MEMORANDUM

To: Timothy Leighton, EPA
From: Jonathan Cohen, ICF
Date: 15 March, 2011

Re: Contract No.: EP-W-06-091 WA 4-02: AEATF Wipe Study Using Trigger Spray a nd Wipe Statistical Review for HSRB

Introduction and Summary In January 2011, AEATF submitted the final report for thei r study “A Study for Measuremen t of Potential Dermal and Inhalation Exposure during Application of a Liquid An timicrobial Pesticide Product Using Trigger Spray and Wipe or Ready-to-Use Wipes for Cleaning Indoor Surfaces.” ICF were asked to analyze the data for Trigger Spray and Wipe from this study to investig ate the relationship between dermal and inhalation exposures and the pesticide product usage. Note that much of the SAS code used for these analyses and some of the 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 Sta tistical Analyses in Agricultural Handler Exposure Task 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: cluster 1, an offi ce space; cluster 2, a retail/shopping center, and; cluster 3, a meeting space. For each test site, six volunteer subjects were selected and ra ndomly assigned different wiping time durations from 30 minutes to 210 minutes. Each subject was given inner and outer dosimete rs to wear and was also given a personal air-sampling pum p to monitor their inha lation exposure. Each subject th en used a trigger spray bottle and rags to wipe horizontal and vert ical surfaces for their as signed wiping time duration. In cluster 1, the DDAC pesticide was diluted as one part concen trated test substance and 64 parts tap wa ter according to the product directions. In clusters 2 and 3, the directions were misinterpreted and the DDAC pesticide was diluted as one part concentrated test substance and 63 parts tap water. Subjects were allowed to take breaks on a ch air away from the wiping site, as needed. The breaks were not included in th e wiping time duration but the air-sam pling pump remained on throughout the breaks. Although the study design was not a probability su rvey, some elements of the design used randomization. These statistical analyses treat the data as either a simple random sa mple or a stratified 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 samples. These analyses used the corrected measurements. The data in the report were entered and compiled into an Excel spreadsheet. This included the units conversion of the amounts of active ingredient from mg into pounds and of the mass from μg to mg. The report data for inhalation exposure were unchanged other than the uni ts conversions. The dermal exposure da ta were used to develop exposure measurements for three 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).Timothy Leighton, EPA 15 March, 2011 Page 2

• 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). 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. As a slightly more conservative (i.e., more health prot ective) approach than the method used in the report, we repl aced 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 the inner dosimeters were below the LOQ, then the total would be replaced by 0.009 mg. If the face and neck measurement was below the LOQ, 50 ng, it was replaced by 25 ng = 0.000025 mg. All the hand wash m easurements in the study were above the LOQ. 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 office site might be correlated because of the physical si milarities of the room, the physical similarities of the surfaces that were wiped, the building char acteristics, the investigators at that lo cation, or other factors that are due to the selected location. For each summary st atistic we present confidence intervals. We also compute the fold relative accuracy of the summary statistics and compare with the st udy design benchmark of 3-fold accuracy. To evaluate the statistical models we present quantile- quantile plots to compare the fit of no rmal 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 use d. We applied this test to the three dermal exposures and to the inhalation 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 re peated measures model to anal yze all three types of dermal exposure in a single statisticalTimothy Leighton, EPA 15 March, 2011 Page 3

model, accounting for within-worker co rrelations and within-lo cation clustering. We also evaluated quadratic regression models. The results for long dermal and long short dermal exposure routes show that the estima ted intra-cluster correlation (ICC) coefficient is zero, which implies that there are no cl ustering and location effects. However, the estimated intracluster correlation (ICC) coefficient for short dermal is 0.2 and for inhalation exposure is 0.3, which implies that there are some clustering and location differences, which one can hypothesize as being primarily due to differences in the wiping surfaces between different buildings. The mixed model results for the four dermal exposure routes all show a positive estimated slope but give inconsistent results for the tests of proportionality (s lope equals one) and independence (slope equals zero). At the 5% level, the proportionality is rejected for long dermal and short dermal , but proportionality is not re jected for long short dermal and all dermal. At the 5% level, the independence is re jected for short dermal, l ong short and all dermal, but independence is not rejected for long de rmal. Using the repeated measures mode l, proportionality and independence are both rejected. The mixed model results for inhalation expo sure show a small slope of 0.2 and the proportionality is rejected. The appendix gives the detailed results of the corresponding analyses when the exposure is normalized by the wiping duration. The appendix also includes an analysis of inhalation exposure normalized by th e product of the pounds of active ingredient handled and the wipi ng duration, and an analysis of inhala tion exposure normalized by the surface area wiped. The results show similar pa tterns to the normalization by amount of active ingredient handled but the slopes are lower, showing less support fo r those alternative exposure models. For inhalation, the data suggest that the exposure is either independent of any of these normalizing variables or is a non-linear function of these normalizing variables. A summary comparing the nor malizing approaches is presented at the end of this memorandum. The mixed model analyses show that in most cases (including the rep eated measures model), the best of the normalizing options considered is the amount of active ingredient handled for de rmal exposures, and is the surf ace area wiped for inhalation exposure. The inhalation exposure measure used for the main analyses presented here is the aver age air concentration (mg/m 3 ) over the entire period that the concentration was measured, which includes the breaks as well as the wiping durations. As an alternative approach we consid ered using the air DDAC mass (mg) which can be estimated as the average air concentration multiplied by the wiping dur ation (hours) and by an estimated 1 m 3 /hour of air breathed in by someone doing light activity. A similar statistical analysis found that the air DDAC mass is not proportional to amount of active ingredient × wiping duration, but there is not enough evidence at the 5% le vel to reject proportionality for the other three normalizing variables (amount of active ingredie nt, wiping duration, surface area wiped). As shown in the summary table 10 below, the best-fitting model for the nor malized air DDAC mass normalizes for the amount of active ingredient used. The appendix includes th e detailed results for this model. Analyses of exposure per pounds of active ingredient handled Table 1 summarizes the normalized exposur e data (per lb active ingredient ha ndled) with the summary statistics from the 18 measurements for each exposure route.Timothy Leighton, EPA 15 March, 2011 Page 4

Table 1. Summary statistics for normalized 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 Inhalation (mg/m 3 /lb AI) Arithmetic Mean 1065.8 1736.2 1544.7 10.2 Arithmetic Standard Deviation 853.9 1083.4 1027.2 10.8 Geometric Mean 859.2 1507.3 1325.1 6.7 Geometric Standard Deviation 1.9 1.7 1.7 2.7 Min 384.2 684.8 668.8 0.4 5% 384.2 684.8 668.8 0.4 10% 455.3 785.3 672.2 3.0 25% 551.6 1046.0 844.8 4.2 50% 731.1 1276.1 1195.0 7.4 75% 1139.9 2250.4 1927.0 12.8 90% 2780.0 2988.6 2929.7 26.5 95% 3478.6 5154.6 4841.8 46.3 Max 3478.6 5154.6 4841.8 46.3

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

c Long Short = Long pants and short sleeves The summary analyses presented in Table 1 use the 18 m easurements with a simple random sampling model that ignores the fact that th e data were selected by choosing three “clusters” representing thre e different location types, and then measuring dermal and inhalation exposures on six subjects in each of the three cluste rs (a total of 18 different volunteer subjects). The six subjects in each cluster were randomly assigned si x different amounts of wiping, as defined by the time to be spent wiping:

• 30 to < 60 minutes

• 60 to < 90 minutes

• 90 to < 120 minutes

• 120 to < 150 minutes

• 150 to < 180 minutes

• 180 to 210 minutes 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.Timothy Leighton, EPA 15 March, 2011 Page 5

• Empirical simple random sampling model. Code “s.” Assu mes that the 18 values of X were randomly drawn from an unspecified distribution. Ignores clustering. Gi ves empirical estimates such as in Table 1 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) 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.Timothy Leighton, EPA 15 March, 2011 Page 6

Table 2 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 2. 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 1047.6 (748.6, 1494.1) 2420.4 (1500.5, 3892.5)

Short pants and short sl eeves 1739.9 (1224.5, 2499.9) 3638.0 (2266.6, 5835.9) Long pants and short slee ves 1533.3 (1162.6, 2050.8) 3222.2 (2148.2, 4835.4) Inhalation (mg/m 3 /lb AI) 11.6 (4.8, 29.9) 37.5 (13.0, 109.6)

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 2 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. The algorithm used was as follows:
Step 1:
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)Timothy Leighton, EPA 15 March, 2011 Page 7

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 because 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 mightTimothy Leighton, EPA 15 March, 2011 Page 8

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 wipe 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 3 to 6 present the estimates, parametric and non-pa rametric confidence intervals and fold relative accuracy values for all the summary statistic s for the three dermal and one inha lation exposure routes, respectively. Table 3. 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 1.9 1.5 2.3 1.2 1.5 2.1 1.3 GSDm 1.9 1.5 2.3 1.2 1.5 2.2 1.3 ICC 0.0 0.0 0.4 0.0 0.6 GMs 859.2 626.2 1185.7 1.4 669.4 1129.4 1.3 GMm 859.2 626.2 1185.7 1.4 669.4 1129.4 1.3 AMs 1065.8 736.7 1468.3 1.4 737.4 1441.4 1.4 AMu 1045.6 745.7 1483.8 1.4 733.3 1452.5 1.4 AMm 1047.6 748.6 1494.1 1.4 740.2 1512.2 1.4 P95s 3478.6 1484.4 5660.2 2.3 1185.7 3478.6 2.9 P95u 2408.6 1483.8 3811.5 1.6 1297.7 3673.4 1.9 P95m 2420.4 1500.5 3892.5 1.6 1342.7 4030.2 1.8Timothy Leighton, EPA 15 March, 2011 Page 9

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 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 1.7 1.4 2.0 1.2 1.4 1.9 1.2 GSDm 1.7 1.4 2.1 1.2 1.4 2.0 1.2 ICC 0.2 0.0 0.6 0.0 0.7 GMs 1507.3 1076.5 2132.2 1.4 1233.9 1868.7 1.2 GMm 1507.3 1076.5 2132.2 1.4 1233.9 1868.7 1.2 AMs 1736.2 1209.0 2447.8 1.4 1337.2 2201.4 1.3 AMu 1727.8 1216.4 2465.3 1.4 1334.3 2216.3 1.3 AMm 1739.9 1224.5 2499.9 1.4 1342.0 2277.7 1.3 P95s 5154.6 2251.5 7514.0 2.3 2516.6 5154.6 2.0 P95u 3560.0 2245.3 5575.9 1.6 2295.0 5013.8 1.6 P95m 3638.0 2266.6 5835.9 1.6 2327.2 5497.9 1.6

Table 5. 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 1.7 1.4 2.1 1.2 1.4 1.9 1.2 GSDm 1.7 1.4 2.1 1.2 1.4 2.0 1.2 ICC 0.0 0.0 0.4 0.0 0.6 GMs 1325.1 1016.8 1735.7 1.3 1063.3 1667.7 1.3 GMm 1325.1 1016.8 1735.7 1.3 1063.3 1667.7 1.3 AMs 1544.7 1150.0 2021.2 1.3 1158.1 1994.4 1.3 AMu 1531.9 1160.2 2038.8 1.3 1154.1 1997.7 1.3 AMm 1533.3 1162.6 2050.8 1.3 1157.9 2047.7 1.3Timothy Leighton, EPA 15 March, 2011 Page 10

Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy P95s 4841.8 2138.5 6653.3 2.3 2071.1 4841.8 2.3 P95u 3213.0 2138.3 4753.6 1.5 2009.8 4612.2 1.6 P95m 3222.2 2148.2 4835.4 1.5 2034.8 4972.7 1.6

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 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 2.7 1.9 4.1 1.5 1.7 3.9 1.6 GSDm 2.9 1.9 4.7 1.6 1.8 4.5 1.6 ICC 0.3 0.0 0.7 0.0 0.7 GMs 6.7 3.1 14.4 2.2 4.5 9.5 1.5 GMm 6.7 3.1 14.4 2.2 4.5 9.5 1.5 AMs 10.2 4.5 25.2 2.5 6.5 14.5 1.6 AMu 11.0 4.7 26.6 2.4 7.0 17.0 1.6 AMm 11.6 4.8 29.9 2.6 7.2 19.8 1.7 P95s 46.3 12.8 153.4 3.6 13.0 46.3 3.6 P95u 34.8 12.6 92.8 2.8 16.2 61.1 2.1 P95m 37.5 13.0 109.6 2.9 16.8 74.5 2.2

Tables 3 and 5 show that the ICC estimated value is zero for the long dermal and long s hort dermal 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. Tables 4 and 6 s how that the ICC estimated va lue is non-zero for the short dermal and inhalation exposure routes showing that the estimated mixed and simple random sampling models are not the same for those cases and that ther e is some variation between the differe nt locations. All of the fold relative accuracy values met the study design benchmark of 3 except for the empirical 95 th percentile for the normalized inhalation exposure. The parametric bootstrap confidence intervals were si milar to the non-parametric bootstrap confidence intervals for the dermal exposure routes, but were generally wider than the non-parametric bootstrap confidence intervals for the inhalation exposure. 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 plots are presented in Figures 1 to 8. TheyTimothy Leighton, EPA 15 March, 2011 Page 11

clearly show that the lognormal distribu tion is a better fit than a normal distribution, and that the lognormal distribution fits reasonably 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 0 500 1000 1500 2000 2500 3000 3500Normalized Long Dermal Exposure

Normal Quantiles

Figure 1Timothy Leighton, EPA 15 March, 2011 Page 12



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

-2 -1 0 1 2 5.5 6.0 6.5 7.0 7.5 8.0 8.5log (Normalized Long Dermal Exposure)

Normal Quantiles

Figure 2Timothy Leighton, EPA 15 March, 2011 Page 13



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

-2 -1 0 1 2 0 1000 2000 3000 4000 5000 6000Normalized Short Dermal Exposure

Normal Quantiles

Figure 3Timothy Leighton, EPA 15 March, 2011 Page 14

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

-2 -1 0 1 2 6.5 7.0 7.5 8.0 8.5 9.0log (Normalized Short Dermal Exposure)

Normal Quantiles

Figure 4Timothy Leighton, EPA 15 March, 2011 Page 15

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

-2 -1 0 1 2 0 1000 2000 3000 4000 5000Normalized Long Short Dermal Exposure

Normal Quantiles

Figure 5Timothy Leighton, EPA 15 March, 2011 Page 16

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

-2 -1 0 1 2 6.5 7.0 7.5 8.0 8.5lnnrmdermls

Normal Quantiles

Figure 6Timothy Leighton, EPA 15 March, 2011 Page 17



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

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

Normal Quantiles

Figure 7Timothy Leighton, EPA 15 March, 2011 Page 18



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

-2 -1 0 1 2 -1 0 1 2 3 4log (Normalized Inhalation Exposure)

Normal Quantiles

Figure 8Timothy Leighton, EPA 15 March, 2011 Page 19

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 wiping times, and hence the amount of active ingredient handled, varied between the su bjects as part of the study design. Other possible models include the same model with a slope not equal to zero or one, the quadratic models discussed below, or models with more complicated relationships between th e exposure and the experimental conditi ons. To evaluate whether the slope is zero, one, or other possible values, we fitted the above sta tistical model and computed confidence intervals for the slope. In the appendix we i nvestigate normalizing by the wiping duration or , for inhalation exposure, by the product of the pounds of active ingredient and wiping duration and by the number of wipes used. 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 7 summarizes the five available methods: Table 7. SAS Methods for Computing the Fixed Effects Denominator Degr ees 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 15 March, 2011 Page 20

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 15 March, 2011 Page 21

dermal, short dermal, and long short dermal exposure agains t the 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 and inhalation exposure against the logarith m of the pounds of active ingredient handled was non-zer o, the Kenwood-Rogers method was used for those mixed models. (As noted above the ICC for the normalized short dermal exposure was es timated to be 0.2, a small but nonzero value; this is not inconsistent with the regression analysis because the regression model allows the slope to be arbitrary but the model for the normalized short dermal exposure assumes the slope is equal to 1.) Note that this issue does not impact the calculated confidence intervals for the summary statistics in Tables 2 to 6, since they us ed a bootstrap method. Table 8 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 handle d. A confidence interval th at 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. Table 8. 95 percent confidence in tervals for the slope of l og 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 0.37 -0.02 0.76 0.78
Simple Linear 0.37 -0.01 0.76 0.77
Short pants and short sleeves Mixed 0.57 0.21 0.93 0.73
Simple Linear 0.57 0.21 0.93 0.72
Long pants and short sleeves Mixed 0.58 0.20 0.97 0.77
Simple Linear 0.58 0/21 0.96 0.76

None Mixed 0.74 0.35 1.12 0.77 Simple Linear 0.65 0.27 1.02 0.74

Inhalation (mg/m 3 ) Mixed 0.25 -0.46 0.96 1.42
Simple Linear 0.15 -0.53 0.83 1.36
Dermal (mg) Any Repeated Measures 0.49 0.03 0.96 0.93Timothy Leighton, EPA 15 March, 2011 Page 22

For the long dermal exposure route, th e confidence interval for the slope incl udes 0 and excludes 1, and the estimated slope is approximately 0.4. Thus the assu mption of proportionality was rejected at the 5% level but the assumption of independence was not rejected. For the short dermal exposure route, the confidence interval for the slope excludes 0 and excludes 1, and the estimated slope is approximately 0.6. Thus the assumption of propor tionality was rejected at the 5% level as was the assumption of independence. For th e long short and all dermal e xposure routes, th e confidence interval for the slope includes 1 and excludes 0, and the es timated slope is approximately 0.6. Thus the assumption of proportionality was rejected at the 5% level and the assumption of independen ce was not rejected. For the inhalation exposure, there is sufficient evidence to reject the hypothesis of a slope of 1 at the 5% significance level. 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 )
So, expected width of confidence interval for slope parameter = 2 × 0.7 = 1.4
The results in Table 8 show that the act ual confidence interval widt hs were less than 1.4 for the dermal exposure routes. However, the actual confidence interval widths were slightly greater than 1.4 for the inhalation exposure route because the standard errors of the slopes in the actual data were greater th an the values estimated using the CMA data prior to the experiment. 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 9 to 13.Timothy Leighton, EPA 15 March, 2011 Page 23

lnderml = 2.4916 +0.373 lnnrm

N 18 Rsq 0.2077 AdjRsq 0.1582
RMSE 0.4896 Simple Linear Regression of Ln Long Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Long Dermal Exposure(mg)

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 9Timothy Leighton, EPA 15 March, 2011 Page 24

lnderms = 4.401 +0.5711 lnnrm

N 18 Rsq 0.4158 AdjRsq 0.3793
RMSE 0.4549 Simple Linear Regression of Ln Short Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Short Dermal Exposure(mg)

-0.5 0.0 0.5 1.0 1.5 2.0

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 10Timothy Leighton, EPA 15 March, 2011 Page 25

lndermls = 4.3634 +0.5845 lnnrm

N 18 Rsq 0.4015 AdjRsq 0.3641
RMSE 0.4797 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)

-0.5 0.0 0.5 1.0 1.5 2.0

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 11Timothy Leighton, EPA 15 March, 2011 Page 26

lnderma = 5.2054 +0.6467 lnnrm

N 18 Rsq 0.4586 AdjRsq 0.4247
RMSE 0.4723 Simple Linear Regression of Ln All Dermal Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog All Dermal Exposure(mg)

-0.5 0.0 0.5 1.0 1.5 2.0

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 12Timothy Leighton, EPA 15 March, 2011 Page 27

lninh = -3.8988 +0.1477 lnnrm

N 18 Rsq 0.0131 AdjRsq -.0486
RMSE 0.8615 Simple Linear Regression of Ln Inhalation Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Inhalation Exposure(mg/m3)

-7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 13Timothy Leighton, EPA 15 March, 2011 Page 28

These simple linear regression results are compared with th e results for the lognormal mixe d models in Figures 14 to 18. Note that in the first three dermal exposure Figures 14 to 16, the regression lines are the same for the mixed and simple linear regression m odels because the estimated ICC parameter was zero.

Figure 14Timothy Leighton, EPA 15 March, 2011 Page 29

Figure 15Timothy Leighton, EPA 15 March, 2011 Page 30

Figure 16Timothy Leighton, EPA 15 March, 2011 Page 31

Figure 17Timothy Leighton, EPA 15 March, 2011 Page 32

Figure 18Timothy Leighton, EPA 15 March, 2011 Page 33

Finally, in Figures 19 and 20 we present regression plots showing the different regression lines for the three clusters based on the mixed models for all dermal and inhalation expo sure. (For the long, short, a nd long short dermal exposure routes, the models predict the same values for all three cluste rs, i.e., they predict the values shown in Figures 14 to 16). The mixed model predicts the highest al l dermal and inhalation exposures in Cl uster 1 (office), and the lowest dermal all dermal and inhalation exposures in Cluster 2 (retail / shopping center), whic h is consistent with the data. These differences are likely attribut able to the different wiping su rfaces in the three buildings.

Figure 19Timothy Leighton, EPA 15 March, 2011 Page 34

Figure 20 The above analyses of the proportionalit y for dermal exposure consistently show similar positive slopes, as one might expect on physical grounds. While all of the estimated sl opes for dermal exposure are positive and approximately 0.5, the confidence intervals were inconsistent about whether they include d zero or included one. To investigate this issue further, the following more complicated statistical model was fitted to the data of all thr ee dermal exposures (excluding the unrealistic 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 RANDOM 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 8. Since the confidence interval does not include one and does not include zero, the proportionality for dermal exposure has not been shown using this statistical model.Timothy Leighton, EPA 15 March, 2011 Page 35

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. 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.Timothy Leighton, EPA 15 March, 2011 Page 36

We will first present the results of fitting these quadratic mo dels to the study data. We will then consider whether these statistical models produce meaningful and useful physical models for antimicrobial exposure. Table 9 presents the fitted quadratic m odels from the study for the mixed models of the four exposure measurements (Long Dermal, Short Dermal, Long Short Dermal, Inhalation) and for the Rep eated Measures model for Dermal exposures. For the Repeated Measures model, the model ha s 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 9. 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 9.80 2.00 -32.28 51.87 1.64 0.00 84.16

Long Dermal Slope 2.55 13.00 -3.70 8.79 1.64 0.00 12.49

Long Dermal Quad 0.16 13.00 -0.30 0.62 1.64 0.00 0.92

Short Dermal Intercept 19.19 14.22 0.05 38.32 1.55 0.07 38.27

Short Dermal Slope 4.94 14.09 -0.68 10.56 1.55 0.07 11.23

Short Dermal Quad 0.32 13.96 -0.09 0.73 1.55 0.07 0.82

Long Short Dermal Intercept 19.96 2.00 -18.23 58.15 1.57 0.00 76.37

Long Short Dermal Slope 5.22 13.00 -0.44 10.89 1.57 0.00 11.34

Long Short Quad 0.34 13.00 -0.07 0.76 1.57 0.00 0.83Timothy Leighton, EPA 15 March, 2011 Page 37

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

Dermal
Inhalation Intercept 10.83 13.88 -25.31 46.98 2.44 0.19 72.29

Inhalation Slope 4.42 13.79 -6.20 15.04 2.44 0.19 21.24

Inhalation Quad 0.31 13.70 -0.47 1.08 2.44 0.19 1.55

Dermal Repeated Measures Slope 4.29 13.30 -2.04 10.62 NA NA 12.64

Dermal Repeated Measures Quad 0.27 13.16 -0.19 0.74 NA NA 0.93

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. Physical Implications Let us now consider the physical implications of these quadratic models. Exponentiati ng both sides of the exposure regression equation (and assumi ng zero error) produces the model Exposure = exp[Intercept + Slope × Log (Pounds of Active Ingredient) + Quad × {Log (Pounds of Active Ingredient)} 2 }] = A(Pounds of Active Ingredient) Slope × exp[Quad × {Log (Pounds of Active Ingredient)} 2 }] where A = exp(Intercept). The final term doe s not simplify unless Quad equals zero. Under the quadratic model, the predicte d exposure will not double if the amount of active ingredient is doubled, which would happen if the same amounts of liquid were sprayed onto the rags but the concentrati on in the bottle is doubled, or if the duration is doubled and the concentration in each spra y bottle is the same. In the first case, the physical model might be explained by some non-linearit y in atmospheric or physical proce sses. In the second case, a physical explanation might be something like the idea that if you wi pe for twice as long, you get mo re tired which increases the probability of larger accidental exposure s, or alternatively that if you wipe twice as lon g, you get more experienced which decreases the probability of exposures. For the DDAC experiment the concentration in each bottle was the same (other than the unplanned slight concentr ation differences of 1/65 versus 1/64 be tween cluster 1 and clusters 2 and 3), so we only have data for the second case and cannot esti mate what would happen in th e first case without making additional assumptions. According to this logic, if the quadratic model is true then the results of the DDAC experiment could only be used directly to estimate exposures when the liq uid concentration is the same as used in the experiment,Timothy Leighton, EPA 15 March, 2011 Page 38

and you would need to make additional assumptions in orde r to use the same model to predict exposures when DDAC is used at a different concentration or, more importantly, when another antim icrobial is used instead of DDAC. If Quad equals zero, then the model becomes the Linear model for log Exposure and the exposure equation becomes Exposure = A(Pounds of Active Ingredient) Slope
Unless Slope = 1, the predicted exposure will not double if the amount of active ingredient is doubled, which again implies non-linearity in the exposure. Howe ver if Quad equals 0 and Slope = 1, th en the exposure is proportional to the amount of active ingredient a nd the model implies that norma lized exposure is physically meaningful, and hence that the results of the DDAC experiment can be used directly to estimate exposure s when DDAC is used at a different concentration or, more importantly, when anot her antimicrobial is us ed instead of DDAC. The primary goal of the analysis should be to test whether or not the exposure s are proportional to the amount of active ingredient, rather than trying to find the best-fitting statisti cal model for the exposure as a function of the amount of active ingredient. The first step should be to use the Linear model for log Expos ure for the proportionality test, which compares the proportionality model with the m odel Exposure = A(Pounds of Active Ingredient) Slope . If the proportionality is rejected, then the Quadratic model and other complicated model formulations could then be considered. However in this case it woul d be desirable to obtain exposure data using different liquid concentrations of DDAC and/or different antimic robials to develop physically realistic mo dels without making untested assumptions. Over-prediction from normalized exposure model. As an approximation, one can use the normalized exposure m odel to estimate exposures even if the proportionality assumption is rejected by the statistica l test. Suppose that the linear model for log Exposure is correct. Then the exposure is given by the equation Exposure estimate from linear model = exp(In tercept) × (Pounds of Active Ingredient) Slope
If the normalized exposure model is used to estimate the e xpected exposure, then the estimated exposure is given by the pounds of active ingredient multip lied by the average normalized exposur e, which is estimated by AMm, the arithmetic mean from the lognormal mixed model. Thus we have Exposure estimate from normalized exposure model = AMm × Pounds of Active Ingredient Suppose that the estimated slope is less than 1. Then the exposure estimate from the normalized exposure model will over-predict the exposure from the linear model if, and only if, the pounds of active ingredient exceeds the following threshold: Threshold = {AMm / exp(Intercept)} 1/(Slope – 1)
These threshold values are given in Table 10.Timothy Leighton, EPA 15 March, 2011 Page 39

Table 10. Minimum Pounds of Active I ngredient for Which Normalized Expos ure Model Over-Predicts Dermal and Inhalation Exposure.
Exposure Route Clothing Model Slope Threshold Level (lb AiaH) Dermal (mg) Long pants and long sleeves Mixed 0.37 0.00081

Short pants and short sleeves Mixed 0.57 0.00080

Long pants and short sleeves Mixed 0.58 0.00078

Inhalation (mg/m3) Mixed 0.25 0.00053

Alternative normalizing variables The appendix gives the tables and graphs with the detailed re sults of the analysis when the exposure is normalized by the wiping duration or, for inhalation exposure only, by th e product of pounds of active i ngredient handled and wiping duration or by surface area wiped. The long dermal and repeat ed measures exposure models are inconsistent with proportionality for the wiping duration. The short dermal, long dermal, and all dermal exposure models are consistent with proportionality for the wiping duration, but the confiden ce intervals are much wider than for the amount of active ingredient. The inhalation exposure m odels are inconsistent with proporti onality for product of pounds of active ingredient handled and wiping duration and are only just consistent with pr oportionality for the surface area wiped (upper bound of 95% confid ence interval is 1.00). 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, calcula ted as the average air concen tration multiplied by the wiping 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 DDAC breathed in by each part icipant. However this is an approxima tion because actual breathing rates are not constant and will vary with the activity as well as the individual. Moreover, the air concentration was measured and averaged over the entire air pumping period, which includes the resting peri ods (breaks) as well as the wiping durations. The analysis shown in the appendix is for the mass normalized by the amount of active ingredient. Using both normalizing variables (amount of active ingredient, wiping duration), th e ICC value is either zero or is small (at most 0.2) for all three dermal routes, showing only a small amount of variability be tween the clusters, i.e., the locations. Using the four normalizing variables (amount of ac tive ingredient, wiping duration, amount of active ingredient × wiping duration, number of wipes) the ICC value for normalized i nhalation exposure (as a concentration) was non-zero and at most 0.3, also showing that the inhalation exposure does not va ry very much between the clusters. For dermal exposure routes normalizing by wiping duration, the slope of 0 was rejected only for the all dermalTimothy Leighton, EPA 15 March, 2011 Page 40

exposure, and the slope of one was rejected only for long dermal exposure and the repeated measures model. For inhalation exposure as a concentration, the confidence inte rvals for the slope included zero and excluded one when normalizing by amount of active ingredient, wiping duration, or amount of active ingredie nt × wiping duration, but included both zero and one when normalizing by the surf ace area wiped. The slope estimates for the inhalation exposure as a concentration were all small (below 0.3) a nd positive. For the inhalation exposure as a mass normalized by the amount of active ingredient, the ICC value was non-zero and the confidence interval for the slope included one and excluded zero. Finally, to compare the four different nor malizing variables, we present Table 11 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 11. The values in Table 11 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 dermal exposure routes except for the long dermal model with a known slope of one. For inhalation exposure, the preferred model fo r normalized exposure as a conc entration uses the surface area wiped. The preferred model for normalized inhalation ex posure as a mass uses the surface area wiped when the slope is allowed to vary and uses the pounds of active ingredient when the slope equals one. Table 11. 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 wiping duration Normalized by pounds of active

ingredient and wiping duration Normalized by surface area wiped

Long Dermal Mixed Any 23.3 26.0 Mixed 1 33.2 31.8 Short Dermal Mixed Any 20.6 27.1 Mixed 1 26.5 30.4 Long Short

Dermal Mixed Any 22.5 29.1

Mixed 1 27.8 32.2 Dermal Repeated Measures Any -2.6 1.1

1 4.5 6.7Timothy Leighton, EPA 15 March, 2011 Page 41

Exposure

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

ingredient and wiping duration Normalized by surface area wiped

Inhalation Concentration (mg/m 3 ) Mixed Any 43.3 43.7 43.6 42.1

Mixed 1 49.1 48.5 60.0 47.3 Inhalation Mass (mg) Mixed Any 41.8 43.7 42.3 41.7

Mixed 1 41.9 43.7 49.1 42.4Timothy Leighton, EPA 15 March, 2011 Page 42

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

Statistic Normalized Long a Dermal (mg/hour) Normalized Short b Dermal (mg/hour) Normalized Long Short c Dermal (mg/hour) Normalized Inhalation (mg/m 3 /hour) Arithmetic Mean 0.62 1.06 0.95 0.0056 Arithmetic Standard Deviation 0.45 0.65 0.62 0.0050 Geometric Mean 0.51 0.90 0.79 0.0040 Geometric Standard Deviation 1.83 1.79 1.84 2.61 Min 0.25 0.39 0.38 0.0002 5% 0.25 0.39 0.38 0.0002 10% 0.27 0.49 0.39 0.0016 25% 0.32 0.56 0.46 0.0027 50% 0.40 0.82 0.69 0.0048 75% 0.76 1.79 1.30 0.0079 90% 1.66 2.07 1.97 0.0086 95% 1.71 2.54 2.39 0.0228 Max 1.71 2.54 2.39 0.0228

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

c Long Short = Long pants and short sleeves
Table 2b. 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 0.61 (0.45, 0.84) 1.38 (0.89, 2.12)

Short pants and short sl eeves 1.06 (0.80, 1.43) 2.32 (1.53, 3.53) Long pants and short slee ves 0.95 (0.70, 1.31) 2.15 (1.38, 3.33) Inhalation (mg/m 3 /hour) 0.0064 (0.0034, 0.0128) 0.0198 (0.0087, 0.0443)Timothy Leighton, EPA 15 March, 2011 Page 43

Table 3b. 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 1.83 1.50 2.23 1.2 1.50 1.99 1.2 GSDm 1.83 1.50 2.26 1.2 1.54 2.05 1.2 ICC 0.00 0.00 0.39 0.00 0.57 GMs 0.51 0.39 0.68 1.3 0.39 0.68 1.3 GMm 0.51 0.39 0.68 1.3 0.39 0.68 1.3 AMs 0.62 0.45 0.83 1.4 0.44 0.82 1.4 AMu 0.61 0.45 0.84 1.4 0.43 0.84 1.4 AMm 0.61 0.45 0.84 1.4 0.44 0.85 1.4 P95s 1.71 0.88 3.05 1.9 0.82 1.71 2.1 P95u 1.38 0.88 2.09 1.6 0.78 1.98 1.8 P95m 1.38 0.89 2.12 1.5 0.81 2.02 1.7

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 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 1.79 1.47 2.17 1.2 1.52 1.96 1.2 GSDm 1.79 1.48 2.19 1.2 1.52 2.00 1.2 ICC 0.00 0.00 0.39 0.00 0.47 GMs 0.90 0.69 1.18 1.3 0.70 1.16 1.3 GMm 0.90 0.69 1.18 1.3 0.70 1.16 1.3 AMs 1.06 0.79 1.41 1.3 0.78 1.36 1.4 AMu 1.06 0.79 1.43 1.3 0.77 1.39 1.4 AMm 1.06 0.80 1.43 1.4 0.78 1.41 1.4 P95s 2.54 1.52 5.00 2.0 1.81 2.54 1.4 P95u 2.32 1.52 3.48 1.5 1.45 3.19 1.6 P95m 2.32 1.53 3.53 1.5 1.46 3.27 1.6Timothy Leighton, EPA 15 March, 2011 Page 44

Table 5b. 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 1.84 1.50 2.26 1.2 1.55 2.02 1.2 GSDm 1.84 1.51 2.28 1.2 1.56 2.06 1.2 ICC 0.00 0.00 0.39 0.00 0.43 GMs 0.79 0.59 1.05 1.3 0.60 1.04 1.3 GMm 0.79 0.59 1.05 1.3 0.60 1.04 1.3 AMs 0.95 0.69 1.28 1.4 0.69 1.23 1.4 AMu 0.95 0.70 1.30 1.4 0.68 1.26 1.4 AMm 0.95 0.70 1.31 1.4 0.68 1.28 1.4 P95s 2.39 1.37 4.80 2.0 1.67 2.39 1.4 P95u 2.15 1.37 3.28 1.6 1.30 2.98 1.6 P95m 2.15 1.38 3.33 1.6 1.31 3.06 1.6

Table 6b. 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 2.61 1.89 3.62 1.4 1.64 3.78 1.6 GSDm 2.65 1.90 3.80 1.4 1.65 4.16 1.6 ICC 0.12 0.00 0.56 0.00 0.60 GMs 0.0040 0.0022 0.0071 1.8 0.0026 0.0057 1.5 GMm 0.0040 0.0022 0.0071 1.8 0.0026 0.0057 1.5 AMs 0.0056 0.0032 0.0118 2.1 0.0038 0.0078 1.5 AMu 0.0063 0.0033 0.0123 2.0 0.0043 0.0090 1.5 AMm 0.0064 0.0034 0.0128 2.0 0.0043 0.0100 1.6 P95s 0.0228 0.0086 0.0744 3.3 0.0083 0.0228 2.8 P95u 0.0192 0.0086 0.0418 2.2 0.0095 0.0319 2.0 P95m 0.0198 0.0087 0.0443 2.3 0.0097 0.0363 2.0Timothy Leighton, EPA 15 March, 2011 Page 45

Table 8b. 95 percent confidence intervals for slope of log exposure versus log hours of wiping duration.

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Dermal (mg) Long pants and long sleeves Mixed 0.32 -0.26 0.91 1.17
Simple Linear 0.32 -0.26 0.90 1.16
Short pants and short sleeves Mixed 0.49 -0.11 1.10 1.21
Simple Linear 0.49 -0.10 1.09 1.20
Long pants and short sleeves Mixed 0.48 -0.16 1.12 1.28
Simple Linear 0.48 -0.15 1.11 1.26

None Mixed 0.63 0.001 1.26 1.26 Simple Linear 0.63 0.008 1.25 1.24

Inhalation (mg/m 3 /hour) Mixed 0.04 -0.89 0.98 1.87
Simple Linear 0.02 -0.94 0.97 1.90
Dermal (mg) Any Repeated Measures 0.38 -0.21 0.97 1.18

Table 9b. Quadratic mixed models with 95% confidence in tervals for the log exposur e versus log hours wiping duration. Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval
Long Dermal Intercept -0.24 2.00 -1.23 0.74 1.72 0.00 1.97

Long Dermal Slope 0.24 13.00 -1.79 2.28 1.72 0.00 4.08

Long Quad 0.07 13.00 -1.72 1.86 1.72 0.00 3.57Timothy Leighton, EPA 15 March, 2011 Page 46

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

Dermal

Short Dermal Intercept 0.24 2.00 -0.77 1.25 1.75 0.00 2.02

Short Dermal Slope 0.05 13.00 -2.04 2.15 1.75 0.00 4.18

Short Dermal Quad 0.40 13.00 -1.43 2.24 1.75 0.00 3.66

Long Short Dermal Intercept 0.12 2.00 -0.95 1.19 1.81 0.00 2.14

Long Short Dermal Slope 0.10 13.00 -2.11 2.31 1.81 0.00 4.43

Long Short Dermal Quad 0.35 13.00 -1.59 2.29 1.81 0.00 3.88

Inhalation Intercept -4.94 8.03 -5.87 -4.02 2.47 0.11 1.86

Inhalation Slope 0.23 13.14 -2.99 3.45 2.47 0.11 6.45

Inhalation Quad -0.17 13.13 -3.00 2.65 2.47 0.11 5.64

Dermal Repeated Measures Slope 0.13 15.01 -1.92 2.19 NA NA 4.11

Dermal Repeated Measures Quad 0.23 15.01 -1.57 2.03 NA NA 3.60Timothy Leighton, EPA 15 March, 2011 Page 47

Table 10b. Minimum Hours Wiping Duration for Which Norm alized Exposure Model Over-Predicts Dermal and Inhalation Exposure.
Exposure Route Clothing Model Slope Threshold Level (hours) Dermal (mg) Long pants and long sleeves Mixed 0.32 1.4

Short pants and short sleeves Mixed 0.49 1.3

Long pants and short sleeves Mixed 0.48 1.3

Inhalation (mg/m3) Mixed 0.04 1.1Timothy Leighton, EPA 15 March, 2011 Page 48



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

-2 -1 0 1 2 0.25 0.50 0.75 1.00 1.25 1.50 1.75Normalized Long Dermal Exposure

Normal Quantiles

Figure 1bTimothy Leighton, EPA 15 March, 2011 Page 49



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

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

Normal Quantiles

Figure 2bTimothy Leighton, EPA 15 March, 2011 Page 50



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

-2 -1 0 1 2 0 0.5 1.0 1.5 2.0 2.5 3.0Normalized Short Dermal Exposure

Normal Quantiles

Figure 3bTimothy Leighton, EPA 15 March, 2011 Page 51

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

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

Normal Quantiles

Figure 4bTimothy Leighton, EPA 15 March, 2011 Page 52

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

-2 -1 0 1 2 0 0.5 1.0 1.5 2.0 2.5Normalized Long Short Dermal Exposure

Normal Quantiles

Figure 5bTimothy Leighton, EPA 15 March, 2011 Page 53

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

-2 -1 0 1 2 -1.0 -0.5 0 0.5 1.0lnnrmdermls

Normal Quantiles

Figure 6bTimothy Leighton, EPA 15 March, 2011 Page 54



### Quantile plot normalized inhalation exposure data with a normal distribution Normalized by Wiping Duration

-2 -1 0 1 2 0 0.005 0.010 0.015 0.020 0.025Normalized Inhalation Exposure)

Normal Quantiles

Figure 7bTimothy Leighton, EPA 15 March, 2011 Page 55



### Quantile plot normalized inhalation exposure data with a lognormal distribution Normalized by Wiping Duration

-2 -1 0 1 2 -9 -8 -7 -6 -5 -4 -3log (Normalized Inhalation Exposure)

Normal Quantiles

Figure 8bTimothy Leighton, EPA 15 March, 2011 Page 56

lnderml = -0.2469 +0.3213 lnnrm

N 18 Rsq 0.0796 AdjRsq 0.0220
RMSE 0.5278 

### Simple Linear Regression of Ln Long Dermal Exposure on Ln Wiping Duration Normalized by Wiping Durationlog Long Dermal Exposure(mg)

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

log Wiping Duration -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 9bTimothy Leighton, EPA 15 March, 2011 Page 57

lnderms = 0.2066 +0.4948 lnnrm

N 18 Rsq 0.1612 AdjRsq 0.1087
RMSE 0.5452 

### Simple Linear Regression of Ln Short Dermal Exposure on Ln Wiping Duration Normalized by Wiping Durationlog Short Dermal Exposure(mg)

-0.5 0.0 0.5 1.0 1.5 2.0

log Wiping Duration -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 10bTimothy Leighton, EPA 15 March, 2011 Page 58

lndermls = 0.0882 +0.4782 lnnrm

N 18 Rsq 0.1387 AdjRsq 0.0849
RMSE 0.5754 Simple Linear Regression of Ln Long Short Dermal Exposure on Ln Wiping Duration Normalized by Wiping Durationlog Long Short Dermal Exposure(mg)

-0.5 0.0 0.5 1.0 1.5 2.0

log Wiping Duration -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 11bTimothy Leighton, EPA 15 March, 2011 Page 59

lnderma = 0.4131 +0.6287 lnnrm

N 18 Rsq 0.2237 AdjRsq 0.1752
RMSE 0.5655 

### Simple Linear Regression of Ln All Dermal Exposure on Ln Wiping Duration Normalized by Wiping Durationlog All Dermal Exposure(mg)

-0.5 0.0 0.5 1.0 1.5 2.0

log Wiping Duration -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 12bTimothy Leighton, EPA 15 March, 2011 Page 60

lninh = -4.913 +0.0151 lnnrm

N 18 Rsq 0.0001 AdjRsq -.0624
RMSE 0.8671 

### Simple Linear Regression of Ln Inhalation Exposure on Ln Wiping Duration Normalized by Wiping Durationlog Inhalation Exposure(mg/m3)

-7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5

log Wiping Duration -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 13bTimothy Leighton, EPA 15 March, 2011 Page 61

Figure 14bTimothy Leighton, EPA 15 March, 2011 Page 62

Figure 15bTimothy Leighton, EPA 15 March, 2011 Page 63

Figure 16bTimothy Leighton, EPA 15 March, 2011 Page 64

Figure 17bTimothy Leighton, EPA 15 March, 2011 Page 65

Figure 18bTimothy Leighton, EPA 15 March, 2011 Page 66

Figure 20bTimothy Leighton, EPA 15 March, 2011 Page 67

Analyses of inhalation exposure per pounds of active ingredient handled and hours of wiping duration. Table and Figure Numbers are Consistent with main text (add “c”). Table 1c. Summary statistics for normalized exposure.

Statistic Normalized Inhalation (mg/m 3 /lb AI/hour) Arithmetic Mean 7.82 Arithmetic Standard Deviation 12.84 Geometric Mean 3.57 Geometric Standard Deviation 3.75 Min 0.12 5% 0.12 10% 0.99 25% 1.90 50% 2.93 75% 7.44 90% 22.71 95% 54.49 Max 54.49

Table 2c. 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) Inhalation (mg/m 3 /lb AI/hour) 8.94 (3.15, 28.92) 33.15 (10.06, 108.51)

Table 6c. 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 /lb AI/hour).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 3.75 2.40 5.98 1.6 2.06 5.89 1.8Timothy Leighton, EPA 15 March, 2011 Page 68

Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDm 3.88 2.42 6.56 1.7 2.08 6.83 1.9 ICC 0.16 0.00 0.61 0.00 0.61 GMs 3.57 1.53 8.53 2.4 2.09 5.90 1.7 GMm 3.57 1.53 8.53 2.4 2.09 5.90 1.7 AMs 7.82 2.83 23.02 2.9 3.44 13.43 2.3 AMu 8.56 3.08 25.75 3.0 3.89 18.10 2.2 AMm 8.94 3.15 28.92 3.2 4.00 22.79 2.5 P95s 54.49 9.89 207.51 5.5 8.41 54.49 6.5 P95u 31.43 9.85 97.04 3.2 10.70 69.44 2.9 P95m 33.15 10.06 108.51 3.3 10.96 85.96 3.0

Table 8c. 95 percent confidence interval s for slope of log exposure versus log (pounds of active ingr edient × hours of wiping duration).

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Inhalation (mg/m 3 /lb AI/ hour) Mixed 0.09 -0.33 0.51 0.83

Simple Linear 0.06 -0.35 0.47 0.82

Table 9c. Quadratic mixed models with 95% confidence inte rvals for the log exposure log (pounds of active ingredient × hours of wiping duration). Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval Inhalation Intercept 0.78 14.16 -15.11 16.68 2.44 0.14 31.79

Inhalation Slope 1.77 14.04 -3.35 6.88 2.44 0.14 10.23

Inhalation Quad 0.13 13.95 -0.27 0.54 2.44 0.14 0.81Timothy Leighton, EPA 15 March, 2011 Page 69

Table 10c. Minimum Pounds of Active I ngredient × Hours of Wiping Duration for Which Normalized Exposure Model Over-Predicts Inhalation Exposure.
Exposure Route Clothing Model Slope Threshold Level (lb AI hour)

Inhalation (mg/m3) Mixed 0.09 0.00076



### Quantile plot normalized inhalation exposure data with a normal distribution Normalized by PoundsAI*Duration

-2 -1 0 1 2 0 10 20 30 40 50 60Normalized Inhalation Exposure)

Normal Quantiles

Figure 7cTimothy Leighton, EPA 15 March, 2011 Page 70



### Quantile plot normalized inhalation exposure data with a lognormal distribution Normalized by PoundsAI*Duration

-2 -1 0 1 2 -3 -2 -1 0 1 2 3 4log (Normalized Inhalation Exposure)

Normal Quantiles

Figure 8cTimothy Leighton, EPA 15 March, 2011 Page 71

lninh = -4.5559 +0.0563 lnnrm

N 18 Rsq 0.0053 AdjRsq -.0569
RMSE 0.8649 

### Simple Linear Regression of Ln Inhalation Exposure on Ln PoundsAI*Duration Normalized by PoundsAI*Durationlog Inhalation Exposure(mg/m3)

-7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5

log PoundsAI*Duration -8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0

Figure 13cTimothy Leighton, EPA 15 March, 2011 Page 72

Figure 18cTimothy Leighton, EPA 15 March, 2011 Page 73

Figure 20cTimothy Leighton, EPA 15 March, 2011 Page 74

Analyses of inhalation expo sure per surface area wiped. Table and Figure Numbers are Consiste nt with main text (add “d”). Table 1d. Summary statistics for normalized exposure.

Statistic Normalized Inhalation (mg/m 3 /sq ft) Arithmetic Mean 0.0000063 Arithmetic Standard Deviation 0.0000044 Geometric Mean 0.0000048 Geometric Standard Deviation 2.5242839 Min 0.0000002 5% 0.0000002 10% 0.0000024 25% 0.0000036 50% 0.0000053 75% 0.0000069 90% 0.0000155 95% 0.0000180 Max 0.0000180

Table 2d. 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) Inhalation (mg/m 3 /sq ft) 0.0000075 (0.0000041, 0.0000142) 0.0000225 (0.0000104, 0.0000481)

Table 6d. 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 /sq ft).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 2.52 1.86 3.44 1.4 1.50 3.91 1.7Timothy Leighton, EPA 15 March, 2011 Page 75

Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDm 2.56 1.87 3.59 1.4 1.51 4.34 1.7 ICC 0.09 0.00 0.53 0.00 0.54 GMs 0.0000048 0.0000028 0.0000082 1.7 0.0000032 0.0000067 1.5 GMm 0.0000048 0.0000028 0.0000082 1.7 0.0000032 0.0000067 1.5 AMs 0.0000063 0.0000039 0.0000132 2.1 0.0000046 0.0000082 1.4 AMu 0.0000074 0.0000041 0.0000138 1.9 0.0000051 0.0000104 1.4 AMm 0.0000075 0.0000041 0.0000142 1.9 0.0000052 0.0000117 1.6 P95s 0.0000180 0.0000103 0.0000802 4.5 0.0000085 0.0000180 2.1 P95u 0.0000220 0.0000103 0.0000457 2.1 0.0000100 0.0000372 2.2 P95m 0.0000225 0.0000104 0.0000481 2.2 0.0000101 0.0000434 2.2

Table 8d. 95 percent confidence intervals for slope of log exposure versus log (surface area wiped).

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Inhalation (mg/m 3 /sq ft) Mixed 0.34 -0.32 1.00 1.32
Simple Linear 0.35 -0.25 0.95 1.21

Table 9d. Quadratic mixed models with 95% confidence interval s for the log exposure versus log (surface area wiped). Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval Inhalation Intercept -15.79 13.89 -61.42 29.85 2.38 0.12 91.27

Inhalation Slope 2.70 13.79 -10.05 15.44 2.38 0.12 25.49

Inhalation Quad -0.16 13.71 -1.05 0.72 2.38 0.12 1.77Timothy Leighton, EPA 15 March, 2011 Page 76

Table 10d. Minimum Square Feet Su rface Area Wiped for Which Normalized Exposure Model Over-Predicts Inhalation Exposure.
Exposure Route Clothing Model Slope Threshold Level (sq ft)

Inhalation (mg/m3) Mixed 0.34 792.1



### Quantile plot normalized inhalation exposure data with a normal distribution Normalized by Surface Area Wiped

-2 -1 0 1 2 0 5.0E-06 1.0E-05 1.5E-05 2.0E-05Normalized Inhalation Exposure)

Normal Quantiles

Figure 7dTimothy Leighton, EPA 15 March, 2011 Page 77



### Quantile plot normalized inhalation exposure data with a lognormal distribution Normalized by Surface Area Wiped

-2 -1 0 1 2 -16 -15 -14 -13 -12 -11 -10log (Normalized Inhalation Exposure)

Normal Quantiles

Figure 8dTimothy Leighton, EPA 15 March, 2011 Page 78

lninh = -7.474 +0.35 lnnrm

N 18 Rsq 0.0863 AdjRsq 0.0292
RMSE 0.8289 

### Simple Linear Regression of Ln Inhalation Exposure on Ln Surface Area Wiped Normalized by Surface Area Wipedlog Inhalation Exposure(mg/m3)

-7.5 -7.0 -6.5 -6.0 -5.5 -5.0 -4.5 -4.0 -3.5

log Surface Area Wiped 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00 8.25

Figure 13dTimothy Leighton, EPA 15 March, 2011 Page 79

Figure 18dTimothy Leighton, EPA 15 March, 2011 Page 80

Figure 20d

Analyses of inhalation mass exposure per amount of active ingredient. Table and Figure Numbers are Consistent with main text (add “e”). Inhalation mass exposure (mg) is esti mated as air concentration (mg/m 3 ) × breathing rate (1 m 3 /hour) × wiping duration (hours). Table 1e. Summary statistics for normalized exposure.

Statistic Normalized Inhalation (mg/lb AI)
Arithmetic Mean 16.64 Arithmetic Standard Deviation 12.14 Geometric Mean 12.48Timothy Leighton, EPA 15 March, 2011 Page 81

Statistic Normalized Inhalation (mg/lb AI)
Geometric Standard Deviation 2.31 Min 1.52 5% 1.52 10% 6.26 25% 7.71 50% 10.88 75% 27.00 90% 37.82 95% 39.37 Max 39.37

Table 2e. 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) Inhalation (mg/lb AI) 18.51 (8.53, 42.33) 53.77 (20.47, 143.56)

Table 6e. 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/lb AI).
Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy GSDs 2.31 1.70 3.37 1.5 1.78 2.99 1.3 GSDm 2.43 1.70 3.87 1.6 1.83 3.35 1.4 ICC 0.37 0.00 0.77 0.00 0.84 GMs 12.48 6.25 24.88 2.0 9.21 16.67 1.4 GMm 12.48 6.25 24.88 2.0 9.21 16.67 1.4 AMs 16.64 8.11 36.85 2.2 12.64 20.78 1.3 AMu 17.74 8.34 38.31 2.2 12.97 23.00 1.4 AMm 18.51 8.53 42.33 2.3 13.25 25.09 1.4 P95s 39.37 20.37 174.00 4.4 30.91 39.37 1.3 P95u 49.59 19.90 120.76 2.5 31.05 71.54 1.6Timothy Leighton, EPA 15 March, 2011 Page 82

Parametric Bootstrap Non-parametric Bootstrap

Parameter Estimate Lower Bound Upper Bound Fold Relative Accuracy Lower Bound Upper Bound Fold Relative Accuracy P95m 53.77 20.47 143.56 2.7 32.21 84.53 1.7

Table 8e. 95 percent confidence interv als for slope of log exposure versus log (amount of active ingredient).

Exposure Route Clothing Model Estimate Lower Upper Confidence Interval Width Inhalation (mg/lb AI) Mixed 0.94 0.30 1.59 1.28
Simple Linear 0.77 0.10 1.44 1.34

Table 9e. Quadratic mixed models with 95% confidence inte rvals for the log exposure ve rsus log (amount of active ingredient). Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval Inhalation Intercept 9.50 13.57 -24.13 43.14 2.50 0.33 67.26

Inhalation Slope 3.13 13.49 -6.76 13.02 2.50 0.33 19.77

Inhalation Quad 0.16 13.44 -0.56 0.88 2.50 0.33 1.45

Table 10e. Minimum Pounds of Active I ngredient for Which Normalized Expos ure Model Over-Predicts Inhalation Mass Exposure.
Exposure Route Clothing Model Slope Threshold Level (lb AiaH)

Inhalation (mg) Mixed 0.94 0.00000086Timothy Leighton, EPA 15 March, 2011 Page 83



### 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 40Normalized Inhalation Mass Exposure)

Normal Quantiles

Figure 7eTimothy Leighton, EPA 15 March, 2011 Page 84

Quantile plot normalized inhalation 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 2.5 3.0 3.5 4.0log (Normalized Inhalation Mass Exposure)

Normal Quantiles

Figure 8eTimothy Leighton, EPA 15 March, 2011 Page 85

lninh2 = 0.9659 +0.7709 lnnrm

N 18 Rsq 0.2705 AdjRsq 0.2250
RMSE 0.8507 Simple Linear Regression of Ln Inhalation Mass Exposure on Ln Pounds Active Ingredient Handled Normalized by Pounds Active Ingredient Handledlog Inhalation Mass Exposure(mg)

-6.0 -5.5 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5

log Pounds Active Ingredient Handled -8.00 -7.75 -7.50 -7.25 -7.00 -6.75 -6.50 -6.25 -6.00 -5.75 -5.50 -5.25

Figure 13eTimothy Leighton, EPA 15 March, 2011 Page 86

Figure 18eTimothy Leighton, EPA 15 March, 2011 Page 87

Figure 20e