Document MJeXbgebvE66vo3dJoQV1wOQk

1/20/2006 3:13 PH FROM: Fas TO: 17572493242 PAGE: 002 OF 012 Risk Analysis, Vol 10, No. 3, 1990 Interpretation of Airborne Asbestos Measurements Jean Chesson,1,5 Jerry D. Rench,12'3 Bradley D. Schultz,4 and Karen L. Milne4 Received July 5, 1939; revised December 11, 1989 Transmission electron microscopy (TEM) is the preferred method of measuring airborne asbestos in buildings, but TEM measurements cannot be used directly in the existing equations relating risk to exposure because the equations are based on measurements made with a different techniquephase contrast microscopy (PCM). Comparison between measurements made by different methods is not simple because the methods differ in the size of panicles they can detect, and the relationship between exposure and disease is thought to depend on, among other things, asbestos fiber size. Previous suggestions for converting TEM measurements to PCM equivalents lack generality be cause they fail to take into account the size distribution of the asbestos particles and the expectation that fiber-size distributions in current nonoccupational environments could differ from the work places of the past on which the risk equations are based. A mathematical model is presented for investigating the conversion of airborne asbestos measurements made by one method to an equiv alent measurement made by another method. "Equivalent" means having the same potential to cause disease. The mode] clarifies the issues of concern and suggests approaches for obtaining meaningful conversion factors that will allow TEM measurements to be used in PCM-based risk equations. KEY WORDS: Asbestos; risk interpretation; transmission electron microscopy; phase contrast- microscopy; fiber size distribution; relative potency. 1. INTRODUCTION An association between exposure to airborne as bestos and cancer has been well established.(1_3) In com mon with most toxic substances, however, the quantitative relationship between the level of asbestos exposure and the risk of disease, especially at the low levels associated with nonoccupational exposure, is less clear. Models re lating asbestos exposure to risk have been fitted to data from epidemiologic studies of occupational exposures and extrapolated to estimate risk at low exposure levels. Although the models used for asbestos share many of the limitations common to high- to low-dose extrapola tion, it is not our intention to review these limitations or suggest alternatives. Instead, we address an important measurement problem that affects the use of the risk models for asbestos--namely, the comparability of air borne asbestos measurements made by different mea surement techniques. This question has become increasingly important as regulatory authorities, courts, investors, building owners, and building occupants grap 1 Chesson Consulting, Inc., 1717 Massachusetts Avenue N.W., Suite 601, Washington, D.C. 20036. 2 Baitelle Arlington Office, 2101 Wilson Blvd., Suite 800, Arlington, Virginia 22201, 1 Present address: SRA Technologies, 4700 King Street, Suite 300, Alexandria, Virginia 22302. _ * Design and Development Branch, TS'798, U.S. Environmental Pro tection Agency, 401 M Street, S. W., Washington, D.C. 20460. ! To whom correspondence should be addressed. ple with widespread concern over exposure to asbestos. 1.1 Background Measuring airborne asbestos exposure is compli cated because the risk of disease is thought to depend on, among other factors, the physical dimensions of as- 437 0572433Z90AmWM37iO6.(KVJ 1950 Sodtty fa: Riifc Auatyasi JRN-20-2006 18:25 92% P.02 1/20/2006 3:13 I'M TO: 17572493242 PACK: 003 OK 012 438 Chesson ei ai. bestos particles. A simple determination of concentration of asbestos particles per volume of air provides only an index of exposure that may be applicable, within a re stricted set of circumstances, but does not fully charac terize the exposure and does not allow comparison between different situations. Occupational exposures used to derive equations re lating risk of disease to exposure are expressed in terms of the concentration in air of fibers measured by phase contras! microscopy (PCM). For the purposes of PCM analysis, a fiber is defined as a particle with roughly parallel sides and a length-to width ratio of 3 or greater. PCM counts only fibers longer than 5 pm and thicker than -- 0.25 fim. Asbestos fibers in this size class will be referred to as "optical" fibers. PCM is not specific for asbestos. Therefore the exposure measurement may include other types of fiber, such as cellulose or glass fiber, in addition to asbestos. Few historical measurements were actually made with PCM since the method was not readily available prior to 1965.!l) Total dust measurements were made with impingers and concentrations were expressed in millions of particles per cubic foot of air. Thus the risk equations already incorporate a conversion from total dust measurements to concentration of optica! fibers. To simplify the discussion, this conversion will be ignored. However, many of the points made with respect to con verting present-day measurements to measurements comparable with historical measurements expressed in optical fibers also apply to converting dust measure ments to optical fibers. Fibers longer than 5 jxm were chosen for the con venience of optical microscopic evaluation, not because there is necessarily any sharp distinction between the risk associated with fibers longer or shorter than this length.T Fibers longer than 5 pm usually make up a small fraction of the total fibers present. Provided the relative abun dances of each size class remain constant, tiie optical fiber count provides an appropriate index of asbestos exposure, since increases in the absolute abundance of any size class arc reflected in the absolute abundance of optical fibers. When size distributions vary from situa tion to situation, the index is distorted and does not nec essarily provide a reliable indication of die relative risk of disease. Although PCM has proven useful in the occupa tional environment, it is less satisfactory in settings where a large proportion of fibers may be nonasbestos, and where most of asbestos structures may be smaller than the size range detectable by PCM. In these situations, transmission electron microscopy (TEM) is the preferred measurement method. TEM can detect, the smallest as bestos fibrils and can distinguish asbestos from nonas bestos structures. 1.2. Objective TEM is the preferred method of measuring airborne asbestos in buildings, but TEM measurements cannot be used directly in the equations relating risk to exposure, because the equations are based on PCM. Various sug gestions for converting TEM measurements to PCM equivalents have been made. Most lack generality' be cause they fail to take into account the size distribution of the asbestos particles and the expectation that fibersize distributions in current nonoccupational environ ments could differ from the workplaces of the past on which die unit risk factors are based. A difference in fiber-size distributions"between these settings potentially provides a bias in estimating exposures, particularly if the likelihood of disease varies with fiber size and the measurement methods of the past have not been able to detect ail of the relevant fiber sizes. In this paper we present a mathematical mode! for investigating the conversion of airborne asbestos measure ments made by one method to an equivalent measurement made by another method. "Equivalent" means having the same potential to cause disease. Tne mode! clarifies the issues of concern and suggests approaches for obtaining meaningful conversion factors that will allow TEM mea surements to be used in PCM-based risk equations. 2. MODEL FOR DERIVING CONVERSION FACTORS 2.1. Description We express the problem generally by considering the conversion of an airborne asbestos measurement made in environment 2 with measurement method 2 (e.g., a building environment measured by TEM) to a value equivalent to a measurement made in environment 1 with measurement method 1 (e.g., occupational environment measured with PCM). From our model we will derive a conversion factor, c. that allows measurements to be placed on a common exposure scale. Once measure ments have been placed on a common scale, their rela tive magnitudes are meaningful (i.e. , a measurement that is. say, three times larger than another measurement rep resents three times the exposure and, for a linear doseresponse curve, three times the risk). The model has three ingredients: JAN-20-2006 18=25 92* P.03 Airborne Asbestos Measurements 439 2. The distribution of structure sizes in each envi ronment (fj and 2. The relative potency of each structure size (r). 3. The ability of each measurement method to de tect each structure size (dl and dz). We will regard/, r, and d as functions of structure size (length and width). However, they may be defined as functions of any quantity of interest. They do not need to b.e continuous functions. In fact, even when consid ering essentially continuous quantities, such as length and width, information will often be based on discrete size categories. Within this context, there is no difficulty in adding additional categories to the model to cater to nonasbestos structures or complex asbestos structures, such as bundles) clusters, or matrices. The function /is a probability density function. That is, the proportion of structures less than or equal tore in length and less than or equal toy in width is given by [ f ftx,y)dxdy Jo Jo Relative potency, r, refers to the ability of a structure !o cause disease and represents 'he cumulative effect of many individual factors (inhalation, clearance from the lung, ere.). The maximum value of r is set arbitrarily at i, so that for any structure of length* and width y, r(x,y) represents the potency of that structure relative to the structure size with maximum potency. For example, r(x,y) - 0.1 indicates that the potential for a structure of this size to cause disease is one tenth that of the most potent size class. Since relative potency of a given structure size may depend on the disease being considered/4* there may be a different relative potency function for each disease. Similarly, different types of asbestos (chrysotiie, amphiboles, etc.) could be treated separately if nec essary. For a given measurement method, d(x,y) represents the probability that a structure in this size class will be detected when it is present in the air. Like r, d represents the cumulative effect of several individual factors. These may include sampling (e.g., sample collection tech niques that deliberately exclude certain structures), method performance (ability of method to detect certain struc tures), and analytical protocol (counting rules that ex clude certain structures). We assume that the total effect of any particular exposure is given by the sum of the effects of each of its component structures (i.e., the sum of the abundance of each structure size weighted by its relative potency). This assumption (which is implicit in most, if not all, work to date) implies that there is r.o interaction between the effects of individual structures. Under these condi tions, the conversion factor, c, is given by Jr Jc - ( df2 i r dj\) (fd} dfx / jd2 <if7) (see Appendix A) where r, d,, and / are all functions of structure length and width. Measurements made in en vironment 2 with method 2 are converted to the same scale as those made in environment 1 with method 1 by multiplying by c. When there is a finite number, k, of discrete cate gories, the integrals can be written as sums. For example Jr df7 could be written as 2 rfo for i 1 to k, where ri is the relative potency of structures in category i and fv is the relative frequency of structures in category i in environment 2. We will use the integral notation because it is more general and easier to write. Most calculations, however, will be simple weighted sums. The conversion factor, c, is the product of two quantities. The first depends on the structure-size distri butions in the two environments,/; and/2, and relative potency, r. This quantity does not depend on either mea surement process. The second quantity depends on the structure-size distributions in the two environments and the sensitivity of the two measurement processes, d. and d2. This quantity does not depend on relative potency, 2.2. Implications Several important observations can be made. 1. The conversion factor, c, always depends on the fiber-size distributions /; and /2, even when /) s f2. Therefore, c is expected to vary from situation to situ ation. There is no single conversion factor that can be applied universally. 2. If the two environments under consideration have the same structure-size distribution (f; =? f2), then c de pends only on/and d. Information on relative potency is not needed to calculate the conversion factor when measurements are made in similar environments. 3. Setting c = (Jdy df, ! Jd2 df2)y will be conserv ative in the sense of overestimating c and hence the estimate of exposure, provided Jr dfz < Jrdfv This will be true when the more potent structure sizes are more common in environment 1 (e.g., where the epidemio logic studies were conducted) relative to environment 2 (where current, nonoccupational exposures are taking place). Using a value of c that is larger than its true value is conservative in the sense that it will inflate measure ments of exposure and hence risk. We will use the expression "'overestimate of exposure'' as a convenient 1/20/2006 3:13 I'M .-KOM: Fax TO: 17572493242 FACE: 005 Or 012 440 Chesson et aU way of expressing this relationship. It should be recog nized, however, that there are many sources of uncer tainty contributing to 3n exposure estimate and making a conservative assumption in one part of the process does not imply that the final estimate will necessarily be an overestimate. The amount by which c is overestimated will de pend on the value of (Jr df21 Jr dfj) and, therefore, can vary from environment to environment. If relative po tency' does not depend on fiber size fi.e., r(x,y) is con stant], then c equals (jd1 dfx / jd2 df2) and no overestimation is involved. 4. If we assume that method 2 detects all structures (or essentially all) and thaijrdf2 < f rdfx as in 3 above, an overestimate of c is given by jd] dfu the proportion of structures detected by method 1 in environment 1. This implies that the proportion of PCM-detectable structures present in die historical occupational environ ment, rather than the present environment, is the critical quantity for placing an upperbound on the conversion of TEM measurements to the same scale as the PCM-based risk equations. Of course, the structure-size distributions in both environments are needed to estimate c. 5. If the same measurement technique is used in both environments (i.e.. d} = d2), c -- (Jr df7! j r dfx) which is not necessarily equal to 1. Merely using -he same measurement technique in two different environ ments does not necessarily provide comparable mea surements of exposure. For example, a PCM measurement in environment 1, which is twice a PCM measurement in environment 2. does not necessarily imply that ex posure in environment 1 is twice that in environment 2. Environment 2 may have a larger proportion of struc tures with high relative potency. 6. The effect on c, and hence estimates of risk, of ignoring a particular size class (e.g., deciding to ignore asbestos structures shorter than a particular length) is determined by the relative potency of that size class weighted by its relative abundance in both environments (Appendix B). The mode! can be used to design more efficient measurement protocols by' identifying size classes that can be ignored and size classes that should receive particular emphasis. 3. DATA SOURCES AND LIMITATIONS The conversion factor, c. can be calculated pre cisely when f,r, and d are known. Although complete information will rarely be available, our model provides a basis for making approximations, determining whether c will be under- or overestimated by a particular ap- proach, and identifying information needed to improve the estimate. Even when information is available, c will be calculated using estimates rather than actual values of f r, and d. The sensitivity of c to the uncertainty associated with the estimates is a topic for future re search. This section provides a brief overview of our current knowledge of size distributions (f), relative po tency (?), and method performance (d). 3.1. Size Distributions Since our focus is on the conversion of present-day measurements made with TEM, we will assume that the size distribution of the current exposure (f2) is weLl char acterized, and that the important unknown is the size distribution associated with past exposures on which the risk equations are based (fj). This assumption conve niently ignores factors such as the effect of different TEM preparation methods on size distributions,155 which can be handled by the model but are beyond the scope of this paper. The remainder of this section concentrates on size distributions associated with past exposures. Fiber-size distributions are essentially unknown for the cohorts of workers that have been the subjects of epidemiologic studies. The lack of data is not surprising because many of the workers experienced their expo sures to asbestos as long ago as the 1930s or 1940s, when monitoring programs were rare and the importance of fiber-distribution analyses was not perceived. For some cohorts it has been possible to construct dose-response relationships through estimates of fiber-exposure levels taken from the. available monitoring data or by using contemporary monitoring data as an index of exposures that occurred in the past. Using scanning electron microscopy (5EM) or TEM, several investigators have analyzed the size distributions of fibers taken from asbestos operations.In some instances, the fibers have been characterized using TEM, and proportional distributions by diameter and length have been ascertained. The principal limitation of these data is not knowing the extent to which the data are representative of the distributions to which workers were exposed long ago. There is good reason to believe that the distributions have changed over time just as exposure levels have undoubtedly been affected by new equipment and exposure-control devices. It is known that dust-con trol strategies have been imposed in many production operations'11'125 and that ventilation systems, as one strategy, can change particle-size distributions, because particle collectors are generally more efficient at captur ing the larger particles.'135 The extent to which recently JAN-20-2006 18-25 92% P.05 1/20/2006 3:13 I'M ?KOM: Fax TO: 1757 24 9324 2 FACE: 006 OF 012 Airborne Asbestos Measurements 441 collected fiber samples are influenced by ventilation sys studies by McDonald et a/.*155 consisted of workers pri tems is unknown, but it is reasonable to assume that the marily involved in the production of textiles, and there fiber-size distributions in samples taken from operations fore the size distribution data for textile processes might in the 1970s may not necessarily be representative of the be considered appropriate; however, friction products exposures encountered by workers decades earlier, when were also produced at this plant and therefore the actual dust-reduction strategies were different or nonexistent. exposure may be a combination of the two distributions. Since PCM does not distinguish asbestos from other There is also uncertainty in the extent to which size- fibers within the optical size range, the PCM measure distribution data collected in one country, such as the ment may also include nonasbestos fibers. Therefore, a data collected in U.S. by Dement and Harris'75 for textile complete characterization of the occupational exposures and friction-product operations, would be applicable to ' requires knowing the contribution from nonasbestos fi the plants studied in other countries, such as the United bers. Investigation of size distributions has concentrated Kingdom or Italy. on asbestos fibers, and information on the proportion of ' nonasbestos optical fibers in each exposure setting is not . available. It is reasonable to assume that, in many of the 3.2.Relative Potency occupational settings, the majority of fibers were asbes tos, but this is by no means certain. Complex asbestos A number of researchers*4,16,175 have suggested that structures {bundles, clusters, and matrices) have also long and thin fibers are more potent than short and thick tended to be ignored by researchers. fibers, particularly with respect to lung cancer, but there Another limitation of the available fiber-size distri have been few advances made in quantifying the risks bution data is the limited number of samples that have of various fiber-size categories. The evidence in favor been taken in the industry. The cohorts that have been of differences in relative potency is for the most part studied consisted of workers employed in numerous op indirect and comes from at least four categories of sources. erations and activities, whereas only a few operations These include animal studies in which exposures were have been considered in the recent studies of fiber dis by tire inhalation route08-205 or by implantation/inocu- tributions. Some of the samples have come from oper lation06*20'225, fiber-deposition studies of auiopsied lung ations which have been the subject of an epidemiologic tissues from workers,*23-255 comparative analyses of an study. For example. Dement and Harris175 took chryso- imal and epidemiologic studies that attempt to reconcile tile samples from.textile, friction, and cement pipe op- study findings according to fiber-dimension character- eiations and amosite from a pipe-finishing plant. Some istics(fi) and other biological evidence.7,27> None of of the textile samples came from the same textile plant these studies alone, however, provides a good data set examined in a cohort investigation by Dement et alS]<'> by which one can estimate relative potency for specific In Table I we attempt to match the epidemiologic size categories of fibers. For example, although consid studies listed in Table 3-31 of the 1986 EPA Airborne erable attention has been given to the fiber-desposition , Asbestos Health Assessment Update05 with data on as patterns found in lung tissues of workers, it has not been bestos fiber-size distributions. These studies were used established that the fiber-size distributions found at death to assess dose-response relationships for lung cancer. In are necessarily the same as those that initiated the disease some instances, the matching is net as ideal as one would years earlier. prefer, particularly where more than one type of asbestos Several investigators have proposed fiber dimensions, | may have been involved. The fiber-size distributions se- particularly for fiber length, which distinguish fiber sizes . lected correspond to the asbestos type thought to be pre- of considerable carcinogenic potency from tbose with little . dominant in a given exposure. Three size categories are or nc potency. The Stanton hypothesis, which is one of used in Table I to summarize each distribution. The sum the best known, suggests that the most potent fibers are mary is for convenient display only. Where applicable, those with a length greater than 8 urn and a width of 0.25 1 subsequent calculations were based on the complete size pur. or less.*165 Another hypothesis by Bertrand and Pez- . distribution provided. When size categories reported in erat*225 propose that the relative potency' of fibers is a con I the literature did not correspond to those used here, es tinuous function of aspect ratio (length divided by width), timates were obtained by linear interpolation. regardless of the fiber length or diameter. One of the tenets ' Given the uncertainties in the appropriateness of of their hypothesis, which was based on a reanalysis of these data for exposures occurring in the past, the selec- the work by Stanton et al(21) is that short fibers may be bon of one data set over another to link to epidemiologic just as carcinogenic as long fibers if the aspect ratio is a j studies is somewhat arbitrary'. For example, the cohort certain critical value. {Note that out model can readily cater JRN-20-2006 18:25 92X P.06 1/20/2006 3:13 PH i'KOM: Fax TO: 17572493242 PAGE: 007 OF 012 442 Chesson et a!. Table I. Epidemiologic Studies Used in EPA's Asbestos Health Assessment Update111 and Possible Asbestos Fiber-Size Distributions Epidemiologic study Dement et a/.'1*1 McDonald et aL'n) Peto3" McDonald et alP*1 Bern,' and Newbouse'1'1 McDonald et ut.tS4) McDonald et al.<iS> Nicholson et al.Wi Rnbino et alPT> Seidman et Sdikoff si all*** Henderson and Enierlincr`liy Weill et al.!<2) Hughes and WcilF^v Pinkeistsin'"ul` Size distribution source Dement and Harris,(7) C1-C3 Demeni and Harris,'71 C1-C3 Dement and Harris,'71 C1-C3 Demerit and Harris.'71 C1-C3 Dement and Harris,1n) C4-C6 Demeni and Harris,'71 C4-C6 Gibbs and Hwang,(in) Tabic 2 Gibbs and Hwan?,`sa) Table 2 Gibbs and Hwang,"r,) Table 2 Demen! and Harris,171 C10-12 See note See note See note See note Size distribution (proportion*) Short6 Long, thin* Optical' 0.79 0.79 0.79 0.79 0.86 0.86 0.97 0.97 0.97 0.57 0.09 0.09 0.09 0.09 0.07 0.07 0.01 0.01 0.01 0.06 0.13 0.13 0.13 0.13 0.07 0.07 0.01 0.01 0.01 0.36 ^Proportions may not sum to 1 due to rounding, ^Length s 5 pm. "Length > 5 wn, diameter < 0.25 p.m. "'Length > 5 pm, diameter > 0.25 pun. 'Mixed exposures--size distribution difficult to characterize. to this hypothesis since relative potency, r, can be any function of length and width). To the best of our knowledge only Pott(,7) provides quantitative estimates of relative potency. Pott's hypoth esized estimates of relative potency are based on obser vations by several investigators. Pits model takes into account fiber length and diameter. For example. Pott suggests that the carcinogenic potency of a fiber is great est at a length of approximately 20 pirn and that 8 pm fibers are one half as potent as 20pm fibers. With regard to fiber diameters, fibers that are approximately 0.1 p.m are the most potent, and fibers 0.5 u.m in diameter are one half as potent as the 0.1 jxm fibers. No distinction is made between fibers causing lung cancer and those causing mesothelioma. Lippmamv45 argues that the crit ical fiber dimensions for these two diseases may be dif ferent. To apply the model presented in this paper, we assume only that the relative potency of long fibers is not iess than the relative potency of short fibers. In many cases this assumption is sufficient to obtain overesti mates of exposure. As additional information on relative potency becomes available, it can be incoiporated in the model to refine the estimate of the conversion factor c. 3.3. Performance of the Microscopy Method The model allows for precise definition of the per formance of the microscopy method used to analyze the sample. For the examples that follow we will assume that TEM detects asbestos structures of every size with probability equal to 1 (i.e., d2 = 1). Although Steel and SmaiipQ) have shown that the probability of detecting small structures is less than 1, and possible effects of different preparation methods are ignored,1(S) the as sumption is adequate for the purposes of illustration. We assume that PCM detects all structures longer than 5 jum and with diameter greater than 0.25 and that structures outside this range are not detected (i.e., dfay) - 1 for* > 5 andy > 0.25, and 0 elsewhere). This is the typical operating range of PCM.(30:s 4. EXAMPLE Table II lists fd1 dfx for the epidemiologic studies in the EPA Health Update,assuming the fiber-size distri butions suggested in Section 3.1. The values in the table are simply an estimate of the proportion of optica] struc tures in the historical environment. We are ignoring any contribution to the PCM measurement from nonasbestos fibers. Appendix C shows that the effect on nonasbestos fibers in the optical size range is to increase the value of Jdj dfx by qjp, where q is the proportion of nonasbestos fibers in the optica] size range and p is the proportion of asbestos fibers (p-+q- 1). Provided q is less than 0.1. the effect of nonasbestos fibers on the estimate of c will be small relative to other sources of uncertainty. JRN-20-2006 18=25 92* P.0? .Airborne Asbestos Measurements 443 Table II. Values of fdt dfl (Proportion of Optical Fibers) for Studies Listed in Table i Epidemiologic study* (ref.) 58,39 Id 15 32 31 33 36 37 34 35 Type of exposure Amosite insuiation manufacture Textile production Textile production Textile production Textile production Friction products Mining and milting Mining and milling Friction products Mining and milling Kt 0.04300 0.02801) 0.02500 0.01400 0.01100 0.00058 G.Q017Q 0.00081 0.00010 0.00060 M df, 0.36 0.13 0.13 0.13 0.13 0.07 0.01 0.01 0.07 0.01 1000 Kt fd, df. 15.4S 3.64 3.25 1.82 1.45 0.04 0.02 0.01 0.01 0.01 "Ordered according to KJd, df,, a measure of relative potency of the exposure with respect to lung cancer. See text for assumptions. 'Unit risks for lung cancer calculated in EPA's Asbestos Health Assessment Update (Ref. 1). In addition to listing information needed to estimate c. Table II also provides insight into relative potency. The conversion factor, q can be expressed as qq, where q - jdl dfx / frdfx and c2 - frdf2i fd2 df2.c .h determined by environment I, whereas q is determined by environ ment 2. Instead of multiplying the measurement made in environment 2 by c and inserting the result in the risk equation, one may equivalently multiply the parameter of die risk equation, K, by q and multiply the measurement made in environment 2 by q. If the effects of different size distributions are the only differences among the epi demiologic studies, then c<K should be constant across all studies. That is, q is an adjustment factor that corrects for size distribution. Setting the constant arbitrarily equal to 1 gives fr dfx - K Jdj df-.. The overall relative potency of the fiber-size distribution associated with each study, JV dfx, is given by the parameter K of the risk equation mul tiplied by the proportion of structures detectable by PCM. Thus K fdx dfx, rather than K, should be used to rank studies in terms of relative potency' of their fiber-size dis tributions. K is inappropriate for ranking because it de pends on both potency and the proportion of structures in the PCM size range. The entries in Table II are ranked according to the estimated value of Kt fd2 dfx, where KL is the proportion ality constant for lung cancer reported in Table 3-31 of the EPA Health Update.W Keeping in mind the uncertainties discussed in Section 3, the rankings suggest that the highest relative potency is associated with amosite insulation man ufacturing, followed by asbestos textile production, and mining and friction products. The rankings are not dissim ilar from those of Kt, but adjustment by q indicates rel ative magnitudes. The relative potencies associated with mining are 3 to 4 orders of magnitude less than the potency associated with amosite-insuiation manufac turing. These differences in overall potency could re flect the effect of different fiber-size distributions as well as the effect of fiber type or other factors specific to the exposure. Consider a hypothetical, nonoccupationa! exposure of 0.02 asbestos structures per cubic centimeter (s/cm3) measured by TEM in which 96% of the asbestos struc tures are shorter than 5 pm, and of the remaining 4%, half (2%) have diameters greater than 0.25 (.im. The current information on relative potency suggests that this size distribution is unlikely to represent a greater relative potency than the majority of occupational studies in Ta ble I (i.e., fr df2 < fr dfx). Therefore taking c = (fd2 dfx I fd2 df2) is expected to overestimate exposure. Since the exposure was measured by TEM, we put fd2 df2 ~ 1 and obtain c = fdx df. To convert the original TEM measurement of 0.02 s/cm3 for insertion in the EPA Health Update risk equa tions, we need to multiply by fdx dfx- The EPA Health Update risk equation for lung cancer was derived ex cluding the mining and milling studies. Therefore, we multiply 0.02 s/cm3 by 0.15, the average value of df, for the remaining studies in Table II, to give 0.003 //cm3, an overestimate of exposure. Estimates of risk can then be read from Table 6-3 of the Health Update. (Table 5-3 is based on U.S. general population death rates and does not consider smoking habits. Details are given in Ref. 1.) For a lifetime exposure beginning at birth, the lifetime risk of death from lung cancer pc? 100,000 per sons is 16 for females and 51 foi males. We have used the EPA Health Update merely as an 444 Chesson et al. example. The approach can be applied to other risk equa tions and to mesothelioma as well as lung cancer. Recall that the extent to which c is overestimated depends on (jr dj2 / jr dff). While the overesrimation approach may be very valuable in obtaining a conserv ative estimate of risk, it does not provide a good basis for comparing two different risk estimates because the degree of overesrimation will vary from environment to environment. When comparisons are desired, additional information on r, beyond merely assuming jr df2 < jr di), should be inserted in the model. 5. CONCLUSIONS AND RECOMMENDATIONS We have developed a flexible model that allows TEM measurements to be used in risk equations based on oc cupational exposures measured with PCM. 'Die model pro vides a basis for proceeding when data are limited as well as a framework for incorporating new information as it becomes available. Information, such as relative potency of different size classes (including complex structures), dif ferences between asbestos types, or more precise descrip tions of method performance, can be incorporated in the mode.l and used to refine estimates of exposure. The model may be used to answer questions such as, "Will it make a difference if the potency of a particular size class is 5. 10, or 100 times another?" and to design measurement methods by quantifying the effect of reducing the emphasis on, or ignoring, certain size classes. In the absence of quantitative information on rela tive potency, we recommend checking the TEM fibersize distribution to determine that it qualitatively rep resents a lower potency than that associated with the occupational exposures used to derive the risk equation. When this is true, multiplying the TEM measurement by the proportion of optical structures in the occupational environment will provide an overestimate of exposuie. APPENDIX A Model for Converting Asbestos Exposure Measurements Between Environments and Analytical Protocols Notation Let.? = the number of structures per unit volume of air; f(x,y) = the frequency distribution of structure size. such that the proportion of structures shorter than x and narrower than y is /ddx dy; (Note that although x andy are used here to represent structure length and width, respectively, the ar gument below applies to any exhaustive and mutually exclusive classification system. For example, a nonasbestos cat egory can be added when considering PCM.) r(x,y) - the relative potency of structures of size x,y\ and d{x,y) - the probability of the measurement process detecting a structure of sizex,y given that the structure is present. Then m, the number of structures detected by the mea surement process is given by m = sjjf(x.y)d(x,y) dxdy and a. the effective exposure in terms of potential for developing disease, is given by a sfff(x,y)r(x,y) dx dy The expression fox a assumes that the total effect of any particular exposure is given by the sum of the effects of each of its component structures (i.e., there is no inter action between structures). Derivation of Conversion Factor Consider two environments, Jj./jfoyJ andr2,/2(xy), and two measurement processes, dx and d2. Suppose measurement process 2 measures m2 in environment 2. The objective is to find m, for measurement process 1 in environment 1, such that m, represents the same ef fective exposure, in terms of potential for developing disease, as w2. Since s2 = 'n2/fjf2(x,y)d2(x,y) dx dy, we have 2 = m2(Jffz(x,y)r(xy) dx dy)j(jjf2(x,y)d2(x,y} dx dy) Similarly = m\Uff\(Ky)r(x,y) dx dy)I(jff.:(x,y)dl(xj>) dx dy) Putting = a2 gives m\ = m2(SSf2(x,y}r{x)y)dx<ty)l[fSf1tx,y)r(x,y)dx<fy) Airborne Asbestos Measurements 445 x UShfayWifay) & dyWUSfifoyHtfcy) dxdy) which can be written more concisely as m, -- cm2: where c = (/r df7 / fr df,) (Jd. df; / fd7 df2) APPENDIX B When Can a Size Class Be Ignored? Let XY represent a subset of possible size classes. Let c* be the conversion factor that would be obtained if size class X\' were ignored. Let p. - df,:. Then f*. the size distribution in environment i ignoring size class XY, is given by //(l -p) for (x,y) e XY fi 0 for fry) $ XY and c* is given by ((> dfi ~ V clfMr dh - /v dfi))ilfdi dfi Wd2 dfz)) If c is the "correct'' conversion factor, then the ratio of c* to c is given by cVc = (1 - E/ df-Jfr <if2)i(l - {^r dfjfr df]} The ratio depends on the relative weighted potency of size class XY in each environment. If rlx.y) - 0 for (x.y) XY, (hen the ratio is one and ignoring the size class has no effect. Similarly, if/, s f7, the ratio is also 1. Note that the equality must be true for all (x,yj. It is not sufficient that/, = /2 fot (x,y) E XY. Depending on the precision with which it is desired to estimate c, there may be a range of other situations for which ignoring a particular size class is acceptable. For example, if the relative weighted potencies in en vironments 1 and 2 are both less than 0.5, then c* differs from c by no more than a factor of 2. This may be an acceptable variation relative to other sources of uncer tainty. Note that relative potency alone is not sufficient to determine the effect of ignoring a size class. The relative potency must be weighted by relative abun dance. APPENDIX C Effect of Nonasbestos Fibers on Calculation of c Define f*(A) as the proportion of particles in class A. such that P`f{x,y) for asbestos particles of lengths and diametery r(A) = q for nonasbestos particles in the optical size range where p+q-1 and /is the size distribution of asbestos particles as defined previously. Let q, be the proportion of nonasbestos particles in environment 1 and q2 be the proportion of nonasbestos particles in environment 2, Then C " (/'" df*2 / fr df,) (Jd, dr, / fd2 dr2) "We will assume r~ 0 for nonasbestos particles. Then, assuming measurement method 2 does not count non asbestos particles, c = (p-Jr df-JpiJr dff) (pjd, df,--q, !Pl) = (Jr dh i Jr dfi) {Jdi df, + qM ACKNOWLEDGMENTS This work benefited from valuable discussions with D. Wayne Berman and Kenny Crump and comments from Eric Chatfield. Data analysis and bibliographic support were provided by Amy Doll of Chesson Con sulting and Debra Egan and Cathy Pickrei of Battelle. The Battelle Task Leader was Barbara Leczynski, and the EPA Project Officer was Mary Frankenberry. This document has been reviewed and approved for publication by the Office of Toxic Substances, Office of Pesticides and Toxic Substances, U.S. Environmental Protection Agency. Opinions are those of the authors and do not reflect official positions of the U.S. EPA. Publication of data in this document does not signify that the contents necessarily reflect the joint or separate views and policies of each sponsoring agency. 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