Environmental Applications of Chemometrics - ACS Publications

15 Statistical Issues in Measuring Airborne Asbestos Levels Following an Abatement Program 1

2

3

3

Jean Chesson, Bertram P. Price, Cindy R. Stroup, and Joseph J. Breen 1

Columbus Laboratories, Battelle, Columbus, OH 43201 National Economic Research Associates, Inc., Washington, DC 20036 Office of Toxic Substances, U.S. Environmental Protection Agency, Washington, DC 20460

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Downloaded by RUTGERS UNIV on December 31, 2017 | http://pubs.acs.org Publication Date: November 6, 1985 | doi: 10.1021/bk-1985-0292.ch015

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Asbestos abatement activity, especially removal pro jects in schools and other public buildings, is ex panding rapidly in response to EPA's recent "Asbestos in Schools" rule. A focal point for the many technical and scientific problems in EPA's asbestos program is the question of how to determine that a contractor has successfully completed an abatement project. The question engulfs the broad debate on biologically effective fibers, sampling strategies and analytical alternatives. For any post-abatement evaluation protocol that is proposed, there are important statistical design and analysis issues that must be addressed. The statistical objectives are to obtain precise and accurate estimates of airborne asbestos levels and to quantify and control the likelihood of a false positive or false negative test result. In this paper the statistical design issues are identified and the relationship between sample size, error rates and cost is analyzed. EPA has not set an exposure standard f o r asbestos. However, the "Friable Asbestos Containing Materials i n Schools, I d e n t i f i c a t i o n and N o t i f i c a t i o n Rule" was promulgated to address the problem of exposure for young people whose r i s k i s increased i f only because of their longer expected l i f e span r e l a t i v e to the latency period associated with asbestos-related disease. The rule requires inspection and testing f o r asbestos, and n o t i f i c a t i o n of maintenance workers, teachers and parent groups i f asbestos i s found. The rule does not require abatement. If asbestos i s present, the choice of an approach and method, i f any, f o r reducing exposure i s l e f t to the local decision-making body. A building owner who decides on abatement i s confronted with a variety of technical and s c i e n t i f i c issues d i r e c t l y a f f e c t i n g the quality of the job to be undertaken. EPA guidance i d e n t i f i e s these

0097-6156/ 85/ 0292-0191 $06.00/ 0 © 1985 American Chemical Society Breen and Robinson; Environmental Applications of Chemometrics ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

ENVIRONMENTAL APPLICATIONS OF CHEMOMETRICS


192

issues and recommends that a program manager be designated to coordinate the a c t i v i t i e s of contractors and consultants. One of the consultant's most important functions i s to ascertain that the project has been successfully completed and that the contractor can be released. EPA guidance on this q u e s t i o n — o f t e n referred to as the "how clean i s clean" i s s u e — h a s been cautious. The Agency has been caref u l not to recommend post-abatement evaluation techniques that have not been thoroughly validated. In Guidance for Controlling Asbestos Containing Materials in Buildings ( J j , EPA offers a recommendation to assess whether a contractor has e f f e c t i v e l y reduced the elevated airborne concentration levels generated while the work was in progress. A visual inspection i s to be conducted to ascertain that a l l asbestos-containing materials have been removed and no debris or dust remains. A i r sampling is also recommended. A slow, long sample (2 l i t e r s per minute for eight hours) should be taken within 48 hours after the work has been completed. It i s recommended that the samples be analyzed by Phase Contrast Microscopy (PCM). Although PCM i s only sensitive to large fibers (may miss long thin f i b e r s ) and does not d i s t i n g u i s h asbestos from other types of f i b e r s , other a n a l y t i c a l methods based on electron microscopy that may be d e f i n i t i v e had not been s u f f i c i e n t l y validated to receive a recommendation at the time the guidance document was prepared. Furthermore, PCM i s satisfactory for i t s intended purpose, namely, to determine i f an asbestos worksite, the abatement area, has been restored to i t s normal condition. As a result of a recent EPA/NBS workshop on "Monitoring and Evaluation of Airborne Asbestos Levels Following an Abatement Program," many of the apparent conflicts among sampling and analytical methods were tempered. A variety of new proposals i n volving both optical microscopy and electron microscopy appeared to be acceptable for post-abatement monitoring. The workshop did not e x p l i c i t l y address questions of uncertainty in the measurement process, the likelihood of reaching a correct conclusion or implementation cost. We address these questions using TEM as an example. With slight modification the approach and solutions obtained are applicable to other sampling and analysis methods. Statistical

Issues

The objective in measuring post-abatement airborne asbestos concentrations is to confirm that the levels in the area of interest do not constitute a public health hazard. To date EPA has not promulgated a numerical exposure standard for airborne asbestos. In general, the s c i e n t i f i c information regarding health e f f e c t s related to exposure to asbestos at environmental levels i s currently i n s u f f icient to serve as a basis for standard setting. However, asbestos abatement projects are ongoing and the parties engaged in this work need c r i t e r i a to determine when a contractor has f u l f i l l e d the requirements. In the absence of an absolute standard, one feasible approach to releasing a contractor i s to base the decision on the comparison of two requirements. We propose a c r i t e r i o n based on a comparison between the postabatement indoor airborne asbestos l e v e l and the ambient (outdoor) level. An area is "clean" when there i s no statistically

Breen and Robinson; Environmental Applications of Chemometrics ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


15.

CHESSON ET AL.

193

Measuring Airborne Asbestos Levels

s i g n i f i c a n t difference between the indoor and ambient l e v e l s . This approach i s not currently under formal consideration for rulemaking. Once a c r i t e r i o n i s accepted i t i s possible to determine an optimal scheme f o r c o l l e c t i n g the necessary data. There are two broad issues that must be addressed—air sampling protocols includ ing quality assurance, and s t a t i s t i c a l sampling designs. Determin ing the best a i r sampling protocol involves decisions about the type of sampling to be used (e.g., whether or not to employ aggressive sampling which involves s t i r r i n g up the a i r ) , flow rates, duration, frequency and type of f i l t e r . Some of these choices are tied to the type of analysis—PCM, SEM, or TEM—that i s to be done. Other choices, for example, rate, duration, and frequency are sample size issues which depend on s t a t i s t i c a l requirements such as false positive rate, false negative rate and s e n s i t i v i t y . Sensitivity in this context means the magnitude of difference between indoor and outdoor or pre and post levels that must be detected with a high probability. A sampling and analysis program should have s u f f i c i e n t s e n s i t i v i t y to detect the smallest difference between indoor and ambient levels that i s considered to be unacceptable. S t a t i s t i c a l Model. In designing an airborne asbestos sampling analysis procedure for determining i f an area i s clean, the physical sampling parameters and the s t a t i s t i c a l design parameters are i n t e r related. For example, s t a t i c area sampling and aggressive l o c a l sampling may dictate different s t a t i s t i c a l designs. The volume of a i r sampled—duration multiplied by sampling r a t e — a f f e c t s detection l i m i t s and v a r i a b i l i t y . Characteristics of the area, i t s s i z e , whether i t i s one contiguous space or partitioned into unique sec tions (rooms), and other distinguishing factors are important. How ever, for our current purpose, we have simplified the discussion. We consider an area the size of a typical room. We can then focus on the generic sampling problem and isolate the relevant s t a t i s t i c a l issues· A typical measurement may be described as Y

i j k = InZijk = U + T i • L

j ( i

) • e (ij) k

(1)

where s

t

n

e

1

1

t

n

^ijk ik"* laboratory analysis taken at the j location i n the i^ time period. (Typically Z i j k w i l l have units of ng/m-* or fibers/m^. The discussion that follows does not depend on the choice of units.) i> j ( i ) * k(ij) random variables representing the contribution of time period, location and£ a n a l y t i c a l ^ error, respectively, with zero means and variances σ^, and σ^. The model represents a completely nested design. We nave i m p l i c i t l y assumed that the measurements have a lognormal d i s t r i b u t i o n . Under this assumption the natural logarithm of the a n a l y t i c a l measurement has a variance that does not vary with i t s mean and standard s t a t i s t i c a l tests can be applied. The variance of an individual measurement i s n

T

L

anc

e

a

r

e

V a r ( Y . ) = a* • ol • o\ jk


(

2

)


194 The variance of the locations, and time i s

average

Var (Ϋ ...)

taken

over

laboratory

analyses,

(

+ o*/IJ + d^/lJK

= σ*/ΐ

3

)


where I , I J , and U K represent the t o t a l number of time periods, locations and laboratory analyses, respectively. Since the purpose of sampling i s to determine, as quickly as possible, i f the airborne asbestos levels are low enough to release the contractor, we r e s t r i c t the discussion to values of I = 1, that i s , a single time interval· Sample A l l o c a t i o n for Estimating Concentration Levels. The variable cost of a sampling program that produces an estimate with variance given i n equation (3) i s C = Cx*J + C *JK

(4)

2

Ci i s the unit cost of c o l l e c t i n g a sample and C i s the analysis cost. The sample size and sample a l l o c a t i o n scheme i s obtained i n one of two ways. Either the cost i s fixed and the variance of the mean is minimized or the variance i s fixed and the cost i s minimized. The f i r s t approach i s used when the budget for sampling and analysis is determined i n advance. The objective in this case i s to use that budget to obtain an estimate with maximum precision (equivalently minimum variance). The second approach i s used when the required precision of the estimator i s specified i n advance. Then the objec tive i s to derive an estimator with the desired l e v e l of precision at the lowest possible cost. 2

Minimum Variance, Fixed Cost.

The mathematical problem i s

2

min mm

+

σ_

bi

L

J,Κ

subject to C J

+ C JK = C

L

where C i s the fixed d o l l a r total available for the sampling laboratory analysis portion of the project. The solution i s J = c/tic^)*

(

6

)

2

and

(a /o ) + CJ E

L

( 7 )

κ = (C!/C2)

2

(a /a ) E

L

To develop a feeling for the s e n s i t i v i t y of the a l l o c a t i o n scheme to values of σ^, and σ , we have prepared examples that r e f l e c t passive sampling, followed by TEM analysis. We use values of Ci = $20 and C = $500 and evaluate the solution for total budgets of $5,000 and $15,000. These figures are based on t y p i c a l costs for TEM analysis. Costs w i l l vary among laboratories and depend on the a n a l y t i c a l method (TEM, SEM, or PCM) chosen. Note that and Ε

2


15.

C H ESSON ET A L.

195

Measuring A irborne A sbestos Levels

are needed to compute the l e v e l of precision achieved, namely, (Var Y ...) Table I shows results for a = .25, .5, 1.0, 1.5, and 2.0 and for σ = 1.0 and 1.5. Results calculated from several studies suggest that t o t a l variation (σ£ + oj?) ranges between 1.0 and 2.0. See (2-4). L

Ε

Table I.

Solution to the Sample A l l o c a t i o n Problem: Minimum Variance, Fixed Cost


Values of Values of L

1.0 Error Bound Κ %

Actual Cost

Nominal Cost

°E/°L

J

.25

5,000 15,000

4.00 4.00

10 29

1 1

89.4 45.5

.50

5,000 15,000

2.00 2.00

10 29

1 1

5,000 15,000

1.00 1.00

10 29

5,000 15,000

0.67 0.67

5,000 15,000

0.50 0.50

a

1.00

1.50

2.0

a

σ

Ε 1.5 Error Bound Κ %

Actual Cost

E/°L

J

4,950 14,830

6.00 6.00

5 15

2 2

159.9 73.6

4,850 15,050

100.0 50.2

4,950 14,830

3.00 3.00

10 29

1

166.4 77.8

4,950 14,830

1 1

140.3 67.3

4,950 14,830

1.50 1.50

10 29

1

10 29

1 1

205.7 92.7

4,950 14,830

1.00 1.00

10 29

1 1

272.4 4,950 116.4 14,830

10 29

1 1

299.8 125.6

4,950 14,830

0.75 0.75

10 29

1 1

370.9 4,950 148.4 14,830

1

1

205.7 4,950 92.7 14,830

Solutions to Equations 7 produce solutions for Κ and J that are not whole numbers. To resolve this problem, we increase Κ to the next integer value and choose J so the cost constraint i s exceeded by the smallest amount possible. For the majority of cases in the table, only one laboratory analysis of the f i l t e r is required, Κ = 1. This happens because the cost of analysis i s large r e l a t i v e to the cost of c o l l e c t i n g an add i t i o n a l sample. The value of Κ w i l l be larger than 1 i f the a n a l y t i c a l v a r i a t i o n , σ , i s larger than the spatial v a r i a t i o n , σ^, by enough to overcome cost d i s p a r i t y . For our example, the r a t i o of σ to Q L must be greater than 5 to cause Κ to be greater than 1. Although the values obtained for J and Κ minimize the variance, we gain more insight into the meaning of the numbers in Table I by describing them in terms of an error bound for estimating asbestos level. A 95% confidence interval for the mean of the l o g transformed data i s Y + 1.96 SD(Y). In terms of untransformed data the confidence bounds are exp(Y - 1.96 SD(Y)), exp(Y + 1.96 SD(Y)). These l i m i t s determine a confidence interval for the median of the untransformed data. The error bound i s calculated as Ε

Ε



196

.l.geSDCY).!

For the case b o u n d i s 89.4

σ = 1.0, percent.

=

Ε

.25

( ) 8

and

C = $5,000, t h e

upper

error

T h i s r e s u l t means we h a v e c o n f i d e n c e l e v e l o f .95 t h a t t h e a c t u a l a s b e s t o s l e v e l w i l l be no g r e a t e r t h a n 89.4 p e r c e n t h i g h e r t h a n t h e estimated l e v e l . F o r t h e same v a l u e s o f σ a n d σ^,, i n c r e a s i n g t h e b u d g e t t o $15,250 y i e l d s a n u p p e r b o u n d o f 45.5 p e r c e n t . That i s , an i n c r e a s e i n t h e b u d g e t by a f a c t o r o f 3 c a n a c h i e v e a r e d u c t i o n i n e s t i m a t i o n e r r o r b y a p p r o x i m a t e l y a f a c t o r o f 2. A fairly real i s t i c b u t c o n s e r v a t i v e c a s e may be σ = = 1.0· In t h i s case, for the $5,000 o p t i o n , the upper bound is 140 percent above the estimated value. F o r t h e $15,000 o p t i o n , t h e u p p e r b o u n d i s 67 p e r cent above the e s t i m a t e d v a l u e . As i n t h e p r e v i o u s c a s e , i n c r e a s i n g the testing budget by a f a c t o r of 3 cuts the estimation error approximately i n h a l f . Ε


Ε

Minimum C o s t , F i x e d V a r i a n c e . S i n c e o u r i n t e r e s t was f o c u s e d o n e s t i m a t i o n e r r o r , we may c h o o s e t o s e t the e r r o r i n advance and allocate s a m p l i n g and a n a l y s i s r e s o u r c e s to minimize c o s t . The m a t h e m a t i c a l p r o b l e m t o be s o l v e d i s min J,Κ subject

to 2

The

(9)

C , J + C„JK

solution

/T

χ

(

2/Tir - ν

1

0

)

is J

=

-¥^

κ = (c./c,) 1 2

^ c

2

— L

σ

T a b l e I I d i s p l a y s n u m e r i c a l r e s u l t s f o r v a l u e s o f σ = 1.0 a n d 1.5 a n d a = . 2 5 , . 5 0 , 1 . 0 0 , 1.50 and 2 . 0 0 . V a l u e s o f J and Κ a r e d e t e r m i n e d f o r c o n f i d e n c e i n t e r v a l s w i t h u p p e r e r r o r b o u n d s e t a t 50 p e r c e n t a n d 100 p e r c e n t a n d c o n f i d e n c e c o e f f i c i e n t s a t 95 percent and 99 p e r c e n t . In g e n e r a l , the table shows t h a t it is very e x p e n s i v e t o go f r o m 95 p e r c e n t t o 99 p e r c e n t c o n f i d e n c e . It is a l s o s i g n i f i c a n t l y m o r e e x p e n s i v e t o o b t a i n a n e s t i m a t e w i t h a 50 p e r c e n t e r r o r t h a n a 100 p e r c e n t e r r o r . For example, i f σ = = 1 . 0 0 , t o be 95 p e r c e n t c e r t a i n t h a t t h e e r r o r i n t h e e s t i m a t e d l e v e l o f a i r b o r n e a s b e s t o s i s l e s s t h a n 50 p e r c e n t r e q u i r e s J = 47 a n d Κ = 1 at a cost of $24,440. I f a 100 p e r c e n t e r r o r i n t h e e s t i m a t e is acceptable, J i s reduced to 16, Κ remains at 1 and the c o s t is $8,320. Ε

L

Ε


15.

CHESSONETAL.

197


Table I I . Solution to the Sample A l l o c a t i o n Problem: Fixed Variance, Minimum Cost


Nominal Error %

Value of eg Confidence %

1.5

1.0 J

Κ

Cost

J

Κ

$

$ .25

.50

50

95 99

25 43

1 1

13,000 22,360

28 48

2 2

28,560 48,960

100

95 99

9 15

1 1

4,680 7,800

10 16

2 2

10,200 16,320

50

95 99

30 51

1 1

15,600 26,520

59 102

1

30,680 53,040

95 99

10 18

1 1

5,200 9,360

20 35

1

95 99

47 81

1 1

24,440 41,120

76 132

95

16 28

1 1

8,320 14,560

26 46

1

99

95 99

76 132

1 1

39,520 68,640

106 183

1

95 99

26 46

1 1

13,520 23,920

36 63

1

95 99

117 203

1 1

60,840 105,560

147 254

1

95 99

40 70

1 1

20,800 36,400

50 87

1 1

100

1.00

50

100

1.50

50

100

2.00

Cost

50

100

1

1

1 1

1

1

1

1


10,400 18,200 39,520 68,640 13,520 23,920 55,120 95,160 18,720 32,760 76,440 132,080 26,000 45,240


198


It should be noted that estimation errors of 50 percent or 100 percent are not unduly large for airborne asbestos measurements. For example, the estimate of a t y p i c a l ambient concentration l e v e l may be 2 nanograms per cubic meter. The bounds for a 100 percent error would be 1 and 4. Although there i s no absolute health standard, i t i s doubtful i f a change from 2 to 4 would affect a decision on whether to release a contractor. That v a r i a t i o n would be well within the range of values found in the ambient distribution. Comparing Two Measurements. The previous discussion introduced the concepts of sample size and sample a l l o c a t i o n for estimating a i r borne concentration l e v e l s . We want to apply those concepts to the comparison of two measurements, inside a building versus ambient levels. Let X and Y denote the two measurements. The models are: (12)

(13)

t n

where X j and Y j are the natural logarithms of the k laboratory analysis taken at the j location. Let X and Y represent the aver age taken over J locations and Κ laboratory analyses. The Y-X, i s represented by difference in means, denoted by W k

k

t

h

W = y?

L j

with expected

X

j

«•

(14) fc

k(j)

c

k(j)

value E(W)

(15)

χ u

=

and variance Var (W) = 2

•

(16) JK

For i l l u s t r a t i v e purposes l e t Κ = 1. Then we must determine the sample size, J , that i s required to ensure a small p r o b a b i l i t y of making an incorrect decision. Two types of error can occur. The two concentrations may be different ( i . e . , δ ^ 0), yet we conclude that they are the same (false negative), or the two concentration may be the same ( i . e . , δ = 0) yet we conclude that they are different (false positive) (see Table I I I ) . In the f i r s t case the contractor i s released even though the work i s unsatisfactory. In the second case the area has to be cleaned again even though i t was already clean enough. Having specified acceptable rates of f a l s e negatives and false positives we can calculate the required values of J and K, given 0·^ and O g .


15.

CHESSON ET AL.

199


Table I I I . The Types of Error that Can Occur and Their Probability of Occurrence


Conclusion

Actual Situation Indoor Level Less Than or Indoor Level Greater Equal to Ambient Level Than Ambient Level

Indoor Level Less Than or Equal to Ambient Level

Correct Decision

False Negative (Conclude 'Clean' When It Is Not)

Probability = l-Ol

Probability = β

Indoor Level Greater Than Ambient Level

False Positive (Conclude 'Not Clean When It Is)

Correct Decision

1

Probability = α

Probability = 1-β (Power)

Significance Level

Table IV gives values of J when the false positive rate i s 5 percent and the f a l s e negative rate i s either 5 percent or 1 per cent. J depends on V and, since Κ = 1, on the sum σ£ + σ§. A convenient empirical measure of precision i n the o r i g i n a l units i s the c o e f f i c i e n t of variation (cv) which i s the standard deviation divided by the mean. Note that σ£ + σ{? = In (1 + c v ) . An alge braic difference, δ, on the logarithmic scale translates into a m u l t i p l i c a t i v e difference on the o r i g i n a l scale. Table V has been prepared using the m u l t i p l i c a t i v e factors. For example, i f the c o e f f i c i e n t of variation i s 2 and the l e v e l is twice the other then seventy-three samples are required to achieve a false negative rate of 5 percent. To achieve a f a l s e neg ative rate of 1 percent, one hundred and twelve samples would be required. As the acceptable difference between levels increase, the required number of sample required decreases. When one l e v e l i s one hundred times the other and the c o e f f i c i e n t of variation i s 1, only three samples are required to achieve a false negative rate of 1 percent. So f a r we have assumed that both a i r levels would have to be determined and therefore that two sets of J samples would have to be collected. In some cases one level may already be available from other records and can be used as a standard of comparison. Table VI shows for this special case how the probability of a false negative depends on the number of samples c o l l e c t e d . For small differences between the measured level and the standard a small sample size has an unacceptable high false negative rate. For example, i f the mean is five times the standard level and the c o e f f i c i e n t of v a r i a t i o n i s 2



200

Table IV. Sample Size (Value of J Given Κ = 1) Required to Ensure a False Positive Rate of 5 Percent and a False Negative Rate of Either 5 Percent or 1 Percent When Comparing Two Means

Difference Between Means


(A)

.75

Coefficient of Variation 2.5 2 1 1.5

3

Probability of False Negative = 5 Percent

2x

23

35

61

72

108

108

5x

5

7

12

16

19

23

lOx

4

5

6

8

10

11

lOOx

2

2

3

3

4

4

112

112

(B)

Probability of False Negative = 1 Percent

2x

33

50

89

112

5x

7

10

17

23

27

33

lOx

5

6

8

11

14

15

lOOx

2

3

4

4

5

5

2 then a sample size of 4 has a false negative rate of 62 percent. In other words, the contractor w i l l be released in 62 percent of the cases in which the actual level i s five times the standard l e v e l . Summary and Conclusions Providing a generally acceptable approach to determining "how clean is clean" for asbestos abatement projects i s complicated by many factors. F i r s t , there i s no absolute standard specifying an acceptable cutoff point for exposure to airborne asbestos. Second, there are a number of competing sampling and analysis protocols that have been proposed. None have been f u l l y validated. F i n a l l y , data from completed studies show that s t a t i s t i c a l sampling and analytic v a r i a b i l i t y may each be as large as 100 percent ( r e l a t i v e to the estimated concentration l e v e l ) . However, even against this background of uncertainty and appar ent imprecision, in some cases i t i s possible to measure airborne asbestos with acceptable precision through replication for a reasonable price. Since there i s no exposure standard, "clean" must be defined by comparing indoor and outdoor l e v e l s . A statistical comparison of indoor versus outdoor measurements that i s s i g n i f i cantly different from zero indicates that the indoor space i s not clean. Tests may be designed that either compare the average of


15.

CHESSONETAL. Table V.

îample Size

J=2


J=3

J=4

J=5

J=10


201

Probability of Detecting a Difference Between a Single Mean and a Standard Level, Given Sample Size J

Actual Mean Relative to Standard

2x 5x lOx lOOx 2x 5x lOx lOOx 2x 5x lOx lOOx 2x 5x lOx lOOx 2x 5x lOx lOOx

.75

.19 .41 .55 .87 .34 .83 .97 1.00 .48 .97 1.00 1.00 .61 1.00 1.00 1.00 .92 1.00 1.00 1.00

Coefficient of Variation 1 2 2.5 1.5

.15 .33 .46 .78 .26 .69 .90 1.00 .36 .89 .99 1.00 .46 .97 1.00 1.00 .78 1.00 1.00 1.00

.12 .26 .36 .65 .19 .52 .75 .99 .26 .73 .93 1.00 .32 .86 .98 1.00 .59 1.00 1.00 1.00

.11 .22 .31 .58 .16 .43 .65 .98 .22 .62 .86 1.00 .27 .75 .95 1.00 .48 .98 1.00 1.00

.10 .20 .28 .53 .15 .38 .58 .96 .19 .55 .79 1.00 .23 .68 .91 1.00 .42 .95 1.00 1.00

3

.10 .19 .26 .50 .14 .35 .53 .93 .18 .50 .74 1.00 .21 .62 .87 1.00 .38 .93 1.00 1.00

a set of indoor measurements with the average of a set of outdoor measurements or compare the average indoor measurements with a known value of the outdoor concentration developed from h i s t o r i c a l data. For the l a t t e r case, comparing the average of a set of indoor measurements to a known outdoor l e v e l , the sample size may be as small as f i v e . From Table V, we see that 5 measurements are s u f f i cient to detect a ten fold difference between an indoor average and a known outdoor level with a .91 probability when the c o e f f i c i e n t of variation i s 2.5. (Note that i f and σ are both equal to 1, the coefficient of variation i s approximately 2.5.) Larger sample sizes detect smaller differences. For example, i f J = 10, a 5 fold difference could be detected with a .95 proba b i l i t y ; a 10 fold difference would almost c e r t a i n l y be detected. (Refer to Table V). Differences that are multiples of 5 or 10 appear to be large. However, i n the testing problem being considered they may be accept able. Ambient outdoor Levels of asbestos tend to be Low, i n the 0-5 ug/m^ range. A f i v e - f o i d or even ten-foLd increase produces a Level that may s t i l l be considered to be within the acceptable range of the typical outdoor l e v e l . Therefore, i t may be necessary only to be able to identify large differences, larger than 5 or 10 times the outdoor l e v e l . Ε




202

If the outdoor leveL must be estimated also ( i . e . , h i s t o r i c a l l y determined levels are thought to be inadequate), then a larger number of samples are required. For a c o e f f i c i e n t of v a r i a t i o n equal to 2.5 and a probability of c o r r e c t l y i d e n t i f y i n g a 10 f o l d difference of .95, 10 samples are required indoors and 10 are required outdoors. (Refer to Table IV). To detect a 5 f o l d increase, a t o t a l of 38 samples are required. When both indoor and outdoor levels must be determined, the sampling experiment can be extremely expensive ( r e c a l l that TEM analysis i s approximately $500 per sample). Reluctance to bear the high cost provides motivation to seek a less expensive solution. Three obvious directions are suggested. F i r s t , refine both the sampling and a n a l y t i c a l protocol to reduce variation. Method studies i n progress should be pursued rigorously to achieve the desired objective. Second, a l t e r the a n a l y t i c a l protocol to reduce cost. Third, u t i l i z e a sampling plan that i s midway between treating the outdoor Level as known and treating i t as unknown. The use of a small number of outdoor samples, possibly only one, combined with h i s t o r i c a l data may be s u f f i c i e n t to confirm the outdoor l e v e l . Results on the refinement of protocols for sampling analysis are forthcoming i n the report on the EPA/NBS workshop on monitoring. Additional work on s t a t i s t i c a l design i s also i n progress to f i n d p r a c t i c a l ways to reduce required sample size which i n turn leads to reductions i n cost and more e f f i c i e n c y i n dealing with contractor release after abatement.

Disclaimer This document has been reviewed and approved for publication by the Office of Toxic Substances, Office of Pesticides & Toxic Substances, U.S. Environmental Protection Agency. The use of trade names or commercial products does not constitute Agency endorsement or recommendation for use.

Literature Cited 1. 2. 3. 4.

"Guidance for Controlling Friable Asbestos-Containing Materials in Buildings," U.S. Environmental Protection Agency, 1983, EPA 560/5-83-002. "Airborne Asbestos Levels in Schools," U.S. Environmental Protection Agency, 1983, EPA 560/5-83-003. "Measurement of Asbestos Air Pollution Inside Buildings Sprayed with Asbestos", U.S. Environmental Protection Agency, 1983, EPA 560/13-80-026. Chesson, J.; Margeson, D. P.; Ogden, J.; Reichenbach, N. G.; Bauer, K.; Constant, P. C.; Bergman, F. J.; Rose, D. P.; Atkinson, G. R.; "Evaluation of Asbestos Abatement Techniques, Phase 1: Removal;" Final Report to U.S. Environmental Protec tion Agency, Contract Nos. 68-01-6721 and 68-02-3938.

RECEIVED July 17, 1985


Environmental Applications of Chemometrics - ACS Publications

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