€Strl FEATURES
Predicting the uncertainties in
RISK A S S E S S M E N T Reducing uncertainty in assessing the risk of environmental contaminants is important to regulatory agencies at the state and federal levels and to nonregulatory agencies that work for environmental health and safety. Efforts to manage risk are driven by actual risk, which can rarely be measured; calculoted risk, which is based on science but whose inclusion often is restricted through regulatory policy; and perceived risk. Calculated health risk within a population exposed to an environmental contaminant is determined by using a release rate or conc e n t r a t i o n at t h e source; the exposure function, which converts the source into the amount contacted by each individual; the organ or tissue dose per unit exposure: and the toxic potency associated with the delivered dose. The actual risk can be more complex and can include temporal a n d spatial relations and functional dependencies amone the source, exposGe, dose, and the incidence of detriment. Nonetheless, in practice, risk often is characterized as a product of four factors: source term, exposure factors, fraction absorbed, and toxic potency. This article illustrates a strategy for evaluating the sources of uncertainty in predictive exposure
A California groundwater case study
1674 Environ. Sci. Technol., Vol. 25, No. 10. 1991
and health risk assessments. Overall uncertainty results from variability i n natural systems and human behavior and our ignorance about them. Two obvious methods are available for reducing this uncertainty: improving the models and expanding t h e data. However, unless our strategy for reducing uncertainty recognizes that the cost of building new models and collecting data must be balanced bv the value of the (nformation obtained, we might squander limited resources for environmental research ( 1 ) . It is possible, nevertheless, to use the analytic framework of statistical decision analysis to determine when additional information would be beneficial
I1 I
I 11,Z).
Thomas E. McKone Kenneth T. Bogen University of California Lawrence Livermore Notionol Laboratory Livermore, CA 94550
Through case studies, we have been working to immove the characterization of u n c e r t a i n t y i n human exposure models and the combined uncertainty in source, exposure, and dose-response models (3-51.We describe here a case study'based on the volatile organic chemical tetrachloroethylene (perchloroethylene, PCE) in California water supplies derived from groundwater. We divide our analysis into five steps. First, we consider the magnitude and variability of PCE concentrations available in
0013-936X/91/0925-1674502.50/0@ 1991 American Chemical Society
large public water supplies in California. Second, we characterize pathway exposure factors (PEFs) for groundwater exposures and estimate the uncertainty for each PEF. Third, we examine models that describe uptake and metabolism to estimate the relation between exposure and metabolized dose. Fourth, we consider the carcinogenic potency of the metabolized PCE dose. Finally, we combine the results to estimate the overall magnitude and uncertainty of increased risk to an individual selected at random from the exposed population, and we explore the important contributions to overall uncertainty. Sensitivity and uncertainty As applied to mathematical models, uncertainty analysis involves the determination of the variation in an output function based on the collective variability of model inputs. In contrast, sensitivity analysis involves the determination of the changes in model response as a result of changes in individual model parameters. Three approaches are useful for assessing uncertainty and sensitivity in mathematical models: differential analysis, responsesurface replacement, and Monte Carlo or modified Monte Carlo (Le., Latin Hypercube Sampling) methods (6, 7).To apply any of these methods, we think of a model as producing an output Y , such as population health risk, that is a function of several input variables, Xi, and time, t: Y=f(X,,X,,X,,
. . . x,,
t)
function (CDF) for Y. However, the PDF or CDF of Y often can be obtained only when we have meaningful estimates of the probability distributions of the input variables Xi, If this information is missing or incomplete, the CDF and PDF for Y still can be constructed, but they should be characterized as screening distributions for parameter uncertainty rather than realistic representations of the uncertainty in Y. Water supply concentrations The first step in our evaluation of uncertainty in risk assessmentsource characterization-requires that we estimate the magnitude and uncertainty of the populationaveraged concentration of PCE in California water supplies. Using survey data compiled by the California Department of Health Services, and referred to as the AB1803 data (S),we estimate that, in 1986, 6.8 million persons in California were supplied with water from large public water systems with at least one well in which PCE contamination had been detected. These data have a number of limitations, however, including incomplete sampling (even though all large water systems in California were sampled), only a limited number of wells in each system was sampled: lack of information on the fraction of the total system supply provided by any single well: limited data on how concentrations vary with time: and no information on the relation between concentrations
in individual wells and concentrations in the water supply lines for individual households. In spite of these limitations, we can construct an empirical probability distribution of PCE concentrations in California water supplies using the AB1803 data and two sets of assumptions. The first set includes the assumptions that surface water and negative samples contain no PCE; all wells within a given water system produce water at the same rate: and the average concentration of PCE in unsampled wells is the same as the average PCE concentration in sampled wells. The second set of assumptions is the same as the first except that the assumption that PCE levels in unsampled wells equal the average PCE concentration is replaced by the assumption that unsampled wells contain no PCE. This assumption is included because the sampled wells in each system were not randomly selected: they were selected because they were expected to contain PCE. On the basis of the AB1803 data and these assumptions, we constructed two empirical distributions of exposed population size versus concentration. These two probability densities, shown in Figure 1, are combined into a single empirical cumulative distribution function for the water supply concentration of PCE for the population at risk. The resulting mean and standard deviation of PCE concentrations in water supplies are listed in Table 1.
(11
The variables X, represent the inputs to the risk assessment model, such as water concentration, exposure factors, metabolism parameters, and cancer potency. In the context of risk assessment models, uncertainty is used to describe random variability in the parameters or measured data used in the models and the imprecision of the analyst’s knowledge about models, their parameters, and their predictions. Describing uncertainty in the output variable Y involves quantification of the range of Y , its arithmetic mean value, the arithmetic or geometric standard deviation of Y, and upper and lower quantile values of Y such as 5% l o w e r b o u n d a n d 95% u p p e r bound. Convenient tools for presenting such information are the probability density function (PDF) and the cumulative distribution
Assumption set 1
-r
Assumption set 2
Envimn. Sci. Technol.. Vol. 25. No. IO. 1991 1675
il
Arithmetic mean and standard deviations of input parameters represented by empirical or lognormal distributions Arithmetic
Distribution type
Arithmetic
standard deviation
Geometric Dtandard deviation
io-'
Empirical
3.5x
Lognormal
1.2 x 10-2
2.5 1.4
Lognormal Lognormal Lognormal Lognormal Lognormal Lognormal Empirical Water-based exposure pathways
In the second step of our analysis, we identify methods for characterizing domestic pathway exposure factors (PEFs) and then estimate uncertainty for each PEF. We consider three domestic exposure pathways: ingestion of PCE in tap water, inhalation of PCE transferred from tap water to indoor air, and dermal uptake of PCE from shower and bath water. The end product of the exposure assessment for contaminants in public water supplies is an estimate of the amount of contaminant contacted per unit body weight over a specific period of time (91. On the basis of EPA recommendations (IO),when environmental concentrations are constant in time, the average exposure for a specified population exposed to a concentration Ck (measured or modeled) in environmental medium k (Le., air, water, or soil) is expressed as the lifetime average chronic daily intake (CDn, in mglkg-day, and is given by CDI=
CR, C. EFxED x [ B W ] X < X AT
c, =
PEF (k+i) x C,
(2)
~
where [CRJBWI is the contact rate per unit body weight such as L (waterllkg-day or m3 (airllkg-day: CJC, is the ratio of concentration in the contact" medium i (Le., air, tap water, milk, soil, etc.) to the concentration in environmental medium k (air, water, soil), units dependent on the two media; EF is the exposure frequency, days per year; ED is I'
1676 Environ.
the exposure duration, years; and AT is the averaging time, days. We use the pathway exposure factor, PEF (k-i), that relates the concentration Ckin medium k to the chronic daily intake, mg/kg-day, during the period ED as a convenient way of making route-to-route exposure comparisons. Ingestion of tap water. We calculate the mean and standard deviation of the PEF for ingestion of groundwater using intake per unit body weight, IJBWin Llkg-day, averaged over a lifetime: PEF (water+water ingestion) = I J B W (31
For this pathway the exposure route is ingestion, the source medium and the contact medium are groundwater, the contact rate is the water intake per unit body weight in Llkg-day, the exposure frequency is 365 days per year, the exposure duration is 70 years, and the averaging time is 25,550 days. We used data compiled by the International Commission on Radiation Protection (ICRP) ( 1 1 ) and EPA (12)to determine that within the California population, the lifetime-averaged arithmetic mean and standard deviation of fluid intake and body weight are, respectively, 1.5 k 0.7 L/day and 58 f 14 kg. The arithmetic mean and standard deviation in the ratio of fluid intake to body weight are estimated by calculating the variance in this ratio under the assumptions that variability in fluid intake and body weight can be represented by lognormal distributions and that fluid intake scales with body weight
Sci. Technol., Vol. 25,No. 10,1991
to the two-thirds power. We estimate the PDF of lifetime average fluid intake per unit body weight to be a lognormal distribution with an arithmetic mean and arithmetic standard deviation of 0.03 and 0.012 L/kg-day, respectively, as summarized in Table 1. Indoor inhalation from tap water. For this pathway the exposure route is inhalation, the source medium is groundwater, the contact medium is indoor air, the contact rate is breathing rate per unit body weight, the exposure frequency is 365 days per year, the exposure duration is 70 years, and the averaging time is 25,550 days. The contaminants available in indoor air are mobilized by showers, baths, toilets, dishwashers, washing machines, and cooking. Exposure to volatile chemicals in tap water by inhalation may be as much or more than exposure from fluid ingestion (131.
The contaminant concentration in air in the shower stall, bathroom, and house is approximated using the water-to-air transfer factor and this simple relationship proposed by Fisk et al. ( 1 4 ) :the concentration of an indoor air contaminant can be estimated as the ratio of the source in mg/h divided by the air exchange rate in m3/h. Based on this model for a house with four occupants, we estimate the ratios of concentrations bathroom air, in shower air, C,,,, e,,,,, and house air, C,,, (all in mg/m3) to the concentration in tap water C , (in mg/L) using
c~hower~cw = (wshowcr
'$dlvR3hoWsr 141
where W,,, is the water use rate in the shower during use, L / h @x is the transfer efficiency of PCE from water to air, the fraction of PCE released from shower water to air in equations 4 and 5, and the fraction of PCE released from all household water uses in Equation 6. Who,,, is the water use in L/h for all household activities and averaged over 24 h; and VRSh,. Br, VRbath,and VRh,,,, are the average air-exchange rates for air in the shower, bathroom, and total house, respectively, m3/h. The PEF for inhalation of contaminants in tap water is estimated as
PEF (water4nhalation) = [BR/BW] X {[[cshower/cw) X ET,) +
(7)
where [BRIBWI i s the ratio of breathing rate to body weight, m3/ kg-day, averaged over a lifetime; and ET,, ET,, and ET, are the exposure time in the shower, the bathroom, and the house, respectivelythe amount of time, in hours per day, that an individual spends in each compartment. We calculate the breathing rate
per unit body weight using data be represented by a triangular disfrom the ICRP and the procedure tribution with a range of 0.1-0.9 described above for fluid intake per and a most likely value of 0.3. Air unit body weight. The result is a exchange rates in the shower, bathlognormal distribution with a n room, and house are based on the arithmetic mean value and arith- assumption that the volumes of metic standard deviation of 0.4 and these compartments are 2, 10, and 0 . 5 m3/kg-day, respectively. The 600 m3, respectively, and that the mean and standard deviation of number of air changes per hour shower duration and water con- ranges from 2 to 10 in the shower, 1 sumption are based on data com- to 10 in the bathroom, and 0.5 to 2 piled by James and Knuiman (15) in the house (13). These distribuon domestic water use from a sam- tions are summarized in Table 2. ple of 3000 households in Perth, Dermal contact and uptake of Australia. We assume that total wa- PCE from water. For this pathway ter use can be represented by a log- the exposure route is dermal connormal distribution with an arith- tact, both the source medium and m e t i c m e a n of 4 2 L / h a n d a the contact medium are water, the geometric standard deviation of 1.4, contact rate is the amount of PCE and that the amount of time an indi- that passes through the skin surface vidual spends in the bathroom can (stroturn corneum) per unit body be represented by a lognormal dis- weight per hour, the exposure time tribution with an arithmetic mean is the number of hours per day of 0.33 h and a geometric standard spent in bathing or showering, the deviation of 1.8. We model the exposure frequency is 365 days per amount of time spent by individu- year, the exposure duration is 70 als in a house with a uniform distri- years, and the averaging time is bution ranging from 8 to 20 h. These 25,550 days. We use the dermal uptake model distributions are summarized in Taof Brown et al. (17), who assumed bles 1 and 2. On the basis of experiments by that dermal uptake of contaminants occurs mainly by passive diffusion McKone and Knezovich (16)and the shower-to-air cross-media mod- through the stratum corneum, that el of McKone (13),we estimate that resistance to diffusive flux through the transfer efficiency of PCE from layers other than the stroturn cornetap water to shower air can be repre- um is negligible, and that steadysented by a triangular distribution state diffusive flux is proportional with a range of 0.1-0.9 and a most to the concentration difference belikely value of 0.6, and that the tween water on the skin surface and transfer efficiency from water to internal body water. The dermalhousehold air for all water uses can uptake PEF is based on the addi-
TABLE 2
Minimum, maximum, and mean values for inputs represented by uniform and triangular distributions DlnribUtlo Pannwrtsr description
Exposure time in the house, ET,, h/day Air exchange rate in the shower, V L . , m'ih Air excha e rate in the bathmom, VR-. m% Air exchange rate in the house, VFL.,, m /h Skin permeability, PC, mih Fraction of skin e x r e d during showering and bat mg. fs. Fraction of inhaled or dermdly absorbed PCEa that is metabolized, Ym, Fraction of in ested PCE metabolized,.$,* Transfer efficiency from water to shower air, qx Transfer efficiency from water to household air, qx
ww
.. .
.. .
Uniform
Uniform Uniform Uniform Uniform Uniform
Uniform
Uniform Triangular Trianguiar
e Perchlomethylene.
Environ. Sci. Technol., Vol. 25, No. io, 1991
ien
tional assumptions that children s p e n d approximately the same amount of time bathing or showering per week as adults and that the amount of time adults spend in showering or bathing is the same as the showering time, ET,, reported above. We calculate the PEF for dermal uptake of PCE as
gen and McKone (20) modeled the data of Ikeda et al. (22) and Ohtsuki et al. (22) on urinary metabolite production in Japanese workers exposed to PCE. In that analysis, Bogen and McKone (20) demonstrated that the fraction of very low levels of inhaled PCE that is metabolized can best be described by the equation f",,
PEF (water+dermal uptake) = [SAIBW x fsa x PC x ET, x CF
=
lim f,,
ci,+o
=
(8)
where SAIBW is total skin surface area per unit bod weight averaged over a lifetime, m Ikg; fsa is the fraction of the total skin surface that is in contact with water during bathing or showering, m'; PC is the chemical-specific dermal permeability constant, m/h; ET, is the exposure time, hlday; and CF is a conversion constant, 1 0 -~~ / m ~ . The ICRP ( 2 1 ) and EPA (12) have reported correlations of skin surface area with body weight. We estimate the variability in surface area per unit body weight by combining these two correlations and using a lognormal distribution of lifetime average body weight with arithmetic mean and standard deviation equal to 58 and 14 kg, respectively. The resulting distribution of surface area to body weight is a lognormal distribution with an arithmetic mean of 0.027 and standard deviation of 0.0025 m2/kg. On the basis of the range of permeability constants reported for volatile compounds by Brown et al. (1 7), we represent the permeability parameter, PC, with a uniform distribution ranging from 0.004 to 0.01 m/h. The fraction of skin surface in contact with water during showering and bathing is represented by a uniform distribution ranging from 0.4 to 0.9. These distributions are summarized in Tables 1 and 2.
Y
Pharmacokinetics and dose PCE is metabolized in mammals to one or more reactive metabolites. Extensive evidence exists that a product of PCE metabolism rather than the parent compound itself is responsible for PCE's carcinogenicity in laboratory animals (28, 19).To address this, we estimate the carcinogenic potencies for PCE as a function of the metabolized dose of PCE. The relationship between applied and metabolized dose of PCE is derived from an analysis of available data on PCE (28). Using a physiologically based pharmacokinetic (PBPK) model, Bo-
where f *mr is the limiting fraction of inhaled PCE metabolized at extremely small doses; Q, is the alveolar ventilation rate, 354 Llh; Q, is the blood flow to the liver compartment, 93 Llh; Pb is the blood-air partition coefficient, 10 L blood/L air; Cin is the concentration in inhaled air, mg/L air; and K is the low-dose metabolic clearance rate, K = Vm,/K,. V, is the maximum metabolic rate, mgyh, and has a best estimate value of 4.1 mglh based on Ikeda et al. (22) and a best estimate value of 1 2 mg/h based on Ohtsuki et al. (22).K, is the Michaelis constant, mg/L, and has a best estimate value of 0.19 mg/L based on Ikeda et al. (22) and a best estimate value of 6.1 mg/L based on Ohtsuki et al. (22).Equation 9 also pertains to the metabolism of any VOC absorbed dermally, because a dermally acquired VOC entering the systemic circulation is subject to pulmonary excretion in the same manner as a respired dose (23). Bogen ( 2 3 ) developed an analogous equation to predict the fraction of very low doses of an orally applied VOC, such as PCE, that is metabolized (f fkmo
=
lim f,, R+O
=
where R is the rate of ingestive infusion, mglh. On the basis of the uncertainty in K, and V,,, values, we represent the uncertainty in the quantities f *mr and f * m o with uniform distributions. The range of f *mr is 0.038-0.46, and f *mo ranges from 0.053 to 0.63. These distributions are summarized in Table 2 . Potency
The term carcinogenic potency as used here refers to the quantitative expression of increased tumorigenic response per unit dose rate at very
1678 Environ. Sci. Technol., Vol. 25,No. IO, 1991
low dose levels. We predicted responses using the multistage doseresponse extrapolation model adopted for regulatory purposes by EPA (24). EPA's health risk assessment document (1 9) and addendum (25) for PCE list upper bound point estimates for PCE cancer potencybased on eight available animalbioassay data sets (26, 27)-ranging from 0.001 to 0.16 (mg/kg-day)-l. PCE also is identified in those reports as a probable human carcinogen, that is, direct evidence of carcinogenicity to humans is characterized as inconclusive. Many sources of uncertainty occur in the EPA potency estimates when they are applied to humans exposed to PCE at doses far below those received by the rodents. For the purpose of this analysis, we address only three uncertainty sources: the statistical estimation error of the multistage potency parameter [the linear coefficient, ql, in the dose representing increased risk per unit dose at low doses ( 2 8 ) ] , conditional on an assumption of validity for this dose-response extrapolation model; the interspecies extrapolation of equivalent effective tumorigenic dose; and the different potency estimates obtained from different bioassay data sets (e.g.,obtained from different studies or pertaining to different species, sexes, or observed types of tumor). To quantify statistical estimation error associated with the linear term q1 in the multistage model, we estimated this term for the eight rodentbioassay data sets considered by EPA (26, 27). We use the same asymptotic maximum likelihood estimation procedure as EPA does (29, 2 5 ) , but we use the estimated lifetime-weighted-average metabolized dose to the animals as the relevant dose for potency estimates instead of the applied dose ( 18). For each bioassay-data set, we generated a cumulative probability distribution function (CDF) for ql, representing presumed cancer potency of PCE to the bioassay animals used. These CDFs were then used to derive a single CDF for potency to humans as follows. Extrapolations of cancer potencies from animal bioassays to humans have been based on the assumption that potency scales with dose per unit surface area ( 1 9, 24, 25) or also with dose per unit body weight (28-30). Under the assumption that equally effective lifetime-weighted average dose rates are in milligrams of PCE metabolized per kilogram of body
weight per day, PCE’s potency would be estimated by the eight CDFs referred to above. According to the alternative surface area extrapolation method, eight corresponding CDFs were obtained by multiplying the values of the original ei ht CDFs by t h e factors 9.’, where w is the bioassay(70/w)’ animal body weight in each corresponding data set (4). Finally, for this analysis, we assumed that each of the bioassay data sets was equally indicative of PCE’s potential human carcinogenicity. Therefore, each of the 16 CDFs obtained was given a probability of 1/16 and they were combined using Monte Carlo sampling to generate a single composite CDF for the predicted potential human cancer potency of PCE. The resulting composite CDF is shown in Figure 2. The arithmetic mean potency from this composite distribution is 0.11 (mg/kg-day)-’, and the distribution has a geometric standard deviation of 4.8. It should be noted that this distribution includes a roughly 0.2 probability that the potency is zero. For this analysis, the approximate relation, Risk = Potency x Dose, was used for risk calculation. The multistage model applied to the bioassay data sets considered, however, has a quadratic term q2 that is necessarily nonzero conditional on q, = 0. Thus, our multiplicative model for uncertainty in predicted increased risk of PCE-related cancer is not strictly accurate when risk is evaluated at or below our estimated 20th-percen-
tile level (where the risk is taken as zero), because the actual multistage predicted risk is nonzero (because it must predict the observed bioassay tumor responses). However, at the relatively low exposure levels associated with ow estimated 20th percentile risk for the California population considered, t h e actual multistage predicted risk becomes extremely small, even when correctly estimated upper bound values for qz conditional on q1 = 0 are used. Therefore, the difference between the latter values and corresponding lower hound zero-risk values yielded by ow approximate linearized approach are de minimis. A new model for risk In this case study, the average individual risk within the population exposed to PCE results from a source term; the exposure factors, which convert the source into contact rates: the fraction of contaminant delivered to target tissues after contact: and the toxic potency associated with the delivered dose. According to current regulatory assumptions, risk is proportional to average population dose at low levels of exposure. According to this model, the lifetime increased probability of cancer following exposure to a carcinogen at a lifetime-weighted average dose rate, D, is assumed to be approximately equal to the product of q1x D,for a very small D, where q1 is a low-dose slope of the dose-response curve (the “potency”) derived fror !t of tumor in-
Composite cumulative probability density function for uncertainty in predicting carcinogenicity of PCE to humans at low dosesa 1”
I
I
I
c 0, 10-
. ..... . ....”
-1
. .....- . ..
104 7010-2 lo-’ Human cancer potency, {mg (rnetabolized)ikg/dayr‘
cidence data. Following this model, the information and models described in the preceding sections can be combined into an overall model of risk of the form
v
Risk =C, x *mo x PEF (water-water ingestion) + f *mr x PEF (water4nhalation) + f *,* x PEF (water-dermal uptake)l x q1 (11) Using the Monte Carlo spreadsheet program Crystal Ball (31),we calculate the composite uncertainty in this risk based on the uncertainty for each input parameter, as defined above and summarized in Table 1. Figure 3 shows the resulting cumulative distribution of risk based on 10,000 simulations. This distribution has an arithmetic mean of 1.0x 10- and a geometric standard deviation of 7.1. The 95% upper bound value of risk from this cumulative distribution is 3.5 x lo-“. In contrast, the risk one would calculate by using the arithmetic mean value of each input is 8.0 x IO-’, and the risk one would calculate using the 95% upper bound value of each input is 1.3 x This last value reveals that the actual upper bound on calculated risk can be substantially overestimated by simply using upper bound values for each component of the risk equation. This “creeping conservatism” is not always obvious to risk managers. From an analysis of the contributions to variance in risk as shown in Figure 3, we find that roughly 65% of the variance is attributable to variance in potency, 20% to variance in concentration, 10% to variance in the parameters of the exposure model, and 5% to variance in the parameters used to convert exposure to metabolized dose (Figure 4). This result reveals that for a compound such as PCE, for which lowdose human potency is based solely on extrapolation from high-dose animal experiments, uncertainties in calculated risk are dominated by the uncertainty in potency. In addition, much uncertainty comes from incomplete information on water concentrations. For PCE in this case study, increasing the complexity and precision of exposure and pharmacokinetic models might increase the credibility of the risk assessment, but much of the uncertainty in calculated risk will remain. One of the issues we have not addressed here is how to distinguish between the relative contribution of uncertainty versus interindividual
Envimn. Sci. Technol., Vol. 25. No. 10, 1991 1679
PCE in groundwaterB
....,,,,,l1,11111111lll11lllllllllllll
3 x lob
3.0
consider carefully the uncertainties of model assumptions and inputs so that effort is directed at those components having the largest contribution to overall variance in model predictions. With the type of information provided in Figures 3 and 4, it is possible to use the analytic framework of statistical decision analysis to determine when additional information would be beneficia1 and when it would not (I, 21. The results here reinforce the observation (33) that decision makers should use an uncertainty analysis to define strategies for reducing uncertainty in risk assessment.
Acknowledgments
Lifafimecancer r
This work was performed under the auspices of the U S Department of Energy
(DOE)at Lawrence Livermore National
Variance attributable tu each component of the risk calculation
variability (Le,, heterogeneity) to the characterization of predicted risk. Uncertainty or model specification error (e.g., statistical estimation error) can be modeled usine a random variable with an identifyed probability distribution. In contrast, interindividual variability refers to quantities that are distributed empirically within a defined population. Such factors as water ingestion, shower duration, and household air exchange rates fall into this latter category. Thus, a more comprehensive characterization of risk would present the re-
sults in Figure 3 as a surface with one axis corresponding to uncertainty in the predicted risk and the other corresponding to interindividual variabilitv in that risk (32). The case stud; in this paper suggests that risk managers should be aware of the uncertainty in risk estimates and include this awareness in their decisions and their communications of risk to the public. Furthermore, the results suggest the need to focus on reducing uncertainty before we develop more sophisticated models; or, at a minimum, suggest there is a need to
1680 Environ. Sci. Technoi.. Vol. 25, No. 10, 1991
Thomas E. McKone is a senior scientist with the Environmental Sciences Division at Lawrence Livermore National Labomtory. He has a Ph.D. in engineering and applied science fmm the university of California, Los Angeles. His research interests include the use of multimedia compartment models in exposure ond health risk assessments, chemical tmnsport and tmnsformation in the envimnment, and economic and health risk impacts of energy and industria1systems.
Kenneth T. Bogen is on envjmnmental health scientist ot Lawrence Livermore National Labomtory, where he works on new methodologiesfor health risk assessment. He received a Dr.P.H. in envimnmental health sciences at the University of California-Berkeley. His current research encompasses cell-kinetic multistage models applied to cancer risk assessment for chemicals and radiation, and in vivo dermal absorption of volatile organic compounds in dilute aqueous solution.
Laboratory under Contract W-7405-Eng48 with funding provided i n part by the Office of Research and Development of the U.S. Environmental Protection Agency under Inter-Agency Agreement Contract DW-8993-4285 a n d i n part by the California Department of Health Services (CDHS), Toxic Substances Control Program through Memorandum of Understanding Agreement 87-T0102. T h e views expressed are those of the authors a n d not necessarily those of the DOE, EPA, or CDHS.
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Determining SULFUR in Coal, Coke, Heating Oil, Diesel Fuel, Jet Fuel, Solvents and Other Organic Materials
The 1760 Sulfur Analyzer Using the oxygen bomb combustion procedure for sample preparation, the Parr 1760 Sulfur Analyzer offers a new, microprocessor controlled, instrumental method for rapid sulfur determinations in calorimeter bomb washings, providing sulfur as well as Btu information from a single sample. Sulfur values up to 6 percent can be determined in less than 5 minutes with accuracy and precision well within ASTM Specs. Full communication capabilities allow the Sulfur Analyzer to be interconnected with the Parr Smart Link Network producing complete fuel test reports for transmission to a laboratory or central computer. For details, write or phone for Bulletin 1200.
PARR INSTRUMENT COMPANY
211 Fifty-third Street Moline, IL 61265 Telex: 270226 9
Phone: 309-762-7716 800-872-7720 Fax: 309-762-9453 CIRCLE 2 ON READER SERVICE CARD
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