MEMORANDUM

To: Timothy Leighton, EPA
From: Jonathan Cohen, ICF
Date: 20 December, 2011

Re: Contract No.: EP-W-06-091 WA 4-02: AEATF Aerosol Study Statis tical Review for HSRB

Introduction and Summary In November 2011, AEATF submitted the fi nal report for their study “A Study for Measurement of Potential Dermal and Inhalation Exposure during Applicat ion of a Liquid Antimicrobial Pes ticide Product Using a Pressurized Aerosol Can for Indoor Surface Disinfecting” ICF were asked to analyze the data from this study to investigate the relationship between dermal and inhalati on exposures and the pesticide product usag e. Note that much of the SAS code used for these analyses and some of th e following description was adapted from Sarkar’s SAS code (which, in turn, was based on code provided by the AHETF) and his June 2010 Statistical Review “Review of Statistical Analyses in Agricultural Handler Exposure Ta sk Force (AHETF) Monographs.”
The report describes the experimental study methodology and the measurements in detail. Briefly, three test sites in Fresno, CA, were selected to represent: cl uster 1, a hotel/motel with a full kitc hen; cluster 2, a hotel/motel without a food preparation area, and; cluster 3, a hot el/motel with a kitchenett e. For each test site, six volunteer subjects were selected and randomly assigned different numbers of aerosol canisters containing C14 ADB AC to be sprayed from 1- 1.5 canisters to 3.5-4 canisters. Each subject was given inner and outer do simeters to wear and was also given a personal air-sampling pump attached to an OVS air sampling tube and a second pers onal air-sampling pump attached to a three stage RespiconTM Particle Sampler to monitor their in halation exposure. The Particle Sampler has three filters of sizes 100 μ m, 10 μ m, and 2.5 μ m that sample particles of sizes 10 to 100 μ m, 2.5 to 10 μ m, and less than 2.5 μ m, respectively. Subjects were also fitted w ith a silicone half-mask respirator which they could volunteer to not use or use during some or all of the spraying time . Each subject then used their assigne d number of aerosol canisters to spray horizontal and vertical surfaces. The percent active ingredient in the first batch of canisters used for this study was 0.126% C14 ADBAC and the percent active ingredient in the second batch of canis ters was 0.104% C14 ADBAC.. Subjects were allowed to take breaks on a chair covered with plastic sheeting in a clean room, as needed. The breaks were not included in the spraying tim e duration but the air-sampling pumps remained on throughout the breaks. Although the study design was not a probability survey, some elements of the design used randomization. These statistical analyses treat the data as ei ther a simple random sample or a stratif ied random sample, where the clusters are the strata.
The exposure measurements in the report were corrected for the average percentage recove ry of field fortification samples and for the removal efficiency of hand wash ( 90.3%) and face and neck (89.4%) wipe samples. The face and neck wipe samples were also corrected using a half-mask re spirator and safety glasses correction factor of 1.43 to account for the area of the face that was covered by the us e of personal protection equipment (PPE). These analyses used the corrected measurements. The data in the report we re entered and compiled into an Excel spreadsheet. This included the units conversion of the amount s of active ingredient fr om mg into pounds and of the mass from μg to mg.Timothy Leighton, EPA 20 December, 2011 Page 2

The report data for inhalation exposure were unchanged other than the units c onversions. The dermal exposure data were used to develop exposure measurements for four dermal exposure routes, as follows:

• Long Dermal . This case represents the dermal exposure fo r a subject wearing long pants and long-sleeved shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, and the six inner dosimeters (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

• Short Dermal . This case represents the dermal exposure for a subject wearing short pants and short-sleeved shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, the outer dosimeters for the lower arm and lower leg, and the six inner dosimet ers (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

• Long Short Dermal . This case represents the dermal exposure for a subject wearing long pants and shortsleeved shirts, without gloves. The ex posure is the sum of the mass from hand wash, face and neck, the outer dosimeter for the lower arm, and the six inner dosimet ers (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

• Hands Only . This case represents the dermal exposure to the hands only and is the mass from hand wash. This case is used for comparison purposes. The report only considered the dermal exposure for the “Long Dermal” case, and used the same definition. However for our analyses we chose a more consistent, and more conserva tive (i.e., more health protec tive) approach to deal with values reported as being below th e level of quantitation (LOQ):

Several of the measured values were be low the level of quantitation (LOQ). The experimental protocol also required that measurements of the inner dosimeters were not taken if the outer dosimeter was below the LOQ, although this did not in fact apply for any of the outer dos imeter measurements made in this study. As a slightly more conservative (i.e., more health protective) approach than the method used in th e report, we replaced any value that was either a non-detect or was not measured by one half the LOQ. If any inner or outer dosimeter value was below the LOQ, 3 μg, each such value was replaced by 1.5 μg = 0.0015 mg. For example, if all th e inner dosimeters were below the LOQ, then the total would be replaced by 0.009 mg. If the face and neck meas urement was below the LOQ, 50 ng, it was replaced by 25 ng = 0.000025 mg. All the hand wash, face and ne ck, and outer dosimeter measuremen ts in the study were above the LOQ. 14 of the 108 inner dosimeter m easurements were below the LOQ. For one subject (AE18, cluster 1), inner dosimeter values we re much higher than all othe r subjects and were higher than the corresponding outer dosimeter pi eces for areas of expected low expos ure such as the torso. The study report suggests that this was due to signific ant C14 ADBAC dermal residues on the sk in prior to report ing for the study, perhaps due to bathing using a product c ontaining C14 ADBAC. No adjustments were made in these analyses for these potential outliers. Inhalation exposure was measured using th e air sampling OVS tubes and using the th ree filters in the Particle Sampler. The inhalation exposure concentration (mg/m 3 ) was calculated by dividing the corr ected residue mass by the volume of air drawn. For the Particle Sampler, the report tabulate d the total C14 ADBAC concen tration based on summing the corrected residues on the three filters, and the percentages of the total corrected residue mass captured on each filter. The following exposure concentrations are analyzed in this memorandum:

• Inhalation Concentration (mg/m 3 ). Concentration measured by the OVS tube.Timothy Leighton, EPA 20 December, 2011 Page 3

• 100 μ m Concentration (mg/m 3 ). Total concentration measured by the Particle Sampler. This was calculated by summing the corrected residues from the three filters at Stage 1 (size 2.5 μ m), Stage 2 (size 10 μ m), and Stage 3 (size 100 μ m), and then dividing this total by the amount of air drawn. This m easures the concentration of all particles less than 100 μ m, and thus estimates the concen tration of inhalable particles.

• 10 μ m Concentration (mg/m 3 ). Concentration of pa rticles less than 10 μ m measured by the Particle Sampler. This value is the sum of the corrected residues from the two filters at Stage 1 (size 2.5 μ m) and Stage 2 (size 10 μ m) divided by the amount of air drawn. This value wa s obtained from the study report tables by multiplying the reported 100 μ m concentration by the sum of the reported per centages for the Stage 1 and Stage 2 filters.

• 2.5 μ m Concentration (mg/m 3 ). Concentration of pa rticles less than 2.5 μ m measured by the Particle Sampler. This value is the corrected residue from the filter at Stage 1 (size 2.5 μ m) divided by the amount of air drawn. This value was obtained from the study re port tables by multiplying the reported 100 μ m concentration by the reported percentage for the Stage 1 filter.

Note that the inhalati on concentration and 100 μ m concentration were measured on di fferent instruments connected to different air pumps. There we re a few cases where the 100 μ m concentration exceeded the inhalation concentration for the same worker despite the fact that th e RespiconTM Particle Sampler has an inlet that restricts particles to be less than 100 μ m in size. In the body of this memorandum we presen t the analysis of the unit or normalized exposure defined as the dermal or inhalation exposure divided by the pounds of active ingredient handled. Estimat es of the arithmetic and geometric means and standard deviation as well as the 95 th percentile are computed using th e empirical data as well as two statistical models: the lognor mal simple random sampling model and the lognormal mixed model. The mixed model includes the possibility of clustering due to the effects of the loca tion. For example, the results for different subjects at the hotel/motel without a food preparation area might be corre lated because of the physical similarities of the rooms, the physical similarities of th e surfaces that were sprayed, the building characteristics, the investigators at that location, or other factors that are due to th e selected location. The cl ustering includes both the random variation between locations as well as the fixed effect of the type of food preparation area (none, full kitchen, or kitchenette). Alternative statistical modeling approaches could have been used to separate out these ra ndom and fixed effects but this was not done due to the small sample size, the n eed to develop exposure fact ors applicable to all po tential uses that do not depend upon the building type, and for consistency between thes e analyses and the previous analyses of the mop and wipe studies. For each summary statistic we present confidence intervals. We also compute the fold relative accuracy of the summary statistics and compare with the study design benchmark of 3-fold accuracy, which was met for all 3 clothing configurations (Long Dermal, Short Dermal, Long Short De rmal) and for the total and filtered particle inhalation exposure (Inhalation, 100 μ m Inhalation, 10 μ m Inhalation, and 2.5 μ m Inhalation). To evaluate the statistical models we present quantile-quan tile plots to compare the f it of normal and lognormal distributions to the data. The statistical models for the normalized exposure assume that the mean value of the logari thm of the exposure is equal to an intercept plus the slope times the logarithm of the am ount of active ingredient use d, where the slope equals 1. To test this assumption, the regression mode l was fitted to the data either usi ng simple random sampling or the mixed model and a 95% confidence interval for th e slope was calculated. A statistical test was used to determine if the slope was 1 or 0, corresponding either to a va lid normalized exposure model or to a case where the exposure is independent of the amount of active ingredient used. We applied this test to the three dermal exposures and to the total inhalationTimothy Leighton, EPA 20 December, 2011 Page 4

exposure using the statistical mixed model. For dermal exposur es it is reasonable to assu me on physical grounds that the same patterns ought to apply to any type of dermal exposure, so that the slope should either be one for all types of dermal exposure or not one for all types of dermal exposure. To evaluate this issue we applied the same proportionality test to a hypothetical all dermal e xposure case representing a janitor with no clothing, using a dermal exposure estimated as the sum of the exposures measured on the face a nd neck, hands, and all the i nner and outer dosimeters. We also developed a statistical repeated measures model to analyze the three main types of dermal exposure (excluding hands only) in a single sta tistical model, accounting for w ithin-worker correlations and within-location clustering. We also evaluated quadratic regression models. The results for all the dermal and inhalation exposure rout es show that the estimated intra-cluster correlation (ICC) coefficient is zero, which implies that there are no clusteri ng and location effects, and therefore, in particular, no differences between exposures when spraying different types of f ood preparation areas. The mixed model results for the four dermal exposure routes all show a positive estimated slope of at least 0.7. These dermal exposure models consistently do not reject proportionality (s lope equals one) at the 5% significance level. These dermal exposure models also consis tently reject independence (slope equals zero) at the 5% significance level, with the sole exception of the mixed model for hands only exposure which ha d a slightly negative lower confidence bound. For inhalation, the estimated slope is 0.4, but proportionali ty is rejected and indepe ndence is not rejected. The appendix gives the detailed results of the corresponding analyses for dermal and inhalation exposure when the exposure is normalized by the spraying dur ation. The results show similar patt erns to the normalization by amount of active ingredient handled but the slop es are lower, showing less support for that alternative exposure models. For inhalation, the data suggest that the exposure is either inde pendent of spraying duration or is a non-linear function of spraying duration. A summary comp aring the normalizing approaches is presen ted at the end of this memorandum. The mixed model analyses show that in most cases, the better of the two normalizing options consid ered is the amount of active ingredient handled. The inhalation exposure measures used for the main analyses presented here are the aver age air concentrations (mg/m 3 ) over the entire period that the concentration was measured, which includes the breaks as well as the spraying durations. As an alternative approach we consid ered using the air C14 ADBAC mass (mg) which can be estimated as the average air concentration multiplied by the spraying duration (hours) and by an estimated 1 m 3 /hour of air breathed in by someone doing light activity. These values were computed for the total inhalation mass as well as the inhalation mass for the three particle sizes. A similar statistical analysis found th at the slope is signific antly greater than 1. The appendix includes the detailed re sults for this model. Analyses of exposure per pounds of active ingredient handled

Tables 1 and 2 summarize the normalized e xposure data (per lb active ingredient handled) with the summary statistics from the 18 measurements for each dermal and inhalation exposure route, respectively.Timothy Leighton, EPA 20 December, 2011 Page 5

Table 1. Summary statistics for normalized dermal exposure.*

Statistic Normalized Long a Dermal (mg/lb AI) Normalized Short b Dermal (mg/lb AI) Normalized Long Short c Dermal

(mg/lb AI) Normalized Hands Only (mg/lb AI) Arithmetic Mean 251.5 653.3 365.7 145.3

Arithmetic Standard Deviation 191.4 257.1 200.4 117.9

Geometric Mean 208.2 602.3 324.0 120.6

Geometric Standard Deviation 1.8 1.5 1.6 1.8

Min 88.3 248.1 142.0 54.1

5% 88.3 248.1 142.0 54.1

10% 97.5 325.2 149.5 54.4

25% 140.2 471.2 248.7 81.8

50% 193.2 648.3 325.8 121.7

75% 253.3 837.4 430.0 154.6

90% 606.0 992.3 688.2 258.6

95% 850.2 1179.2 953.4 571.2

Max 850.2 1179.2 953.4 571.2

*Using Empirical simple random sampling model

a Long = Long pants and long sleeves b Short = Short pants and short sleeves

c Long Short = Long pants and short sleevesTimothy Leighton, EPA 20 December, 2011 Page 6

Table 2. Summary statistics for no rmalized inhalation exposure.*

Statistic Normalized Inhalation (mg/m 3 /lb AI) Normalized 100 μ m Inhalation (mg/m 3 /lb AI) Normalized 10 μ m Inhalation (mg/m 3 /lb AI) Normalized 2.5 μ m Inhalation (mg/m 3 /lb AI) Arithmetic Mean 59.5 47.6 25.3 11.3

Arithmetic Standard Deviation 28.1 25.0 16.1 8.5

Geometric Mean 53.3 41.9 21.3 9.1

Geometric Standard Deviation 1.6 1.7 1.8 1.9

Min 21.4 14.9 7.5 3.0

5% 21.4 14.9 7.5 3.0

10% 23.4 20.6 9.7 4.2

25% 40.8 29.2 14.4 5.2

50% 54.3 41.8 17.9 8.5

75% 82.5 54.4 30.2 14.2

90% 114.0 91.2 57.4 25.8

95% 114.2 92.1 61.0 36.8

Max 114.2 92.1 61.0 36.8

*Using Empirical simple random sampling model The summary analyses presented in Tables 1 and 2 use th e 18 measurements with a simple random sampling model that ignores the fact that the data were selected by choosing three “cluster s” representing three di fferent location types, and then measuring dermal and inhalation e xposures on six subjects in each of the three clusters (a total of 18 different volunteer subjects). The six subjects in each cluster were randomly assigned six different amounts of aerosol to be sprayed, as defined by the number of canisters:

• 1 to 1.5 canisters

• 1.5 to 2 canisters

• 2 to 2.5 canisters

• 2.5 to 3 canisters

• 3 to 3.5 canistersTimothy Leighton, EPA 20 December, 2011 Page 7

• 3.5 to 4 canisters The statistical analyses use the followi ng three alternative statistical models. Let X be the normalized exposure and X = exp(Y) so that Y = log (X), where log denotes the natural logarithm. LnGM is the log of the geometric mean. Let Z95 be the 95 th percentile of a standard normal distribution, approximately 1.645.

• Empirical simple random sampling model. Code “s.” Assu mes that the 18 values of X were randomly drawn from an unspecified distribution. Ignores clustering. Gives empirical estimates such as in Tables 1 and 2 above.

o Y = LnGM + Error. Error is independent a nd identically distributed with mean 0.

o AMs = Arithmetic mean of X values

o GMs = Geometric mean of X values = exp(LnGM) (= GMu)

o GSDs = Geometric standard deviation of X values (= GSDu)

o P95s = 95 th percentile of X values

• Lognormal simple random sampling model. Code “u.” Assu mes that the 18 values of X were randomly drawn from a log-normal distribution. Ignores clustering.

o Y = LnGM + Error. Error is normall y distributed with mean 0, variance Vu, and stan dard deviation Su = √ Vu.

o AMu = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 Vu)

o GMu = Modeled geometric mean of X values = exp(LnGM)

o GSDu = Modeled geometric standard deviation of X values = exp(Su)

o P95u = Modeled 95 th percentile of X values = exp(LnGM) exp(Z95×Su)

• Lognormal mixed model. Code “m.” Assumes that thr ee cluster effects were randomly drawn from a normal distribution and that the 18 within-clu ster error terms were independently randomly drawn from another normal distribution. The error term for each s ubject is the sum of the cluster eff ect for the subject’s cluster and the within-cluster error term.

o Y = LnGM + Cluster + Error. Cluster is normally distributed with mean 0, variance Vc, and standard deviation Sc = √ Vc. Error is normally distributed with mean 0, variance Vw, and standard deviation Sw

= √ Vw. Define V = Vc + Vw and S = √ V. V is the variance of Y, and S is the standard deviation of Y.

o ICC = Intra-cluster correlation coefficient = Vc/V.

o AMm = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 V)

o GMm = Modeled geometric mean of X values = exp(LnGM)

o GSDm = Modeled geometric standard deviation of X values = exp(S)

o P95m = Modeled 95 th percentile of X values = exp(LnGM) exp(Z95×S)Timothy Leighton, EPA 20 December, 2011 Page 8

For the lognormal mixed model, the ICC value estimates the clustering effect and lies be tween 0 (no clustering) and 1 (complete clustering and negligible within -cluster variation). If ICC = 0, then th e lognormal mixed model is identical to the lognormal simple random sampling model and the paramete rs (AM, GM, GSD, and P95) are identical for those two models. Table 3 presents the arithmetic mean and 95 th percentile estimates from the lognorma l mixed model, together with 95% confidence intervals, for all the exposur e routes. These are the values of AMm and P95m. The other summary statistics are presented in more detail below.

Table 3. Arithmetic mean and 95 th percentile estimates from lognormal mixed model for normalized exposure.

Exposure Route Clothing Arithmetic Mean (95% confidence interval) 95 th percentile (95% confidence interval) Dermal (mg/lb AI) Long pants and long sleeve s 248.1 (185.1, 338.6) 551.5 (358.5, 844.6)

Short pants and short sl eeves 660.5 (536.5, 819.6) 1221.2 (894.0, 1669.0) Long pants and short slee ves 366.7 (287.4, 472.4) 734.6 (511.6, 1050.9) Hands only 142.4 (106.7, 191.4) 311.2 (204.7, 471.2) Inhalation (mg/m 3 /lb AI) 60.3 (47.2, 77.6) 120.7 (84.1, 172.7) 100 μ m Inhalation (mg/m 3 /lb AI) 48.1 (37.2, 63.0) 99.5 (67.9, 145.3)

10 μ m Inhalation (mg/m 3 /lb AI) 25.5 (18.9, 35.1) 57.4 (37.0, 88.7)

2.5 μ m Inhalation (mg/m 3 /lb AI) 11.3 (8.1, 16.1) 26.8 (16.6, 43.2)

For each exposure route, the above three statistical models we re fitted to the observed data and the summary statistics listed above were calculated together w ith 95% confidence intervals. The 95% confidence intervals in Table 3 were computed using a parametric bootstrap. Confidence intervals computed using a non-parametric bootstrap are presented below. For these calculations, the parametric bootstrap si mulations were all generated from the fitted lognormal mixed model, even for the empirical and simp le random sample summary statistics, on the basis that the mixed model is the best choice for modeling the data, even if the summary sta tistics are developed from a simpler statistical model. For example, in Tables 1 and 2, the empirical arithmetic mean s are presented, which are the arithmetic means of the 18 measurements. To estimate the uncertainty of those empirical arithmetic means, data are simulated from the lognormal mixed model to calculate the parametric bootstrap confidence intervals. The arit hmetic means in Table 3 are estimated using the lognormal mixed model, which is also used to es timate the confidence intervals in Table 3. The unit exposure estimates (from the lognormal mixed m odel) displayed in Table 3 are reco mmended over the empirical arithmetic means and 95 th percentiles displayed in Tables 1 and 2. The algorithm used was as follows:
Step 1:Timothy Leighton, EPA 20 December, 2011 Page 9

Simulate 18 random variables Y, X from the estimated lognormal distribution superimposed upon the observed sampling structure - --; C = LnGM + RanNor(Seed)×Sc; Y = C + RanNor(Seed) ×Sw; X = exp(Y);
where: LnGM = intercept of mixed effect log-log regression model Sc = square root of between cluster variance Sw = square root of within cluster variance under mixed-effect model.
Step 2:

For Y:

Calculate GMs = exp(EAM)
Calculate GSDs = exp(Su)
Calculate AMu = GMs×exp(0.5×Su×Su)
Calculate P95u = GMs× exp(Z95×S) Fit mixed lognormal model to simulated Y values

Under mixed-effects model:

Calculate GMm = exp(intercept of mixed-effects model)
Calculate GSDm = exp(square root (total variance V under mixed-effects model))
Calculate ICC = Vc /V Calculate AMm = exp(intercept + 0.5×V) Calculate P95m = exp(intercept + Z95×S)

where:
EAM = sample arithmetic average of Y
Su = standard deviation of Y
V = total variance under mixed-effects model S = square root of V
Vc = between cluster variance.

For X:

Calculate arithmetic mean AMs
Calculate 95 th percentile P95s Step 3: Repeat Steps 1 and 2 10,000 times.
Steps 1 to 3 result in 10,000 values each for GSDs, GSDm, ICC, GMs, GMm, AMs, AMm, AMu, P95s, P95m, and P95u. 95% confidence intervals can be defined for each parameter by the 2.5 th and 97.5 th percentiles (lower and upper, respectiv ely) of the bootstrap distribution of that corresponding parameter. Note that by definition, GSDs = GS Du and GMs = GMu. Also note that GMs = GMm for this situation becauseTimothy Leighton, EPA 20 December, 2011 Page 10

the experiment is balanced with 3 clusters and 6 subjects in each cluster; this implies that th e intercept is the same value fo r both the simple random sampling and mixed models. Fold relative accuracy ( fRA ) is a measure that can be used to determine how well a statistic can describe its population parameter. Let us assume θ is a parameter and T is the sample statistic of θ (i.e., an estimate of θ ). If the 2.5 th and 97.5 th percentiles of the sampling dist ribution of T can be denoted by T 2.5 and T 97.5 , respectively, then the 95 th percentile of sample fold relative accuracy can be theoretically calculated using the following formula provided in the AHETF Governing Document (AHETF, 2007; pg. 136): fRA 95 = Max (T 97.5 / θ
, θ / T 2.5 )

The actual value of θ is unknown. Thus, fRA 95 was calculated by substituting θ with T. If the fRA 95 of a statistic were equal to 3, then it would be correct to sa y: “At least 95% of the time the sample statistic will be accurate to within 3- fold of the population value”. Accord ing to the AHETF Governi ng Document, the statistical design of the exposure monitoring study should be adequate to produce a fRA 95 less than or equal to 3. Thus the confidence intervals calculated in the above algorithm can be used to estimate the fold relative accuracy and compare th e observed fRA with the study design benchmark of 3. If the observed fold relative accuracy is grea ter than 3, this means that the experiment did not meet the benchmark, which would be due to differences betw een the distributions of the CMA data used to design the study and the experimental data collected in the study. If the fold re lative accuracy benchmark is not met, then it might be desirable to collect more data for this scenario in order to meet the benchmark. Fo ld relative accuracy was not computed for the ICC since the estimated ICC is 0 in many cases.

The HSRB reviewers of the statistical analyses of the Mop Study (“AEATF M op Study Statistical Review for HSRB,” 19 November 2010, original version dated 28 September, 2010) suggested that a non-para metric bootstrap approach should also be considered. The non-parame tric bootstrap method should be more r obust since it does not assume that the fitted parametric model is the co rrect one. For the non-parametric bootstrap, exactly the same approach was used except that Step 1 above is replaced by the following:
Step 1:
Simulate 18 random variables Y, X by resampling at random with replacement from the original data:
For Cluster j, the original exposure data are X(1), X(2), ..., X(n j ), where n j is the number of workers in cluster j (n j equals 6 for the aerosol study data).
Sample n j values at random with replacement from the exposure values X(1), X(2), ..., X(n j ). This gives the 6 simulated random variables X from cluster j.
Repeat for all three clusters. (j = 1, 2, and 3).
Y = log(X). The Y, X values were independently resa mpled from the three clusters in order to preserve the covariance structure. Tables 4 to 11 present the estimates, parametric and non-parametric confidence intervals and fold relative accuracy values for all the summary statistics for the four derm al and four inhalation e xposure routes, respectively.Timothy Leighton, EPA 20 December, 2011 Page 11

Table 4. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized long dermal exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.8 1.5 2.2 1.2 1.4 2.1 1.3 GSDm 1.8 1.5 2.2 1.2 1.4 2.2 1.3 ICC 0.0 0.0 0.4 0.0 0.6 GMs 208.2 158.3 274.7 1.3 163.6 270.9 1.3 GMm 208.2 158.3 274.7 1.3 163.6 270.9 1.3 AMs 251.5 182.6 332.9 1.4 179.4 342.5 1.4 AMu 248.1 184.1 336.6 1.4 180.2 343.3 1.4 AMm 248.1 185.1 338.6 1.4 181.6 349.4 1.4 P95s 850.2 357.2 1206.3 2.4 301.1 850.2 2.8 P95u 551.5 356.5 833.0 1.5 315.3 863.3 1.7 P95m 551.5 358.5 844.6 1.5 323.0 891.3 1.7

Table 5. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized shor t dermal exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.5 1.3 1.8 1.2 1.4 1.7 1.1 GSDm 1.5 1.3 1.8 1.2 1.4 1.7 1.1 ICC 0.0 0.0 0.4 0.0 0.7 GMs 602.3 492.8 737.5 1.2 504.3 722.2 1.2 GMm 602.3 492.8 737.5 1.2 504.3 722.2 1.2 AMs 653.3 532.9 812.1 1.2 546.6 767.6 1.2 AMu 660.5 536.0 816.9 1.2 549.9 776.5 1.2 AMm 660.5 536.5 819.6 1.2 556.1 777.8 1.2 P95s 1179.2 893.7 2156.7 1.8 843.7 1179.2 1.4 P95u 1220.9 888.7 1651.1 1.4 955.9 1446.4 1.3 P95m 1221.2 894.0 1669.0 1.4 982.1 1473.4 1.2Timothy Leighton, EPA 20 December, 2011 Page 12

Table 6. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for different statis tical models of the normalized long short dermal exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.6 1.4 1.9 1.2 1.4 1.8 1.2 GSDm 1.6 1.4 2.0 1.2 1.4 1.9 1.2 ICC 0.0 0.0 0.4 0.0 0.6 GMs 324.0 257.5 409.1 1.3 263.7 403.3 1.2 GMm 324.0 257.5 409.1 1.3 263.7 403.3 1.2 AMs 365.7 285.6 466.3 1.3 287.0 460.1 1.3 AMu 366.7 287.2 471.1 1.3 288.2 464.8 1.3 AMm 366.7 287.4 472.4 1.3 290.5 466.3 1.3 P95s 953.4 509.9 1417.9 1.9 442.7 953.4 2.2 P95u 734.6 509.1 1038.7 1.4 500.0 1002.4 1.5 P95m 734.6 511.6 1050.9 1.4 514.1 1016.6 1.4

Table 7. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized hands only exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.8 1.5 2.2 1.2 1.4 2.2 1.3 GSDm 1.8 1.5 2.2 1.2 1.4 2.3 1.3 ICC 0.0 0.0 0.4 0.0 0.5 GMs 120.6 92.4 158.0 1.3 95.4 156.2 1.3 GMm 120.6 92.4 158.0 1.3 95.4 156.2 1.3 AMs 145.3 105.9 189.3 1.4 104.1 202.8 1.4 AMu 142.4 106.7 191.4 1.3 104.7 200.2 1.4 AMm 142.4 107.2 192.4 1.4 104.9 206.0 1.4 P95s 571.2 203.9 666.6 2.8 174.0 571.2 3.3 P95u 311.2 203.6 464.9 1.5 181.4 511.6 1.7 P95m 311.2 204.7 471.2 1.5 183.5 547.8 1.8Timothy Leighton, EPA 20 December, 2011 Page 13

Table 8. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for different statis tical models of the normaliz ed inhalation exposure (mg/m 3 /lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.6 1.4 1.9 1.2 1.4 1.8 1.2 GSDm 1.6 1.4 2.0 1.2 1.4 1.9 1.2 ICC 0.0 0.0 0.4 0.0 0.5 GMs 53.3 42.3 67.2 1.3 43.0 65.6 1.2 GMm 53.3 42.3 67.2 1.3 43.0 65.6 1.2 AMs 59.5 46.9 76.6 1.3 47.9 72.2 1.2 AMu 60.3 47.2 77.4 1.3 48.1 73.6 1.3 AMm 60.3 47.2 77.6 1.3 48.5 73.9 1.2 P95s 114.2 83.8 233.0 2.0 83.6 114.2 1.4 P95u 120.7 83.7 170.7 1.4 87.7 153.1 1.4 P95m 120.7 84.1 172.7 1.4 89.1 157.2 1.4

Table 9. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 100 μ m inhalation exposure (mg/m 3 /lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.7 1.4 2.0 1.2 1.4 1.9 1.2 GSDm 1.7 1.4 2.0 1.2 1.4 1.9 1.2 ICC 0.0 0.0 0.4 0.0 0.5 GMs 41.9 32.8 53.6 1.3 33.3 52.4 1.3 GMm 41.9 32.8 53.6 1.3 33.3 52.4 1.3 AMs 47.6 36.8 62.1 1.3 37.2 58.8 1.3 AMu 48.1 37.1 62.8 1.3 37.3 60.0 1.3 AMm 48.1 37.2 63.0 1.3 37.5 60.4 1.3 P95s 92.1 67.6 199.4 2.2 83.5 92.1 1.1 P95u 99.5 67.5 143.5 1.5 67.6 129.5 1.5 P95m 99.5 67.9 145.3 1.5 68.4 132.6 1.5Timothy Leighton, EPA 20 December, 2011 Page 14

Table 10. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 10 μ m inhalation exposure (mg/m 3 /lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.8 1.5 2.2 1.2 1.5 2.1 1.2 GSDm 1.8 1.5 2.3 1.2 1.5 2.1 1.2 ICC 0.0 0.0 0.4 0.0 0.4 GMs 21.3 16.1 28.2 1.3 16.4 28.0 1.3 GMm 21.3 16.1 28.2 1.3 16.4 28.0 1.3 AMs 25.3 18.7 34.5 1.4 18.8 33.1 1.3 AMu 25.5 18.8 34.9 1.4 18.7 34.0 1.4 AMm 25.5 18.9 35.1 1.4 18.8 34.1 1.4 P95s 61.0 36.9 127.6 2.1 36.4 61.0 1.7 P95u 57.4 36.8 87.5 1.6 36.0 80.9 1.6 P95m 57.4 37.0 88.7 1.6 36.4 82.2 1.6

Table 11. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 2.5 μ m inhalation exposure (mg/m 3 /lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.9 1.6 2.4 1.2 1.6 2.2 1.2 GSDm 1.9 1.6 2.4 1.3 1.6 2.3 1.2 ICC 0.0 0.0 0.4 0.0 0.4 GMs 9.1 6.7 12.3 1.4 6.8 12.4 1.4 GMm 9.1 6.7 12.3 1.4 6.8 12.4 1.4 AMs 11.3 7.9 15.7 1.4 7.8 15.4 1.4 AMu 11.3 8.0 15.9 1.4 7.9 15.8 1.4 AMm 11.3 8.1 16.1 1.4 7.9 15.9 1.4 P95s 36.8 16.5 64.3 2.2 15.1 36.8 2.4 P95u 26.8 16.5 42.5 1.6 15.7 40.8 1.7 P95m 26.8 16.6 43.2 1.6 15.9 41.9 1.7Timothy Leighton, EPA 20 December, 2011 Page 15

Tables 4 to 11 show that the ICC estimated value is zero fo r all the dermal and inhalation exposure routes showing that the estimated mixed and simple random sampling models are the same for those cases and that there is no variation between the different locations and types of food preparation area. Al l of the fold relative acc uracy values met the study design benchmark of 3 except for the empirical 95 th percentile for the normalized hands only exposure using the nonparametric bootstrap confidence interval. The parametric bootstrap confidence interval s were similar to the nonparametric bootstrap confidence intervals for all the dermal and inhalation exposure routes. Quantile-quantile plots of the normalized exposure values we re used to evaluate whether the data were lognormally distributed, as implied by the assumed statistical models. In each case the quantile-quantile plot compared the observed quantiles of the 18 measured values with the corresponding quantiles of a nor mal or lognormal distribution. A perfect fit would imply that the plotted values li e in a straight line. The quantile-quantil e plots are presented in Figures 1 to 16. They clearly show that the lognormal di stribution is a bette r fit than a normal distri bution, and that the lognormal distribution fits reason ably well for all of the exposure routes. 

### Quantile plot normalized long dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 200 400 600 800 1000Normalized Long Dermal Exposure

Normal Quantiles

Figure 1Timothy Leighton, EPA 20 December, 2011 Page 16



### Quantile plot normalized long dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 4.0 4.5 5.0 5.5 6.0 6.5 7.0log (Normalized Long Dermal Exposure)

Normal Quantiles

Figure 2Timothy Leighton, EPA 20 December, 2011 Page 17



### Quantile plot normalized short dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 200 400 600 800 1000 1200Normalized Short Dermal Exposure

Normal Quantiles

Figure 3Timothy Leighton, EPA 20 December, 2011 Page 18

Quantile plot normalized short dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25log (Normalized Short Dermal Exposure)

Normal Quantiles

Figure 4Timothy Leighton, EPA 20 December, 2011 Page 19

Quantile plot normalized long short dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 200 400 600 800 1000Normalized Long Short Dermal Exposure

Normal Quantiles

Figure 5Timothy Leighton, EPA 20 December, 2011 Page 20

Quantile plot normalized long short dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 4.5 5.0 5.5 6.0 6.5 7.0lnnrmdermls

Normal Quantiles

Figure 6Timothy Leighton, EPA 20 December, 2011 Page 21



### Quantile plot normalized hands only exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 100 200 300 400 500 600Normalized Hands Only Exposure

Normal Quantiles

Figure 7Timothy Leighton, EPA 20 December, 2011 Page 22



### Quantile plot normalized hands only exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 3.5 4.0 4.5 5.0 5.5 6.0 6.5log (Normalized Hands Only Exposure)

Normal Quantiles

Figure 8Timothy Leighton, EPA 20 December, 2011 Page 23



### Quantile plot normalized inhalation conc exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 20 40 60 80 100 120Normalized Inhalation Conc Exposure)

Normal Quantiles

Figure 9Timothy Leighton, EPA 20 December, 2011 Page 24

Quantile plot normalized inhalation conc exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75log (Normalized Inhalation Conc Exposure)

Normal Quantiles

Figure 10Timothy Leighton, EPA 20 December, 2011 Page 25



### Quantile plot normalized 100um conc exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 20 40 60 80 100Normalized 100um Conc Exposure)

Normal Quantiles

Figure 11Timothy Leighton, EPA 20 December, 2011 Page 26



### Quantile plot normalized 100um conc exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 2.5 3.0 3.5 4.0 4.5 5.0log (Normalized 100um Conc Exposure)

Normal Quantiles

Figure 12Timothy Leighton, EPA 20 December, 2011 Page 27



### Quantile plot normalized 10um conc exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 10 20 30 40 50 60 70Normalized 10um Conc Exposure)

Normal Quantiles

Figure 13Timothy Leighton, EPA 20 December, 2011 Page 28



### Quantile plot normalized 10um conc exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 2.0 2.5 3.0 3.5 4.0 4.5log (Normalized 10um Conc Exposure)

Normal Quantiles

Figure 14Timothy Leighton, EPA 20 December, 2011 Page 29



### Quantile plot normalized 2.5um conc exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 5 10 15 20 25 30 35 40Normalized 2.5um Conc Exposure)

Normal Quantiles

Figure 15Timothy Leighton, EPA 20 December, 2011 Page 30



### Quantile plot normalized 2.5um conc exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 1.0 1.5 2.0 2.5 3.0 3.5 4.0log (Normalized 100um Conc Exposure)

Normal Quantiles

Figure 16Timothy Leighton, EPA 20 December, 2011 Page 31

These statistical models for the norma lized exposure assume that the exposu re is proportional to the normalizing variable pounds of active ingredient handled. More precisely, the assumed st atistical models are of the form Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error Terms where Slope = 1. Possible alternative models include the sa me formulation with a Slope of zero, implying that the exposure does not depend upon the amount of active ingredie nt handled, even though the amount of active ingredient handled varied between the subjects as part of the study design. Other possible models include the same model with a slope not equal to zero or one, the quad ratic models discussed below, or models with more complicated relationships between the exposure and the experimental conditions. To evaluate whether the sl ope is zero, one, or other possible values, we fitted the above statistical model and computed confidence interv als for the slope. In the appendix we investigate normalizing by the spraying duration. To analyze the proportionality, we also c onsidered an additional hypot hetical clothing scenario with no clothing at all. The dermal exposure for the No clothing scenario was cal culated by summing all the inne r and outer dermal exposure measurements:

All Dermal . This case represents the dermal exposure for a subject wearing no clothes. The e xposure is the sum of the mass from hand wash, face and neck, and the six inner and six outer dosimeters (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

We can use these statistical models to calculate confiden ce intervals for the slope. The calculation of the confidence intervals depends upon the value of the denominator degrees of freedom for the mixed models used. A review of the alternative methods for calculating the de nominator degrees of freedom for fixe d effects in a mixed model using the SAS MIXED procedure is given in an article by Schaalje et al 1 . Based on that article, the following Table 12 summarizes the five available methods: Table 12. SAS Methods for Computing the Fixed Effects Denominator Degrees of Freedom in PROC MIXED.

DDF Method SAS Abbreviation Comments

Residual residual Uses resi dual degrees of freedom. Ignores covariance structure as defined by the RANDOM and REPEATED statements. This method is not recommended.

Containment contain Defa ult method when RANDOM statements are present. Accounts for the minimum contribution of the random effects that syntactically

1 Schaalje, G. B., J. B. McBride, G. W. Fellingham. “Approximations to Distributions of Test Statistics in Complex Mixed Linear M odels Using SAS® Proc MIXED” Proceedings of the Twenty Sixth Annual SAS Users Group International Conference . April 2001. Long Beach, CA. ISBN 1-58025-864-6. SAS Institute, Cary, NC 27513.Timothy Leighton, EPA 20 December, 2011 Page 32

DDF Method SAS Abbreviation Comments

contain the fixed eff ects of interest.

Between-Within bw Default method when REPEATED statements are present and RANDOM statements are not present. Only exact when the data are balanced and the design is a repeated measures design with compound symmetry, and where the levels of the within-subjects effects are not replicated within any of the subjects. Otherwise the method is at best approximate and can be unpredictable. Satterthwaite / Fai-Cornelius satterth Designed to approximate the denominator degrees of freedom for split-plot designs with complicated covariance structures and/or unbalanced data sets. Kenwood-Rogers kr Designed to approximate the denominator degrees of freedom for designs with complicated covariance structures and/or unbalanced data sets. Results from simulations suggest better performance than the Satterthwaite method. If a covariance parameter has zero variance then this method ignores that covariance.

To interpret this table for this study, note that the RANDOM statement was used to define the cluster effect. If the ICC equals zero, then there is no clustering and the cluster variance equals zero. The REPEATED statement was used to define the repeated measures model. A balanced data set is one where each treatment combination is applied to the same number of subjects. For this study, this implies that there are the same number of wo rkers in every cluster, and each worker has the same number of measured exposure values. The study data were balanced since there were 6 workers in each cluster, each with th e same number of exposure measurements. Based on this summary, the recommended me thods are the containment method for the mixed models when the ICC parameter is zero, and the Kenwood-Rogers me thod for the mixed models where the ICC parameter is non-zero or for the repeated measures model (detailed be low). (For other applicatio ns, the Kenwood-Rogers method would be preferred in general if the data are sufficiently unbalanced, but it is not easy to provide rules as to how this should be defined.) The confidence intervals for the regressi on coefficients presented in this memorandum follow these recommendations. In particular, since th e ICC parameters in the mixed regressi on models for the logarithm of the longTimothy Leighton, EPA 20 December, 2011 Page 33

dermal, short dermal, long short dermal, all hands, and inhalation exposure against th e logarithm of the pounds of active ingredient handled were all zero, the containment method was used in those cases. However, since the ICC parameter in the mixed regression models for the logarithm of the all dermal exposure ag ainst the logarithm of the pounds of active ingredient handled was non-zero, although the value was only 0.002, the Kenwood-Rogers method was used for that mixed model. Note that this issue does not impact the calculated confidence intervals for the summary statistics in Tables 4 to 11, since they were based on a bootstrap method. Table 13 shows the 95% confidence intervals for the slope calculated from the above model, either assuming the lognormal simple random sampling model for the errors or th e lognormal mixed model for the errors. Also shown is the width of the confidence interval for the slope. A confiden ce interval that includes one but not zero supports the assumptions of the normalized exposure models. A confidence in terval that includes zero but not one suggests that the exposure does not depend on the amount of active ingredient handled. A confidence interval that includes both zero and one suggests that either the basic statistical model is incorr ect or there are not enough data to statistically infer whether the slope is zero or one. The Repeated Measures statistical model (bottom ro w) is described and discussed below. Regression models for the filter measurements by si ze fraction are not presented in this memorandum. Table 13. 95 percent confidence intervals for the slope of log exposure versus log pounds active ingredient handled.

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Dermal (mg) Long pants and long sleeves Mixed 0.81 0.08 1.54 1.47
Simple Linear 0.81 0.08 1.53 1.45
Short pants and short sleeves Mixed 1.01 0.47 1.55 1.07
Simple Linear 1.01 0.48 1.54 1.06
Long pants and short sleeves Mixed 0.87 0.25 1.48 1.24
Simple Linear 0.87 0.26 1.48 1.22
Hands Only Mixed 0.70 -0.01 1.40 1.40 Simple Linear 0.70 0.00 1.39 1.39

None Mixed 1.02 0.55 1.49 0.94 Simple Linear 1.02 0.56 1.48 0.92

Inhalation (mg/m 3 ) Mixed 0.43 -0.11 0.97 1.08
Simple Linear 0.43 -0.11 0.96 1.07Timothy Leighton, EPA 20 December, 2011 Page 34

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Dermal (mg) Any Repeated Measures 1.28 0.78 1.77 0.99

For all of the dermal exposure cases ex cept for the mixed model for hands only, the confidence interval for the slope includes 1 but not 0. Thus, for these cas es, the assumption of propor tionality was not rejected and the assumption of independence was rejected. For the mixed model for hands on ly, the confidence interval fo r the slope includes both 1 and 0 (although the lower bound is nearly zero, so that the assumptions of propor tionality and independence were both not rejected. For the inhalation exposure, there is sufficient evidence to reject the hypothesis of a slope of 1 at the 5% significance level. A few of the slope values in Table 13 are slightly above 1. Since the confidence intervals include 1, these cases provide good support for the proportionality assumpti on. As discussed below, when the slope is greater than one, the predicted means from the normalized exposure mode l will underestimate the predicted me ans from the mixed model with an estimated slope (of the log exposure agai nst the log amount of activ e ingredient) when the am ount of active ingredient is high. However, this underestimation will be negligible when the slope is only slightly above 1, except if the amount of active ingredient handled is extremely high. Based on the available CMA data, the experi ment was designed to be able to dete ct whether the slope was 0 or 1 using a test at the 5% significan ce level with a power of 80%. On that basis, the experiment was designed to make the expected confidence interval width equal to 1.4:

Given:
Power = 1 – P(type II error) = 1- β = 0.80;
Significance level = P(type I error) = α = 0.05;
(Eq. 1) Predicted 95% Confidence Interval (two sided) for the regression slope = Sample estimate of slope ± 1.96 × Standard Error
Effect Size = (Z 1- α /2 + Z 1- β ) × Standard Error
Here, Z P is the p th percentile of a standard normal distribution:

Z 1- α /2 = Z 0.975 = 1.96;

Z 1- β = Z 0.80 = 0.84

Z 1- α /2 + Z 1- β = 2.8
(Eq. 2) Standard Error = Effect Size ÷ 2.8
Substituting Standard Error into (Eq. 1):
Predicted 95% Confidence Interval (two sided) for the regression slope = Sample estimate ± 1.96 × (Effect Size ÷ 2.8) = Sample estimate ± 0.7 × Effect Size
Here, Effect Size = 1 – 0 = 1 (i.e., slope = 1 under H 1 vs. slope = 0 under H 0 )Timothy Leighton, EPA 20 December, 2011 Page 35

So, expected width of confidence interval for slope parameter = 2 × 0.7 = 1.4
The results in Table 13 show that the actual confidence interval wi dths were less than 1.4 for all the exposure cases except for the long pants and long sleeves scenario where the wi dth was slightly higher, 1.5. For the simple linear regression analyses based on the simple random sampling model, the relationship between the exposure and the amount of activ e ingredient is displayed in the followi ng regression plots in Figures 17 to 22.

lnderml = 4.2195 +0.8093 lnnrm

N 18 Rsq 0.2592 AdjRsq 0.2129
RMSE 0.6047 Simple Linear Regression of Ln Long Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Long Dermal Exposure (mg)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 17Timothy Leighton, EPA 20 December, 2011 Page 36

lnderms = 6.4691 +1.0117 lnnrm

N 18 Rsq 0.5049 AdjRsq 0.4740
RMSE 0.4428 Simple Linear Regression of Ln Short Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Short Dermal Exposure (mg)

-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 18Timothy Leighton, EPA 20 December, 2011 Page 37

lndermls = 4.995 +0.866 lnnrm

N 18 Rsq 0.3608 AdjRsq 0.3208
RMSE 0.5095 Simple Linear Regression of Ln Long Short Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Long Short Dermal Exposure (mg)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 19Timothy Leighton, EPA 20 December, 2011 Page 38

lnderma = 6.9721 +1.0178 lnnrm

N 18 Rsq 0.5805 AdjRsq 0.5543
RMSE 0.3824 Simple Linear Regression of Ln All Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog All Dermal Exposure (mg)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 20Timothy Leighton, EPA 20 December, 2011 Page 39

lndermh = 3.0157 +0.6971 lnnrm

N 18 Rsq 0.2208 AdjRsq 0.1721
RMSE 0.5788 Simple Linear Regression of Ln Hands Only Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Hands Only Exposure (mg)

-2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 21Timothy Leighton, EPA 20 December, 2011 Page 40

lninh1 = 0.6138 +0.4269 lnnrm

N 18 Rsq 0.1519 AdjRsq 0.0989
RMSE 0.4459 Simple Linear Regression of Ln Inhalation Conc Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Inhalation Exposure (mg/m3)

-3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 22Timothy Leighton, EPA 20 December, 2011 Page 41

These simple linear regression results are compared with th e results for the lognormal mixe d models in Figures 23 to 28. In all these cases, the regression line s are the same for the mixed and simple linear regression models because the estimated ICC parameter was zero. Although th ese regression lines in these figures and the same as in Figures 17 to 22, they are included for consistenc y with the previous reviews.

Figure 23Timothy Leighton, EPA 20 December, 2011 Page 42

Figure 24Timothy Leighton, EPA 20 December, 2011 Page 43

Figure 25Timothy Leighton, EPA 20 December, 2011 Page 44

Figure 26Timothy Leighton, EPA 20 December, 2011 Page 45

Figure 27Timothy Leighton, EPA 20 December, 2011 Page 46

Figure 28Timothy Leighton, EPA 20 December, 2011 Page 47

Finally, in Figure 29 we present a regressi on plot showing the slightly different regression lines for the three clusters based on the mixed model for all dermal exposure. For the other dermal clothing confi gurations and the inhalation exposure, the mixed models predict the same values for all three clusters.

Figure 29 The above analyses of the proportionalit y for dermal exposure consistently show similar positive slopes, as one might expect on physical grounds. All of the estimated slopes fo r dermal exposure are positive and approximately 0.8, and all the confidence intervals contained 1. To investigate this issue further, the follo wing more complicated statistical model was fitted to the data of all three dermal exposures (excludi ng the unrealistic hands only and no clothing case) for all 18 subjects. The model was of the form: Log (dermal exposure) = LnGM (cloth ing type) + Slope × Log (Pounds of Ac tive Ingredient) + Cluster + Error In this model, the intercept depends upon the clothing type, so there are three intercepts. Th e slope is the same for all three clothing types, The Cl uster term accounts for possible clustering eff ects due to the locati on. Finally, to account for the expected correlations between different dermal exposure measurem ents on the same worker, the three error terms (one per clothing type) for each worker are assumed to be correlated (with an unspecif ied covariance matrix), but errors for different workers are assumed to be independent . Thus in SAS terminology, the Cluster effect is a RANDOMTimothy Leighton, EPA 20 December, 2011 Page 48

effect and the Error is a REPEATED effect where the subj ect is the worker. We will ca ll this model the “Repeated Measures” model. The confidence interval for the slope using this statistical model is shown in the bottom row of Table 13. Since the confidence interv al includes one and does not include zero, the proportionality for dermal exposure has been shown using this statistical model.
Quadratic models The proportionality test was based on a linear model for log exposure versus log pounds active ingredient handled. The HSRB suggested that a quadratic m odel should also be considered. There are two quadratic models that could be consider ed. Since the original linear model is of the form Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error Terms, the main quadratic model is of the form Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Quad × {Log (Pounds of Active Ingredient)} 2 + Error Terms. Note that the quadratic term is the square of the logarith m of the pounds of active ingredie nt rather than the logarithm of the square; the latter approach pr oduces an ill-defined model with two mu ltiples of the logari thm of the pounds of active ingredient. Another approach might be to consid er a quadratic model for exposure:
Exposure = Intercept + Slope × (Pounds of Active Ingredient) + Quad × (Pounds of Active Ingredient) 2 + Error Terms. We do not recommend this second approach for these data since the exposures are known to be non-negative and the quantile plots indicate that the exposure data are better modeled using a log-normal distribution than using a normal distribution. Furthermore, unless the in tercept is zero, this model predicts a nonzero exposure when the pounds of active ingredient is zero , and so a more realistic (though possibly poorer-fitting) model of this form would have a zero intercept. For other e xposure data a proportionality te st could be carried out by fitt ing the zero intercept model Exposure = Slope × (Pounds of Active Ingredient) + Quad × (Pounds of Active Ingredient) 2 + Error Terms and testing if Quad equals zero. The parsimony principle suggests that the ap propriate statistical procedure for this study is to first fit the quadratic regression model for the l ogarithm of the exposure Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Quad × {Log (Pounds of Active Ingredient)} 2 + Error Terms.Timothy Leighton, EPA 20 December, 2011 Page 49

If the coefficient Quad is statisticall y significant at the 5% level, which is equivalent to requiring that the 95% confidence interval does not include zero, than the quadratic model is supported. Otherwise th e linear model should be used. Table 14 presents the fitted quadratic models from the study for the mixe d models of five exposure measurements (Long Dermal, Short Dermal, Long Short Dermal, Hands Only, Inhalation) and for the Repeated Measures model for Dermal exposures. For the Repeated Measures model, the mode l has different intercepts ( but the same Slope and Quad coefficients) for the three different derm al exposures. In view of the earlier di scussion about denominator degrees of freedom, the confidence intervals for cas es where the ICC parameter is non-zero and for the Repeated Measures model are calculated using the Kenwood-Rogers method. The confiden ce intervals for other cases where the ICC parameter is zero are calculated using the containment method.

Table 14. Quadratic mixed models with 95% confidence in tervals for the log exposure versus log pounds active ingredient handled.
Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval
Long Dermal Intercept -9.04 2.00 -137.34 119.27 1.86 0.00 256.61

Long Dermal Slope -3.67 13.00 -25.37 18.04 1.86 0.00 43.41

Long Dermal Quad -0.38 13.00 -2.20 1.45 1.86 0.00 3.64

Short Dermal Intercept -4.86 2.00 -98.59 88.86 1.57 0.00 187.45

Short Dermal Slope -2.81 13.00 -18.67 13.04 1.57 0.00 31.71

Short Dermal Quad -0.32 13.00 -1.65 1.01 1.57 0.00 2.66

Long Short Dermal Intercept -7.96 2.00 -115.82 99.90 1.68 0.00 215.72

Long Short Dermal Slope -3.51 13.00 -21.75 14.74 1.68 0.00 36.49Timothy Leighton, EPA 20 December, 2011 Page 50

Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval
Long Short Dermal Quad -0.37 13.00 -1.90 1.16 1.68 0.00 3.06

Hands Only Intercept 20.71 2.00 -101.33 142.75 1.80 0.00 244.08

Hands Only Slope 6.67 13.00 -13.98 27.31 1.80 0.00 41.29

Hands Only Quad 0.50 13.00 -1.23 2.23 1.80 0.00 3.46

Inhalation Intercept -38.66 13.19 -81.35 4.03 1.51 0.00 85.39

Inhalation Slope -12.83 13.18 -27.21 1.55 1.51 0.00 28.76

Inhalation Quad -1.11 13.17 -2.32 0.09 1.51 0.00 2.41

Dermal Repeated Measures Slope -1.29 12.63 -15.98 13.41 NA NA 29.39

Dermal Repeated Measures Quad -0.21 12.62 -1.45 1.02 NA NA 2.46

Since the 95% confidence intervals for Qu ad include zero in every case, the quadr atic coefficient is not statistically significant and the quadratic models are not supported. Threshold Analyses As described above, the following two mi xed models were fitted to the de rmal and inhalation exposure data.

Linear mixed model: Log (Exposure) = Intercept1 + Slope × Log (Pounds of Active I ngredient) + Cluster + Error Normalized exposure mixed model: Log (Exposure) = Intercept2 + Log (Pounds of Active Ingredient) + Cluster + Error,Timothy Leighton, EPA 20 December, 2011 Page 51

which is mathematically the same as
Log (Exposure/Pounds of Active Ingredie nt) = Intercept2 + Cluster + Error
The intercepts for these two models are de noted as Intercept1 and In tercept2 since their estimated values will in general be different.
Cluster is a normally distributed random effect variable with independent, id entically distributed values for each cluster, and Error is a normally distribut ed error variable with inde pendent, identically distributed values for each total exposure measurement. If the linear mixed model has a slope of 1, then the model is mathematically the same as the normalized exposure mixed model.

These two statistical models can be co mpared by calculating the threshold valu e of the pounds of active ingredient at which both models predict the same mean exposure. The threshold values are computed as follows.
Suppose first that the linear mi xed model for log Exposure is correct. Then the predicted mean exposure for a given amount of active ingredient is given by the equation Predicted mean exposure fr om linear mixed model = exp(Intercept1) × (Pounds of Active Ingredient) Slope × exp( 1⁄2 V1) (1)

where V1 is the total variance for the lin ear mixed model, calculated as the sum of the cluster variance and the error variance. The predicted mean exposure is the expected value of the exposure fo r a given amount of active ingredient and thus estimates the average (arithmetic mean) exposure for a large number of scenarios that are all using the same amount of active ingredient. Suppose instead that the normalized exposure mixed model fo r log Exposure is correct. Then the predicted mean exposure is given by the equation Predicted mean exposure from nor malized exposure mixed model = exp(Intercept2) × (Pounds of Active Ingredient) × exp( 1⁄2 V2) = AMm × Pounds of Active Ingredient (2)

where V2 is the total variance for the normalized exposure mixed model, calculate d as the sum of the cluster variance and the error variance. AMm is the estimated average normalized exposure, AMm = exp(Intercept2 + 1⁄2 V2) We now have two estimates of the predicted mean exposure for a given amount of active in gredient, equations (1) and (2). The graphs in Figures 30 to 34 below compare the pr edicted means for each clothi ng configuration (Long Dermal, Short Dermal, Long Short Dermal, Hands Only) and for total inhalation exposure. The tw o estimates (1) and (2) are equal if the pounds of ac tive ingredient equals the Threshold value: Threshold = {AMm / exp(Intercept1 + 1⁄2 V1)} 1/(Slope – 1)

The Threshold values are tabulated in Table 15 below.Timothy Leighton, EPA 20 December, 2011 Page 52

Suppose that the estimated slope is less than 1 (which is true for all the cases st udied here except for the Short Dermal exposure which had an estimated slope slightly greater th an 1). The predicted mean exposure from the normalized exposure mixed model will be greater than the predicted m ean exposure from the linear mixed model for amounts of active ingredient above the th reshold (right hand side of the graph). The predicted mean exposure from the normalized exposure mixed model will be less than the predicted m ean exposure from the linear mixed model for amounts of active ingredient below the threshold (left hand side of the graph). What this means is that if we assume proportionality and use the normalized exposure mixed model, then we w ill tend to over-predict the e xposure unless the amount of active ingredient is below the threshold. (If the amount of active ingr edient is below the threshold, then it will be low enough that the exposure will not usually be of concern). For the Short Dermal exposure, the estimated slope was grea ter than one. In this excep tional case the inequalities are reversed: The predicted mean exposure from the normalized exposure mixed model will be greater than the predicted mean exposure from the linear mixed model for amounts of activ e ingredient below the thres hold (left hand side of the graph). The predicted mean exposure from the normalized e xposure mixed model will be less than the predicted mean exposure from the linear mixed model fo r amounts of active ingredient above th e threshold (right hand side of the graph). Although this case shows a tendency for exposure es timates from the normalized exposure mixed model to under-predict exposure, it is cl early seen from the graph that the two curves are numerically extremely close so that the under-prediction is very small. Table 15. Threshold values for the amount of active ingredient.
Exposure Route Clothing Model Slope Threshold Level (lb active ingredient) Dermal (mg) Long pants and long sleeves Mixed 0.81 0.00295

Short pants and short sleeves Mixed 1.01 0.00174*

Long pants and short sleeves Mixed 0.87 0.00297

Hands only Mixed 0.70 0.00285

Inhalation (mg/m3) Mixed 0.43 0.00272

*For this case, slope > 1 and so the normalized expos ure mixed model under-predicts exposure for pounds of active ingredient above the threshold.Timothy Leighton, EPA 20 December, 2011 Page 53

Figure 30Timothy Leighton, EPA 20 December, 2011 Page 54

Figure 31Timothy Leighton, EPA 20 December, 2011 Page 55

Figure 32Timothy Leighton, EPA 20 December, 2011 Page 56

Figure 33Timothy Leighton, EPA 20 December, 2011 Page 57

Figure 34 Alternative normalizing and exposure variables The appendix gives the tables and graphs with the detailed re sults of the analysis when the exposure is normalized by the spraying duration. All the dermal exposure models are consistent with proportionality for the spraying duration. The estimated slopes for spraying duration are consistently lo wer than the slopes for the amount of active ingredient handled. The confidence intervals for the slopes are generally a littl e narrower than for the amount of active ingredient handled. The inhalation exposure m odels are inconsistent with pr oportionality for spraying duration. The appendix also gives the tables and gr aphs with the detailed results of the analysis when the inhalation exposure concentration is converted to an estimated mass, calculate d as the average air concentration multiplied by the spraying duration (hours) and by an estimated 1 m 3 /hour of air breathed in by someone doi ng light activity. This value estimates the mass of C14 ADBAC breathed in by each participant. Ho wever this is an approximation because actual breathing rates are not constant and will vary with the activity as well as the individua l. Moreover, the air concentration was measured and averaged over the entire air pumping period, wh ich includes the resting periods (breaks) as well as the wiping durations. The analysis shown in the appendix is for the mass normalized by the amount of active ingredient, calculated for total inhalation and for the three particle size limits.Timothy Leighton, EPA 20 December, 2011 Page 58

Using both normalizing variables (amount of active ingredient, spraying duration), th e ICC value is either zero or is small (at most 0.2) for all the exposure routes, showing only a small amount of va riability between the clusters, i.e., the locations including the type of food preparation area. Finally, to compare the two different nor malizing variables, we present Table 16 that gives the valu es of minus twice the log-likelihood “-2LL” for the alte rnative approaches and exposure rout es. -2LL is a measure of how well a statistical model fits the data and this can be used to compare different models for the same data. (-2LL is a relative measure that can only be used to compare different models for the same data, such as the various models for the 18 long dermal exposure values. -2LL cannot be used to compare different data such as the long dermal and short dermal exposure). Using this measure, the models with the lowest -2LL values are prefe rred, and the preferred models in each row are shown in bold in Table 16. The values in Table 16 are -2LL for each of the mixed and repeated measures models. The log-likelihood values were computed by f itting the models using the maximum likelihood method. The rows where the slope is 1 give the -2LL values for the models where the regr ession slope is set to be 1 so the exposure is normalized by dividing the exposure by the normalizing va riable. The rows where the slope = “Any” give the -2LL values for the more general models where the regression slop e is arbitrary so the exposure is normalized by dividing the exposure by some power of the normalizing variable, NRM p . The mixed models using the pounds of active ingredient are the preferred models fo r all the exposure routes except for the hands only model with an unknown slope. Table 16. Minus twice the log-lik elihood for different mixed models (smaller is better). Preferre d model is shown in bold.

Exposure

Route Model Slope Normalized by pounds of active ingredient Normalized by spraying duration

Long Dermal Mixed Any 30.9 31.8

Mixed 1 31.2 33.8

Short Dermal Mixed Any 19.6 25.0

Mixed 1 19.6 26.6

Long Short

Dermal Mixed Any 24.7 27.2

Mixed 1 24.9 29.8Timothy Leighton, EPA 20 December, 2011 Page 59

Exposure

Route Model Slope Normalized by pounds of active ingredient Normalized by spraying duration Hands Only Mixed Any 29.3 28.4

1 30.2 30.7

Dermal Repeated Measures Any -34.2 -26.0

1 -33.0 -25.6

Inhalation Concentration (mg/m 3 ) Mixed Any 19.9 21.7

Mixed 1 24.9 32.0Timothy Leighton, EPA 20 December, 2011 Page 60



### APPENDIX
Analyses of exposure per spraying duration (hours) Table and Figure Numbers are consiste nt with the main text (add “b”). Table 1b. Summary statistics for normalized dermal exposure.

Statistic Normalized Long a Dermal (mg/hour) Normalized Short b Dermal (mg/hour) Normalized Long Short c Dermal (mg/hour) Normalized Hands Only (mg/hour) Arithmetic Mean 1.73 4.57 2.54 0.98 Arithmetic Standard Deviation 1.31 1.99 1.42 0.75 Geometric Mean 1.41 4.07 2.19 0.82 Geometric Standard Deviation 1.89 1.69 1.77 1.79 Min 0.44 1.25 0.71 0.27 5% 0.44 1.25 0.71 0.27 10% 0.63 1.90 0.98 0.44 25% 0.96 2.85 1.43 0.50 50% 1.40 5.04 2.35 0.77 75% 1.95 6.02 3.24 1.16 90% 3.85 7.00 4.38 1.68 95% 5.87 8.15 6.59 3.63 Max 5.87 8.15 6.59 3.63

a Long = Long pants and long sleeves b Short = Short pants and short sleeves

c Long Short = Long pants and short sleevesTimothy Leighton, EPA 20 December, 2011 Page 61

Table 2b. Summary statistics for no rmalized inhalation exposure.

Statistic Normalized Inhalation (mg/m 3 /hour) Arithmetic Mean 0.42 Arithmetic Standard Deviation 0.24 Geometric Mean 0.36 Geometric Standard Deviation 1.84 Min 0.12 5% 0.12 10% 0.14 25% 0.26 50% 0.39 75% 0.53 90% 0.88 95% 0.93 Max 0.93

Table 3b. Arithmetic mean and 95 th percentile estimates fr om lognormal mixed model for normalized exposure.

Exposure Route Clothing Arithmetic Mean (95% confidence interval) 95 th percentile (95% confidence interval) Dermal (mg/hour) Long pants and long sleeve s 1.72 (1.25, 2.42) 4.01 (2.53, 6.34)

Short pants and short sl eeves 4.72 (3.23, 6.99) 9.96 (6.02, 16.42) Long pants and short slee ves 2.58 (1.90, 3.57) 5.62 (3.62, 8.69) Hands only 0.97 (0.72, 1.31) 2.13 (1.40, 3.25) Inhalation (mg/m 3 /hour) 0.44 (0.29, 0.67) 1.01 (0.58, 1.75)

Table 4b. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized long dermal exposure (mg/hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.89 1.53 2.34 1.24 1.54 2.16 1.23 GSDm 1.89 1.54 2.36 1.25 1.57 2.20 1.21Timothy Leighton, EPA 20 December, 2011 Page 62

Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy ICC 0.00 0.00 0.39 0.00 0.76 GMs 1.41 1.05 1.90 1.35 1.10 1.88 1.33 GMm 1.41 1.05 1.90 1.35 1.10 1.88 1.33 AMs 1.73 1.24 2.37 1.40 1.23 2.36 1.40 AMu 1.72 1.25 2.41 1.39 1.25 2.39 1.38 AMm 1.72 1.25 2.42 1.40 1.28 2.40 1.39 P95s 5.87 2.52 9.31 2.34 2.16 5.87 2.72 P95u 4.01 2.51 6.25 1.60 2.42 6.04 1.66 P95m 4.01 2.53 6.34 1.59 2.54 6.12 1.58

Table 5b. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized short dermal exposure (mg/hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.69 1.41 2.05 1.21 1.48 1.88 1.14 GSDm 1.72 1.42 2.15 1.25 1.48 2.01 1.16 ICC 0.21 0.00 0.66 0.00 0.84 GMs 4.07 2.84 5.89 1.45 3.35 5.01 1.23 GMm 4.07 2.84 5.89 1.45 3.35 5.01 1.23 AMs 4.57 3.19 6.77 1.48 3.78 5.42 1.21 AMu 4.68 3.21 6.85 1.46 3.84 5.56 1.22 AMm 4.72 3.23 6.99 1.48 3.94 5.57 1.20 P95s 8.15 5.96 20.77 2.55 6.31 8.15 1.29 P95u 9.69 5.96 15.55 1.63 7.57 11.57 1.28 P95m 9.96 6.02 16.42 1.66 7.92 12.28 1.26Timothy Leighton, EPA 20 December, 2011 Page 63

Table 6b. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for different statis tical models of the normalized long short dermal exposure (mg/hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.77 1.47 2.13 1.21 1.52 1.95 1.16 GSDm 1.77 1.47 2.16 1.22 1.54 2.01 1.15 ICC 0.04 0.00 0.46 0.00 0.80 GMs 2.19 1.64 2.95 1.35 1.76 2.79 1.28 GMm 2.19 1.64 2.95 1.35 1.76 2.79 1.28 AMs 2.54 1.87 3.51 1.38 1.98 3.21 1.28 AMu 2.58 1.89 3.55 1.38 2.00 3.28 1.29 AMm 2.58 1.90 3.57 1.38 2.05 3.28 1.27 P95s 6.59 3.59 12.20 1.85 3.27 6.59 2.01 P95u 5.59 3.59 8.52 1.56 3.93 7.37 1.42 P95m 5.62 3.62 8.69 1.55 4.12 7.46 1.37

Table 7b. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for different statis tical models of the normalized hands only exposure (mg/hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.79 1.48 2.18 1.22 1.43 2.17 1.25 GSDm 1.79 1.49 2.20 1.23 1.44 2.27 1.26 ICC 0.00 0.00 0.39 0.00 0.59 GMs 0.82 0.62 1.07 1.32 0.64 1.06 1.30 GMm 0.82 0.62 1.07 1.32 0.64 1.06 1.30 AMs 0.98 0.72 1.29 1.37 0.71 1.34 1.38 AMu 0.97 0.72 1.31 1.35 0.71 1.34 1.38 AMm 0.97 0.72 1.31 1.36 0.72 1.37 1.41 P95s 3.63 1.39 4.62 2.61 1.19 3.63 3.05 P95u 2.13 1.39 3.21 1.54 1.29 3.40 1.66 P95m 2.13 1.40 3.25 1.53 1.31 3.64 1.70Timothy Leighton, EPA 20 December, 2011 Page 64

Table 8b. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for different statistical models of the normalized inhalation exposure (mg/m 3 /hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.84 1.50 2.28 1.24 1.54 2.10 1.20 GSDm 1.87 1.50 2.38 1.28 1.55 2.23 1.21 ICC 0.17 0.00 0.62 0.00 0.66 GMs 0.36 0.24 0.54 1.50 0.28 0.46 1.27 GMm 0.36 0.24 0.54 1.50 0.28 0.46 1.27 AMs 0.42 0.28 0.65 1.53 0.33 0.53 1.28 AMu 0.43 0.29 0.66 1.52 0.34 0.55 1.29 AMm 0.44 0.29 0.67 1.54 0.34 0.56 1.28 P95s 0.93 0.58 2.35 2.52 0.63 0.93 1.47 P95u 0.98 0.57 1.66 1.71 0.68 1.30 1.44 P95m 1.01 0.58 1.75 1.74 0.71 1.39 1.42Timothy Leighton, EPA 20 December, 2011 Page 65



### Quantile plot normalized long dermal exposure data with a normal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 0 1 2 3 4 5 6Normalized Long Dermal Exposure

Normal Quantiles

Figure 1bTimothy Leighton, EPA 15 March, 2011 Page 66



### Quantile plot normalized long dermal exposure data with a lognormal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 -1.0 -0.5 0 0.5 1.0 1.5 2.0log (Normalized Long Dermal Exposure)

Normal Quantiles

Figure 2bTimothy Leighton, EPA 15 March, 2011 Page 67



### Quantile plot normalized short dermal exposure data with a normal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 1 2 3 4 5 6 7 8 9Normalized Short Dermal Exposure

Normal Quantiles

Figure 3bTimothy Leighton, EPA 15 March, 2011 Page 68

Quantile plot normalized short dermal exposure data with a lognormal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 0 0.5 1.0 1.5 2.0 2.5log (Normalized Short Dermal Exposure)

Normal Quantiles

Figure 4bTimothy Leighton, EPA 15 March, 2011 Page 69

Quantile plot normalized long short dermal exposure data with a normal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 0 1 2 3 4 5 6 7Normalized Long Short Dermal Exposure

Normal Quantiles

Figure 5bTimothy Leighton, EPA 15 March, 2011 Page 70

Quantile plot normalized long short dermal exposure data with a lognormal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 -0.5 0 0.5 1.0 1.5 2.0lnnrmdermls

Normal Quantiles

Figure 6bTimothy Leighton, EPA 15 March, 2011 Page 71



### Quantile plot normalized hands only exposure data with a normal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Normalized Hands Only Exposure

Normal Quantiles

Figure 7bTimothy Leighton, EPA 15 March, 2011 Page 72



### Quantile plot normalized hands only exposure data with a lognormal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 -1.5 -1.0 -0.5 0 0.5 1.0 1.5log (Normalized Hands Only Exposure)

Normal Quantiles

Figure 8bTimothy Leighton, EPA 15 March, 2011 Page 73



### Quantile plot normalized inhalation conc exposure data with a normal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 0 0.2 0.4 0.6 0.8 1.0Normalized Inhalation Conc Exposure)

Normal Quantiles

Figure 9bTimothy Leighton, EPA 15 March, 2011 Page 74

Quantile plot normalized inhalation conc exposure data with a lognormal distribution Normalized by Hours Spraying Duration

-2 -1 0 1 2 -2.5 -2.0 -1.5 -1.0 -0.5 0log (Normalized Inhalation Conc Exposure)

Normal Quantiles

Figure 10bTimothy Leighton, EPA 15 March, 2011 Page 75

Table 13b. 95 percent confidence inte rvals for the slope of log expos ure versus log spraying duration.

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Dermal (mg) Long pants and long sleeves Mixed 0.61 -0.01 1.22 1.23
Simple Linear 0.61 -0.00 1.22 1.22
Short pants and short sleeves Mixed 0.73 0.19 1.28 1.10
Simple Linear 0.67 0.17 1.18 1.01
Long pants and short sleeves Mixed 0.61 0.07 1.14 1.07
Simple Linear 0.61 0.07 1.14 1.07
Hands Only Mixed 0.61 0.05 1.18 1.12 Simple Linear 0.61 0.06 1.17 1.11

None Mixed 0.79 0.33 1.25 0.92 Simple Linear 0.71 0.27 1.15 0.88

Inhalation (mg/m 3 ) Mixed 0.23 -0.30 0.76 1.06
Simple Linear 0.22 -0.24 0.68 0.92
Dermal (mg) Any Repeated Measures 0.91 0.36 1.45 1.09Timothy Leighton, EPA 15 March, 2011 Page 76

lnderml = 0.0014 +0.608 lnnrm

N 18 Rsq 0.2183 AdjRsq 0.1694
RMSE 0.6212 Simple Linear Regression of Ln Long Dermal Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog Long Dermal Exposure (mg)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 17bTimothy Leighton, EPA 15 March, 2011 Page 77

lnderms = 1.121 +0.6737 lnnrm

N 18 Rsq 0.3341 AdjRsq 0.2925
RMSE 0.5135 Simple Linear Regression of Ln Short Dermal Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog Short Dermal Exposure (mg)

-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 18bTimothy Leighton, EPA 15 March, 2011 Page 78

lndermls = 0.4423 +0.6062 lnnrm

N 18 Rsq 0.2637 AdjRsq 0.2177
RMSE 0.5468 Simple Linear Regression of Ln Long Short Dermal Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog Long Short Dermal Exposure (mg)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 19bTimothy Leighton, EPA 15 March, 2011 Page 79

lnderma = 1.62 +0.7108 lnnrm

N 18 Rsq 0.4224 AdjRsq 0.3863
RMSE 0.4487 Simple Linear Regression of Ln All Dermal Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog All Dermal Exposure (mg)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 20bTimothy Leighton, EPA 15 March, 2011 Page 80

lndermh = -0.5389 +0.6143 lnnrm

N 18 Rsq 0.2558 AdjRsq 0.2093
RMSE 0.5656 Simple Linear Regression of Ln Hands Only Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog Hands Only Exposure (mg)

-2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 21bTimothy Leighton, EPA 15 March, 2011 Page 81

lninh1 = -1.6948 +0.2248 lnnrm

N 18 Rsq 0.0629 AdjRsq 0.0043
RMSE 0.4687 Simple Linear Regression of Ln Inhalation Conc Exposure on Ln Hours Spraying Duration Normalized by Hours Spraying Durationlog Inhalation Exposure (mg/m3)

-3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00

log Hours Spraying Duration -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50

Figure 22bTimothy Leighton, EPA 15 March, 2011 Page 82

Figure 23bTimothy Leighton, EPA 15 March, 2011 Page 83

Figure 24bTimothy Leighton, EPA 15 March, 2011 Page 84

Figure 25bTimothy Leighton, EPA 15 March, 2011 Page 85

Figure 26bTimothy Leighton, EPA 15 March, 2011 Page 86

Figure 27bTimothy Leighton, EPA 15 March, 2011 Page 87

Figure 28bTimothy Leighton, EPA 15 March, 2011 Page 88

Figure 29.1bTimothy Leighton, EPA 15 March, 2011 Page 89

Figure 29.2bTimothy Leighton, EPA 15 March, 2011 Page 90

Figure 29.3bTimothy Leighton, EPA 15 March, 2011 Page 91

Figure 29.4b Table 14b. Quadratic mixed models with 95% confidence intervals fo r the log exposure versus log spraying duration.
Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval
Long Dermal Intercept -0.22 2.00 -1.68 1.24 1.85 0.00 2.93

Long Dermal Slope -0.23 13.00 -1.87 1.41 1.85 0.00 3.28

Long Dermal Quad -0.50 13.00 -1.41 0.41 1.85 0.00 1.82

Short Dermal Intercept 0.99 11.16 0.32 1.66 1.67 0.11 1.34Timothy Leighton, EPA 15 March, 2011 Page 92

Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval

Short Dermal Slope 0.03 13.35 -1.30 1.35 1.67 0.11 2.65

Short Dermal Quad -0.42 13.04 -1.15 0.30 1.67 0.11 1.45

Long Short Dermal Intercept 0.25 2.00 -1.04 1.54 1.72 0.00 2.57

Long Short Dermal Slope -0.14 13.00 -1.58 1.31 1.72 0.00 2.88

Long Short Dermal Quad -0.44 13.00 -1.24 0.36 1.72 0.00 1.60

Hands Only Intercept -0.60 2.00 -1.99 0.79 1.79 0.00 2.78

Hands Only Slope 0.39 13.00 -1.17 1.94 1.79 0.00 3.11

Hands Only Quad -0.14 13.00 -1.00 0.73 1.79 0.00 1.73

Inhalation Intercept -1.85 12.33 -2.45 -1.24 1.59 0.04 1.21

Inhalation Slope -0.40 13.61 -1.65 0.85 1.59 0.04 2.51

Inhalation Quad -0.38 13.21 -1.07 0.30 1.59 0.04 1.37

Dermal Repeated Measures Slope 0.32 12.60 -1.03 1.68 NA NA 2.71

Dermal Repeated Measures Quad -0.35 12.49 -1.09 0.40 NA NA 1.49Timothy Leighton, EPA 15 March, 2011 Page 93

Table 15b. Threshold values for th e amount of active ingredient.
Exposure Route Clothing Model Slope Threshold Level (hours) Dermal (mg) Long pants and long sleeves Mixed 0.61 0.40908

Short pants and short sleeves Mixed 0.73 0.40208

Long pants and short sleeves Mixed 0.61 0.40425

Hands only Mixed 0.61 0.40758

Inhalation (mg/m3) Mixed 0.23 0.37555Timothy Leighton, EPA 15 March, 2011 Page 94

Figure 30bTimothy Leighton, EPA 15 March, 2011 Page 95

Figure 31bTimothy Leighton, EPA 15 March, 2011 Page 96

Figure 32bTimothy Leighton, EPA 15 March, 2011 Page 97

Figure 33bTimothy Leighton, EPA 15 March, 2011 Page 98

Figure 34bTimothy Leighton, EPA 15 March, 2011 Page 99

Analyses of inhalation mass exposure per amount of active ingredient Table and Figure Numbers are consistent with main text (add “c”). Inhalation mass exposure (mg) is esti mated as air concentration (mg/m 3 ) × breathing rate (1 m 3 /hour) × spraying duration (hours). Table 2c. Summary statistics for no rmalized inhalation mass exposure.

Statistic Normalized Inhalation Mass (mg/lb AI) Normalized 100 μ m Inhalation Mass (mg/lb AI) Normalized 10 μ m Inhalation Mass (mg/lb AI) Normalized 2.5 μ m Inhalation Mass (mg/lb AI) Arithmetic Mean 24.6 19.2 10.0 4.4 Arithmetic Standard Deviation 10.5 8.7 5.1 2.6 Geometric Mean 22.3 17.6 8.9 3.8 Geometric Standard Deviation 1.6 1.5 1.6 1.8 Min 6.7 8.7 3.9 1.0 5% 6.7 8.7 3.9 1.0 10% 13.3 9.5 4.8 1.9 25% 15.2 14.2 5.9 2.3 50% 23.9 16.0 8.5 3.9 75% 35.7 25.0 13.6 5.6 90% 39.1 32.0 20.7 8.8 95% 42.5 41.1 20.9 11.1 Max 42.5 41.1 20.9 11.1Timothy Leighton, EPA 15 March, 2011 Page 100

Table 3c. Arithmetic mean and 95 th percentile estimates from lognormal mixed model for normalized inhalation mass exposure.

Exposure Route Arithmetic Mean (95% confidence interval) 95 th percentile (95% confidence interval) Inhalation mass (mg/lb AI) 25.1 (19.8, 32.0) 49.4 (34.8, 69.8)

100 μ m inhalation mass (mg/lb AI) 19.4 (14.1, 26.9) 36.7 (24.0, 56.1)

10 μ m inhalation mass (mg/lb AI) 10.1 (7.8, 13.3) 20.2 (13.8, 29.5)

2.5 μ m inhalation mass (mg/lb AI) 4.5 (3.3, 6.2) 10.0 (6.5, 15.6)

Table 8c. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized inhalation mass exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.6 1.4 1.9 1.2 1.4 1.9 1.2 GSDm 1.6 1.4 1.9 1.2 1.4 1.9 1.2 ICC 0.0 0.0 0.4 0.0 0.5 GMs 22.3 17.9 28.0 1.3 17.9 27.4 1.2 GMm 22.3 17.9 28.0 1.3 17.9 27.4 1.2 AMs 24.6 19.7 31.7 1.3 20.1 29.3 1.2 AMu 25.1 19.8 32.0 1.3 20.3 29.8 1.2 AMm 25.1 19.8 32.0 1.3 20.5 29.9 1.2 P95s 42.5 34.7 93.4 2.2 36.2 42.5 1.2 P95u 49.4 34.6 69.1 1.4 36.7 60.5 1.3 P95m 49.4 34.8 69.8 1.4 37.0 62.2 1.3Timothy Leighton, EPA 15 March, 2011 Page 101

Table 9c. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 100 μ m inhalation mass exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.5 1.3 1.8 1.2 1.4 1.7 1.1 GSDm 1.6 1.3 1.9 1.2 1.4 1.8 1.1 ICC 0.2 0.0 0.7 0.0 0.7 GMs 17.6 12.9 24.0 1.4 14.9 20.7 1.2 GMm 17.6 12.9 24.0 1.4 14.9 20.7 1.2 AMs 19.2 14.0 26.4 1.4 16.0 22.6 1.2 AMu 19.3 14.1 26.6 1.4 16.0 22.7 1.2 AMm 19.4 14.1 26.9 1.4 16.1 23.1 1.2 P95s 41.1 23.7 67.0 1.7 26.2 41.1 1.6 P95u 35.8 23.7 53.3 1.5 26.7 44.1 1.3 P95m 36.7 24.0 56.1 1.5 27.2 47.5 1.4

Table 10c. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 10 μ m inhalation mass exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.6 1.4 1.9 1.2 1.4 1.8 1.2 GSDm 1.6 1.4 2.0 1.2 1.4 1.9 1.1 ICC 0.0 0.0 0.5 0.0 0.7 GMs 8.9 6.9 11.5 1.3 7.3 11.0 1.2 GMm 8.9 6.9 11.5 1.3 7.3 11.0 1.2 AMs 10.0 7.7 13.1 1.3 8.0 12.3 1.2 AMu 10.1 7.8 13.2 1.3 8.0 12.5 1.3 AMm 10.1 7.8 13.3 1.3 8.1 12.6 1.3 P95s 20.9 13.7 39.6 1.9 13.8 20.9 1.5 P95u 20.1 13.7 28.9 1.5 14.3 26.2 1.4 P95m 20.2 13.8 29.5 1.5 14.5 27.1 1.4Timothy Leighton, EPA 15 March, 2011 Page 102

Table 11c. Arithmetic mean, geometric mea n, geometric standard deviation, and 95 th percentiles (with 95% confidence intervals and fold relative accuracy), for diffe rent statistical models of the normalized 2.5 μ m inhalation mass exposure (mg/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 1.8 1.5 2.2 1.2 1.5 2.1 1.2 GSDm 1.8 1.5 2.2 1.2 1.5 2.2 1.2 ICC 0.0 0.0 0.4 0.0 0.6 GMs 3.8 2.9 5.1 1.3 3.0 4.9 1.3 GMm 3.8 2.9 5.1 1.3 3.0 4.9 1.3 AMs 4.4 3.3 6.1 1.4 3.4 5.6 1.3 AMu 4.5 3.3 6.2 1.4 3.5 5.7 1.3 AMm 4.5 3.3 6.2 1.4 3.5 5.8 1.3 P95s 11.1 6.4 22.1 2.0 5.7 11.1 1.9 P95u 10.0 6.4 15.3 1.6 6.8 13.7 1.5 P95m 10.0 6.5 15.6 1.6 6.9 14.5 1.5



### Q uantile plot normalized inhalation mass exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 10 20 30 40 50Normalized Inhalation Mass Exposure)

Normal Quantiles

Figure 9cTimothy Leighton, EPA 15 March, 2011 Page 103

Quantile plot normalized inhalation mass exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 1.5 2.0 2.5 3.0 3.5 4.0log (Normalized Inhalation Mass Exposure)

Normal Quantiles

Figure 10cTimothy Leighton, EPA 15 March, 2011 Page 104



### Quantile plot normalized 100um mass exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 5 10 15 20 25 30 35 40 45Normalized 100um Mass Exposure)

Normal Quantiles

Figure 11cTimothy Leighton, EPA 15 March, 2011 Page 105



### Quantile plot normalized 100um mass exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75log (Normalized 100um Mass Exposure)

Normal Quantiles

Figure 12cTimothy Leighton, EPA 15 March, 2011 Page 106



### Quantile plot normalized 10um mass exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5Normalized 10um Mass Exposure)

Normal Quantiles

Figure 13cTimothy Leighton, EPA 15 March, 2011 Page 107



### Quantile plot normalized 10um mass exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25log (Normalized 10um Mass Exposure)

Normal Quantiles

Figure 14cTimothy Leighton, EPA 15 March, 2011 Page 108



### Quantile plot normalized 2.5um mass ex posure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 2 4 6 8 10 12Normalized 2.5um Mass Exposure)

Normal Quantiles

Figure 15cTimothy Leighton, EPA 15 March, 2011 Page 109



### Quantile plot normalized 2.5um mass exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-2 -1 0 1 2 0 0.5 1.0 1.5 2.0 2.5log (Normalized 100um Mass Exposure)

Normal Quantiles

Figure 16cTimothy Leighton, EPA 15 March, 2011 Page 110

Table 13c. 95 percent confidence inte rvals for the slope of log inhalation exposure ma ss versus log pounds active ingredient handled.

Exposure Route Model Estimate Lower Upper Confidence Interval Width Inhalation mass (mg) Mixed 1.55 1.02 2.08 1.05
Simple Linear 1.55 1.03 2.07 1.04

lninh5 = 6.3267 +1.5491 lnnrm

N 18 Rsq 0.7136 AdjRsq 0.6957
RMSE 0.4338 Simple Linear Regression of Ln Inhalation Mass Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Inhalation Mass Exposure (mg)

-5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5

log Pounds Active Ingredient Handled -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6 -5.4 -5.2

Figure 22cTimothy Leighton, EPA 15 March, 2011 Page 111

Figure 28c Table 14c. Quadratic mixed models with 95% confidence interval s for the log inhalation mass exposure versus log pounds active ingredient handled.
Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval

Inhalation

mass Intercept -18.51 2.00 -106.93 69.92 1.53 0.00 176.85

Inhalation

mass Slope -6.83 13.00 -21.79 8.13 1.53 0.00 29.92

Inhalation

mass Quad -0.70 13.00 -1.96 0.55 1.53 0.00 2.51Timothy Leighton, EPA 15 March, 2011 Page 112

Table 15c. Threshold values for the amount of active ingredient.
Exposure Route Model Slope Threshold Level (lb active ingredient)

Inhalation mass (mg) Mixed 1.55 0.00295*

*For this case, slope > 1 and so the normalized expos ure mixed model under-predicts exposure for pounds of active ingredient above the threshold.

Figure 34c