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The purpose of this discussion is to

1) briefly discuss how Monte Carlo procedures work and could be applied in exposure assessments and

2) summarize recent efforts by three investigators to apply Monte Carlo procedures to assessments involving dioxin-like compounds.

Basically, Monte Carlo is a generic statistical method which generates a distribution for an analytical output of a mathematical model using the distributions of the input variables. Computer simulations are used to repeatedly generate outputs based on parameter inputs, where values for parameters are selected from their distributions. The outputs are compiled and expressed as a frequency distribution. In the context of exposure assessment, a Monte Carlo application could involve developing distributions for each of the parameters in the exposure equation and generating a distribution showing how the exposure levels vary in the exposed population. The final distribution can be interpreted as the probabilities of one individual (randomly selected from the exposed population) experiencing various exposures. Since exposure levels are not only a function of the exposure parameters but also of the concentration in exposure media, another application of the Monte Carlo method would be to estimate the distribution of exposure media concentrations using mathematical models for fate and transport.

Monte Carlo techniques can be a powerful tool for expressing variability and evaluating scenarios in exposure assessments. However, its use requires detailed input data which is frequently unavailable. Although the procedure may make an analysis look more elegant, it may actually yield misleading results if based on poor data. Accordingly, exposure assessors should be very cautious when trying to apply Monte Carlo techniques or interpreting the results.

table Table 7-20. Uncertainties associated with beef and milk ingestion exposure algorithms.
Generally, Monte Carlo procedures should be applied only when credible distribution data are available for most of the key variables.

Distribution data refers to empirical information on the statistical variation of the variable that is relevant to the site assessed.

Usually this data should be obtained from surveys conducted at the site of interest. However, data on human behavioral characteristics could be obtained from survey
information based on populations distant from the site, if comparability can be established.
expand table Table V3 7-20

Paustenbach et. al. (1992a) used Monte Carlo procedures to develop soil cleanup levels for 2,3,7,8-TCDD at residential and industrial sites. The following exposure pathways were included: dermal contact, soil ingestion, dust inhalation and fish ingestion. For each parameter a range of values was identified (on the basis of reported values in the literature) and a uniform distribution assumed. These assumptions are summarized in Table 7-21. For the residential scenario, the soil level corresponding to the 50th percentile (defined as 50% of the population being exposed below a risk of 10-5) was 17 ppb and the 95th percentile was 7 ppb. For the industrial scenario (outdoors), the soil level corresponding to the 50th percentile was 160 ppb and the 95th percentile was 50 ppb.

Anderson et. al. (1992) used Monte Carlo procedures to describe the distribution of exposures to 2,3,7,8-TCDD occurring in various U.S. population segments as a result of ingesting fish caught near pulp and paper mills. The populations considered were all U.S. residents, all sportfishermen, U.S. residents living near (within 50 km) mills, and sportfishermen living near mills. The distributions for the various parameters were derived by either fitting idealized curves to empirical data or using personal judgement. These distributions are summarized in Table 7-22. The distribution of 2,3,7,8-TCDD concentrations in fish was derived from data collected in EPA's National Study of Chemical as exposure parameters. Distributions were developed for input factors and Monte Carlo Residues in Fish (EPA, 1992b). The following 50th and 95th percentile risks were estimated (using EPA cancer potency values):

    • all US residents - 1 x 10-9 & 3 x 10-7
    • near mill residents - 4 x 10-8 & 2 x 10-6
    • all sportfishermen - 2 x 10-8 & 3 x 10-6
    • near mill sportfishermen - 6 x 10-7 & 2 x 10-5
table Table 7-21. Distributions for a Monte Carlo exercise which developed soil cleanup levels at residential and industrial sites. table Table 7-22. Summary of Monte Carlo distributions used in a fish consumption assessment.
expand table Table V3 7-21 expand table Table V3 7-22

McKone and Ryan (1989) developed an exposure assessment procedure based on simple steady state transfer factors called PEFs or pathway exposure factors. These factors were applied to two paths: air/plant/food and soil/plant/food. This is an example of Monte Carlo techniques being applied to estimate exposure media concentrations as well techniques were used to estimate the distribution of exposures. The procedure was demonstrated using 2,3,7,8-TCDD and four pathways: ingestion of fruit/vegetables, grains, meat and dairy products. The distributions used for the various input parameters are summarized in Table 7-23.

The three articles discussed above differ widely in how they have applied Monte Carlo methods, particularly in the selection of input parameter distributions. In some cases, it appears that uniform distributions were assumed due to the lack of data needed to support more complex distributions. The central values in these ranges probably occur more often than those near the ends, so the uniform distribution assumption probably underestimates the occurrence of central values and overestimates the occurrence of values near the ends of the distribution. Clearly more data are needed to better support input parameter distributions.

These three articles are just a small set of the growing body of literature on the topic of applying Monte Carlo methods to exposure and risk assessments. For example, the application of Monte Carlo methods to problems involving ...

table Table 7-23. Summary of Monte Carlo distributions used in food chain study.
... contaminated groundwater and related exposure pathways such as ingestion, indoor air inhalation and dermal contact with water has recently been examined (McKone and Bogen, 1991). Although this work does not deal specifically with dioxin, it may be informative to readers generally interested in Monte Carlo procedures.

Similarly, Paustenbach has published additional articles dealing with the application of Monte Carlo methods to exposure problems involving other chemicals (Pasutenbach et al. 1991; Paustenbach, et al., 1992a). Burmaster has also published numerous articles on this topic which may be of general interest to readers (ie. Burmaster and Stackelberg, 1991).
expand table Table V3 7-23
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