970 18288 35018 55304 78593 73175

Lognormal shape 7956 145791 5426 16628 31856 50330 71545 66609

Correct E-R curve, full APEX table 124 30204 57 550 1950 4600 8722 7669 

Correct E-R curve, lognormal 103 27867 47 458 1649 3968 7677 6721 

 Probit 

Table 4-1 in Appendix C of Final REA 9000 93300 8600 11100 17000 26400 39200 36000

Duplicating Table 4-1 calculation 9012 92803 8624 11162 17044 26406 39124 35948

Full APEX table 1091 87601 557 3726 10261 20172 33281 30100

Lognormal shape 976 86532 488 3454 9771 19513 32508 29349

Correct E-R curve, full APEX table 35 24036 11 244 1121 3004 6157 5335 

Correct E-R curve, lognormal 25 21577 9 175 844 2381 5094 4376 

8. The RIA substantially underestimates the uncertainty in hospital admissions due to SO2

We have only cursorily examined the RIA, but some errors are immediately apparent. The 

calculation of the number of hospital admissions due to SO2 depends entirely on a single paper 

(Schwartz et al., 1996) that is not listed in any of the reference lists in the RIA. Fortunately the 

Docket entry provides enough of the title to identify it. Examination of that paper shows that the 

coefficient used in the RIA for estimation of the number of respiratory hospital admissions was 

itself estimated by using a single-pollutant model, and that coefficient is not statistically 

significant. Two other pollutants, O3 and PM10, were more strongly statistically associated with 

hospital admissions in single-pollutant models, but no multi-pollutant models were attempted 

(nor were single-pollutant models stratified by levels of other pollutants, as suggested earlier in 

that same paper). 

Since PM2.5 is subsequently identified in the RIA (in the co-benefits assessment) also as a 

putative cause of hospital admissions, and because SO2 and other pollutant concentrations are 

highly correlated (Schwartz et al., 1996, under “Multipollutant models”), at the very least a joint 

analysis of the hospital admission data with both SO2 and PM10 or PM2.5 or a similar PM-related 

variable is essential. Without such an analysis, any correlation between PM-related pollutant 
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concentrations and SO2 concentrations in the data evaluated in the paper may lead to erroneous 

attribution of effects, and substantially underestimate the uncertainties in quantitative evaluation 

of the coefficients (assuming that the effects examined are indeed causally related to the 

pollution measured examined). Further, since it is entirely plausible that O3 and, indeed, other 

unmeasured components of air pollution result in respiratory-related hospital admissions, a 

simultaneous evaluation of at least three (SO2, PM, and O3) pollution-related variables is 

essential to adequately account for uncertainties. 

There appears to be no identifiable reason that EPA did not obtain the original data used for this 

study and perform the multi-pollutant evaluation required for adequate evaluation of 

uncertainties — with the result that the uncertainty band for SO2-related hospital admissions is 

certainly much too narrow. 

9. The RIA co-benefits assessment is based entirely on an incorrect assumption 

The RIA co-benefits assessment relies on the unstated assumptions that sulfate PM can be 

considered equivalent to any other form of PM, and that sulfate PM, at ambient concentrations, 

causes disease and death. These assumptions are incorrect. The vast weight of scientific 

evidence shows that sulfate particulate matter at the levels encountered in ambient air (or, for 

that matter, at substantially higher levels) is not harmful in any respect. That EPA failed entirely 

to evaluate this evidence — even in an uncertainty analysis — indicates an unjustified bias. 

Sulfate is essential to life, and animals deficient in sulfate fail to thrive (Markovich, 2001; Food 

and Nutrition Board, Institute of Medicine, 2004. Many essential biochemicals, such as 

chondroitin sulfate (a component of cartilage) and cerebroside sulfate (an essential part of the 

nervous system), can be synthesized only if the body contains sufficient quantities of sulfate. 

Sulfate occurs naturally in ordinary foods and drinking water, and is also formed in vivo by 

oxidation of the sulfur-based amino acids, methionine and cysteine. Sulfate in blood is freely 

filtered in the kidney and then reabsorbed by means of tubular sulfate transporters. Typically, 

reabsorption occurs at about the maximum rate; therefore, any excess sulfate leaves the body via

urine. In other words, body burdens of sulfate are maintained by homeostasis, and when more 

sulfate is present than is needed for cell function and growth, this extra sulfate is readily 

excreted. On average, we ingest (and/or synthesize) about 4,000,000 micrograms of sulfate 

every day (Food and Nutrition Board, Institute of Medicine, 2005). Thus, to someone trained in 

nutrition, the idea that absorbing an extra 100 or so micrograms of sulfate via inhalation could be 

deadly is nonsensical. 

 

Numerous experimental studies of the effects of inhaled fine and ultrafine particles (PM2.5) of 

sulfate compounds have been conducted (reviewed by Schlesinger, 2007 and Schlesinger and 

Cassee, 2003; also Utell et al., 1983; Amdur, 1989; NTP, 1996; Cassee et al., 2002; Tunnicliffe 

et al., 2003; Dorman et al., 2005; Tapin et al., 2006; Wallenborn et al., 2008; and Heyder et al., 

2009). With the exception of sulfuric acid mists at high concentrations, these sulfates have failed 

to elicit significant toxic effects, much less cause death. Note that: 
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• The types of sulfates tested have included ammonium sulfate, ammonium bisulfate, 

ammonium ferrosulfate, sodium sulfate, sodium hydrogen sulfate, ferrous sulfate, ferric 

sulfate, manganese sulfate, nickel sulfate, zinc sulfate, zinc ammonium sulfate, and 

sulfuric acid. 

• Exposure concentrations have ranged from 4 to greater than 1,000,000 μg/m3

, with 

almost all exposures in excess of 100 μg/m3

, well above ambient sulfate levels (which 

typically are on the order of 2 – 8 μg/m3

 as an average). 

• Exposure periods have ranged from about 15 minutes to a lifetime (for laboratory 

rodents). 

• Subjects have included healthy adults, young adults with asthma, young rats, aging rats, 

rats with chemically induced pulmonary hypertension, mice, rabbits, guinea pigs, guinea 

pigs with protein-induced asthmatic tendencies, dogs, and rhesus monkeys. 

• Effects on lung function and structure, immunological responses, the heart, and cancer 

have been examined, with lung responses of greatest interest. 

These studies have indicated that the sulfate anion is remarkably nontoxic: to the extent that 

sulfate-based compounds do exhibit toxicity, it is because of the cation (such as iron or 

hydrogen) with which sulfate combines, and not the sulfate per se. Thus, ferrous and ferric 

sulfates in air are moderately toxic — causing transient irritation of the upper respiratory system 

— but this is equally true of the other soluble iron salts in air — such as ferrous chloride, ferric 

chloride, and ferric nitrate — since it is the iron cation that matters, not the anion, whether it is 

sulfate, nitrate, or chloride. Similarly, sulfuric acid is a strong acid and thus strong irritant, but, 

again, this is not due to the sulfate anion, but instead to the hydrogen cations which, by 

definition, acidify substances (such as mucous membranes) with which they come into contact. 

Sulfuric acid mist can thus affect respiratory function, of asthmatics more than others, but 

exposures to concentrations larger than 100 μg/m3

 are required to cause any measurable, 

transient changes in asthmatics (Utell et al., 1983). 

Sulfate salts, as noted above, are less toxic than sulfuric acid. Rhesus monkeys exposed to 920 

μg/m3 manganese sulfate for 65 days showed no ill effects (Dorman et al., 2005), and mice and 

rats exposed to nickel sulfate hexahydrate at 120 μg/m3 (rats) or 250 μg/m3 (for mice) for their 

lifetimes showed no increase in tumors or pulmonary lesions (NTP, 1996). Female mice did 

develop atrophy of the olfactory epithelium, probably due to the nickel cation rather than the 

sulfate anion. Dogs exposed for 13 months to acidic sodium hydrogen sulfate at 4,500 μg/m3

were extensively evaluated throughout a study by Heyder et al. (2009). Exposed animals 

evidenced only minor changes in lung function, no changes in the alveolar-capillary membrane 

system, no change in particle clearance, and no loss of lung cell integrity. Mucociliary clearance 

was increased by exposure. Changes in a few biochemical markers suggested marginal effects of 

exposure on redox balance and induction of a weak inflammatory response. The investigators 

deemed this chronic exposure to acidic particles to have produced no pathophysiologic injury. 

Exposures to sulfates at concentrations smaller than 100 μg/m3 have produced inconsistent and/or 

ambiguous changes. Observations at the lower ends of exposure ranges include small and 

inconsistent changes in lung function in humans exposed briefly to 16 μg/m3 zinc ammonium 
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sulfate; increases in TNFα in alveolar macrophages of rabbits exposed briefly to 75 μg/m3 

sulfuric acid (reviewed by Schlesinger and Cassee, 2003); and some alterations in biochemical 

and electrolyte parameters in rats exposed for 90 days to 30 μg/m3

 manganese sulfate (Tapin et 

al., 2006). 

The failure of controlled exposures to sulfates to produce marked toxicity in humans or in 

laboratory rodents accords with the occupational experience. Regulations and guidelines for 

worker exposure to chemicals are developed by the Occupational Safety and Health 

Administration (OSHA), the National Institute for Occupational Safety and Health (NIOSH), and 

American Conference of Governmental Industrial Hygienists (ACGIH). To prevent respiratory 

irritation, occupational exposures to ferrous sulfate and ferric sulfate are limited by OSHA, 

NIOSH, and ACGIH to no more than 1,000 μg/m3 in workplace air. The same limit is set by 

OSHA and NIOSH for sulfuric acid; ACGIH, citing pulmonary function decrements, 

recommends an upper limit of 200 μg/m3

.

22 The other sulfate salts are considered to be inert, and 

so are limited only as generic “nuisance dusts” to levels of 5,000 μg/m3 for respirable particles 

(NIOSH, 1974; NIOSH, 2005; ACGIH, 2008). 

Other information casts doubt on the purported lethality of sulfate. Various sulfate compounds 

— including metal sulfates, such as cupric sulfate, ferric and ferrous sulfates, and zinc sulfate — 

are listed by the Food and Drug Administration (FDA) as “generally recognized as safe” when 

added to food as intended.23 Further, with regard to metal sulfates, read the label of an ordinary, 

over-the-counter, multi-vitamin and mineral supplement, and you will find that some of the 

essential metals, such as copper, iron, and zinc, are supplied as sulfate salts. Thus, for example, 

a prenatal vitamin and mineral pill may contain 30,000 micrograms of iron, as ferrous sulfate 

(http://emedicine.medscape.com/article/259059-overview). 

More than 250 sulfate compounds are approved by the FDA for use as drugs.24 These drugs may 

be used chronically, such as Adderall and various asthma medications. Indeed, the inhaled 

asthma medication albuterol is formulated as the sulfate salt, and a puff of albuterol sulfate 

contains thousands of micrograms of sulfate per cubic meter (Green et al., 2002). 

None of the sulfate salts is known to be lethal: exposure to more than 1,000,000 μg/m3

ammonium sulfate in air for three days was not lethal to rats (Pepelko et al., 1980). Sulfuric acid 

mist, as expected (based on its acidity), can be lethal when inhaled, but only at concentrations of 

about 30,000 μg/m3

 and higher (Wolff et al., 1979). 

In sum, small concentrations of sulfate compounds, such as those present in ambient air, are not 

known or expected to be toxic, and these compounds are benign at even much higher 

concentrations. Even massive concentrations of sulfates are not known to cause death, even 

 

22 Occupational exposures to strong-inorganic-acid mists containing sulfuric acid can cause cancer in workers 

(IARC, 1992), but such exposures do not occur in (non-occupational) ambient air. 

23http://www.fda.gov/Food/FoodIngredientsPackaging/GenerallyRecognizedasSafeGRAS/GRASSubstancesSCOGS

Database/default.htm

24 http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm
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from respiratory disease. The co-benefits analysis asserts not only that airborne sulfates do cause 

death (at all concentrations, however small), but that they somehow cause all kinds of deaths — 

not only from respiratory disease, but also from heart disease, cancers of all types, strokes, 

diabetes, Alzheimer’s disease, influenza and pneumonia, kidney disease, and so on.25 There is 

no known chemical, physical, or biological agent, however potent, that does all this. 

10. Erratum 

The discussion in Our Comments at page 19 contains an error. The second equation should read: 

100 2

2

4

E

bb c

λ

λ

λ = + +

(the factor 2 in the numerator was inadvertently omitted in this description; all the calculations 

used the correct equation shown here — see the “Predicted” column in the relevant sheets of the 

workbooks). 

11. Addendum 

For completeness, we give here the explicit formulae used for the lognormal concentration 

distribution case. Suppose the exposure concentration distribution is a lognormal distribution 

with median concentration μ (ppm) and standard deviation σ of logarithm of concentration. 

Then for the logistic and probit population distribution functions for E100 given in Section 6.3, 

the expected fraction26 of the population exposed to concentrations exceeding their E100 is given 

by: 

ln ( )

2 2

Logistic: , 2;1

Probit:

1

LL L

P P

P

I β γ μ σγ

μβγ

σ γ

+

  + Φ    +  

where Iln is a logistic-normal integral given by 

( ) ( ) ( ) 2

ln

1 , ; exp 1 exp n

I a b n t a bt

π

∞ −

−∞ = −+ +   ∫  

 

25 Moreover, at the allowable occupational limit of 1,000 μg/m3 in workplace air for ferric/ferrous sulfate, the cobenefits analysis would apparently have us believe that the total mortality rate would be increased by a factor of 

about 12 — which means that more than 90% of workers’ deaths would be attributable to such exposures. This is 

not credible. 

26 Since the relevant population is that of hyperresponsive asthmatics, the calculations for the “Correct E-R curve” in 

Table 5 and Table 6 also include the fraction 0.875 of the asthmatic population that is hyperresponsive (see Our 

Comments) — the APEX modeling omitted accounting for this fraction. 
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12. Acknowledgement 

These comments were funded by our employer, Cambridge Environmental Inc., with the 

exception of Section 9, which is adapted from an expert report written by one of us (LCG) on 

behalf of Cinergy Corp. in a lawsuit involving, among other things, the question of whether 

sulfate in ambient air is lethal. 

13. References 

Amdur, M.O. (1989). Health effects of air pollutants: sulfuric acid, the old and the new. 

Environ Health Perspect 81:109–113. 

American Conference of Industrial Hygienists (ACGIH) (2008). Supplement to the 7th Edition of 

Documentation of the Threshold Limit Values. Table of Contents and Entry for Sulfuric 

Acid. Cincinnati, OH. 

Cassee, F.R., Arts, JHE, Fokkens, P.H.B., Spoor, S.M., Boere, A.J.F., van Bree, L., and 

Dormans, J.A.M.A. (2002). Pulmonary effects of ultrafine and fine ammonium salts 

aerosols in healthy and monocrotaline-treated rats following short-term exposure. 

Inhalation Toxicology 14:1215–1229. 

Dorman, D.C., Struve, M.F., Gross, E.A., Wong, B.A., and Howroyd, P.C. (2005). Sub-chronic 

inhalation of high concentrations of manganese sulfate induces lower airway pathology in 

rhesus monkeys. Respiratory Research 6:121. 

Green, L.C., Crouch, E.A.C., Ames, M.A., and Lash, T.L. (2002). What’s wrong with the 

National Ambient Air Quality Standard (NAAQS) for fine particulate matter (PM2.5)? 

Regul. Toxicol. Pharmacol. 35(3):327–337. 

Heyder, J., Beck-Speier, I., Ferron, G.A., Josten, M., Karg, E., Kreyling, W.G., Lenz, A-G., 

Maier, K.L., Reitmeier, P., Ruprecht, L., Takenaka, S., Wohland, T., Ziesenis, A., and 

Schulz, H. (2009). Long-term responses of canine lungs to acidic particles. Inhalation 

Toxicology 21(11)920–932. 

Horstman, D., Roger, L.J., Kehrl, H., and Hazucha, M. (1986). Airway sensitivity of asthmatics 

to sulfur dioxide. Toxicol. Ind. Health 2(3):289–298. 

Institute of Medicine, Food and Nutrition Board (2004). Dietary Reference Intakes for Water, 

Potassium, Sodium, Chloride, and Sulfate. Washington, DC: The National Academies 

Press. 

International Agency for Research on Cancer (IARC) (1992). IARC Monographs on the 

Evaluation of Carcinogenic Risks to Humans, Volume 54, Occupational Exposures to 

Mists and Vapours from Strong Inorganic Acids; and Other Industrial Chemicals. IARC, 

Lyon, France. ISBN 92 832 1254-1. Available at available at 

http://monographs.iarc.fr/ENG/Monographs/vol54/index.php, accessed Feb. 7, 2010. 
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Linn, W.S., Avol, E.L., Peng, R.C., Shamoo, D.A., and Hackney, J.D. (1987). Replicated 

exposure-response study of sulfur dioxide effects in normal, atopic, and asthmatic 

volunteers. Am. Rev. Respir. Dis. 136:1127–1134. 

Linn, W.S., Avol, E.L., Shamoo, D.A., Peng, R.C., Spier, C.E., Smith, M.N., and Hackney, J.D. 

(1988). Effect of metaproterenol sulfate on mild asthmatics’ response to sulfur dioxide 

exposure and exercise. Arch. Environ. Health 43:399–406. 

Linn, W.S., Shamoo, D.A., Peng, R.C., Clark, K.W., Avol, E.L., and Hackney, J.D. (1990). 

Responses to sulfur dioxide and exercise by medication-dependent asthmatics: effect of 

varying medication levels. Arch. Environ. Health 45:24–30. 

Linn, W.S., Venet, T.G., Valencia, L.M., Anzar, U.T., Spier, C.E., and Hackney, J.D. (1983). 

respiratory effects of sulfur dioxide in heavily exercising asthmatics. Am. Rev. Respir. 

Dis. 127(3):278–283. 

Markovich, D. (2001). Physiological roles and regulation of mammalian sulfate transporters. 

Physiol Rev 81(6):1499–1533. 

National Institute of Occupational Safety and Health (NIOSH) (1974). Criteria for a 

Recommended Standard: Sulfuric Acid. Cincinnati, OH:U.S. Department of Health and 

Human Services. 

National Institute of Occupational Safety and Health (NIOSH) (2005). NIOSH Pocket Guide to 

Chemical Hazards. Washington, DC.:U.S. Department of Health and Human Services. 

Available at http://www.cdc.gov/niosh/npg

National Toxicology Program (NTP) (1996). Toxicology and Carcinogenesis Studies of Nickel 

Sulfate Hexahydrate (Cas No. 10101-97-0) in F344/N rats and B6C3F1 Mice (Inhalation 

Studies). Technical Report No. 454. Research Triangle Park, NC: U.S. Department of 

Health and Human Services. 

Pepelko, W.E., Mattox, J.K., and Cohen, A.L. (1980). Toxicology of ammonium sulfate in the 

lung. Bull. Environ. Contam. Toxicol. 24(1):156–160. 

Post E, and Mahoney H. (2009). TRIM, Total Risk Integrated Methodology, Users Guide for 

TRIM.RiskHuman Health-Probabilistic Application for the SO2 NAAQS Risk Assessment. 

October 2009. Part of EPA-HQ-OAR-2007-0352-0105. 

Roger, L.J., Kehrl, H.R., Hazucha, M., and Horstman, D.H. (1985). Bronchoconstriction in 

asthmatics exposed to sulfur dioxide during repeated exercise. J. Appl. Physiol. 

59(3):784–791. 

Schlesinger, R.B. (2007). The health impact of common inorganic components of fine 

particulate matter (PM 2.5) in ambient air: a critical review. Inhalation Toxicology 

19(10):811–832. 

Schlesinger, R.B. and Cassee, F. (2003). Atmospheric secondary inorganic particulate matter: 

the toxicological perspective as a basis for health effects risk assessment. Inhalation 

Toxicology 15(3):197–235. 
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Schwartz, J., Spix, C., Touloumi, G., Bachárová, L., Barumamdzadeh, T., le Tertre, A., 

Piekarksi, T., Ponce de Leon, A., Pönkä, A., Rossi, G., Saez, M., and Schouten, J.P. 

(1996). Methodological issues in studies of air pollution and daily counts of deaths or 

hospital admissions. J. Epidemiol. Community Health 50(Suppl):S3–S11. 

Tapin, D., Kennedy, G., Lambert, J., and Zayed, J. (2006). Bioaccumulation and locomotor 

effects of manganese sulfate in Sprague-Dawley rats following subchronic (90 days) 

inhalation exposure. Toxicol. Applied Pharmacol. 211:166–174. 

Tunnicliffe, W.S., Harrison, R.M., Kelly, F.J., Dunster, C., and Ayres, J.G. (2003). The effect of 

sulphurous air pollutant exposures on symptoms, lung function, exhaled nitric oxide, and 

nasal epithelial lining fluid antioxidant concentrations in normal and asthmatic adults. 

Occup. Environ. Med. 60(11):e15. 

U.S. Environmental Protection Agency (EPA) (1986). Review of the National Ambient Air 

Quality Standards for Sulfur Oxides: Updated Assessment of Scientific and Technical 

Information. Addendum to the 1982 OAQPS Staff Paper. EPA 450/05 86-013, 

December 1986. 

U.S. Environmental Protection Agency (EPA) (1994). Review of the National Ambient Air 

Quality Standards for Sulfur Oxides: Assessment of Scientific and Technical Information. 

Supplement to the 1986 OAQPS Staff Paper Addendum. EPA-452/R-94-013, September 

1994. 

Utell, M.J., Morrow P.E., Speers D.M., Darling J., Hyde R.W. (1983). Airway responses to 

sulfate and sulfuric acid aerosols in asthmatics. An exposure-response relationship. Am. 

Rev. Respir. Dis. 128:444–450. 

Wallenborn, J.G., Evansky, P., Shannahan, J.H., Vallanat, B., Ledbetter, A.D., Schladweiler, 

M.C., Richards, J.H., Gottipolu, R.R., Nyska, A., and Kadavanti, U.P. (2008). 

Subchronic inhalation of zinc sulfate induces cardiac changes in healthy rats. Toxicol. 

Applied Pharmacol. 232:69–77. 

Wolff, R.K., Silbaugh, S.A., Brownstein, D.G., Carpenter, R.L., and Mauderly, J.L. (1979). 

Toxicity of 0.4- and 0.8-microm sulfuric acid aerosols in the guinea pig. J Toxicol 

Environ Health 5(6):1037–1047. 

14. Appendix: Calculations 

Lack of time and budget prevent a detailed description of all the calculations performed in these 

comments. To ensure reproducibility and allow examination of all the data and methods, we 

here provide copies (as embedded files within this PDF document) of the Excel workbooks used, 

and give a short description of them. Further information, and in particular information on 

practical use of the macros within these workbooks, may be obtained from the first author 

(EACC). These workbooks are generally updates of those provided with Our Comments. 

WARNING: all the workbooks REQUIRE the included add-in EACC_funs.xla (which is 

unchanged from the version embedded in Our Comments); in addition, several of them also 

contain macros [the macros are needed to re-run the results, but are not needed to view the 

results, so may be disabled on opening; the add-in is required to view the results]. 
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EACC_funs.xla

An add-in for Excel 2000 or 2003 (does not work for Excel 2007). Required for the other 

workbooks to work correctly. Must be installed before opening any of the other spreadsheets. 

See EACC_functions.pdf for detailed instructions. 

EACC_functions.pdf 

Instructions for installation, and descriptions of the functions, macros, and added menu items 

included with EAC_funs.xla. 

gpl.txt 

The license under which EACC_funs.xla may be redistributed. 

Raw_data 2.xls 

Sheets with summaries of all available individual-level data, including our entry of the individual 

measurements from Linn et al. (1987), and comparisons with EPA summaries. This has been 

updated to correct all identified errors, and now includes also Linn et al. (1983). 

Table 3-1 Analyses 2.xls 

Reproduction of the EPA likelihood analysis of Table 3-1 of Appendix C of the REA (sheet 

“REA_Analysis”), a partially corrected version that assumes that the entries in in Table 3-1 of 

Appendix C of the REA are multinomial27 in nature but does not otherwise correct the entries 

there (sheet “REA_Improved”), a sheet “REA_corrected” that incorporates all the data entry 

corrections in the Final REA analysis, and a sheet “Independence assumption” that performs the 

calculations described in Section 3. 

Within study replicates 2.xls 

Performs the analysis of within-study replicates described in Section 6.1 

Between study replicates 2.xls 

Performs the analysis of between-study replicates described in Section 6.2. 

sRaw_analysis_final 2.xls 

Performs all the individual exposure-response calculations (sheet “DR-analysis”), and then the 

E100 distribution parameter evaluation (sheet “Combined”). 

Fit_EPA_curves.xls 

Evaluates best-fit curves to Final REA & EPA tabulated “exposure-response” curves. 

Exposure distributions 2.xls

 

27 This corresponds to each individual exhibiting a dose-response curve with no variability, so that response at one 

dose would necessarily entail a response at every higher dose. This does not actually happen, but is closer than the 

“independence” assumption of the REA. 
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Sheet “Factors” estimates the multipliers for concentrations for the different scenarios from 

Table 8-14 of the Final REA, and fits the APEX output results with lognormals. Sheet 

“Common” contains the parameters for the “exposure response” curves (from 

“Fit_EPA_curves.xls” and “sRaw_analysis_final 2.xls”) used in other sheets. Sheets “Greene” 

and “St. Louis” perform the calculations described in Section 7. In addition, sheet “St. Louis” 

has the example calculation described in Section 4.