PRINCIPLES OF TOXICOLOGY

18.6 PROBABILISTIC VERSUS DETERMINISTIC RISK ASSESSMENTS 463
A second problem confronting the risk assessor is management of uncertainty in the risk assessment
process. As described elsewhere in this chapter, there are numerous sources of uncertainty in risk
calculations, including uncertainty in the selection of models and assumptions, and in measurements
of risk related parameters. As part of a deterministic calculation of risk, a choice must be made for
each of these so that a risk estimate can be made. For regulatory purposes, conservative choices are
usually made; models and assumptions that tend to provide higher estimates of risk are selected from
among the range of plausible alternatives. The reason for conservative choices by regulatory agencies
in the face of uncertainty is well understood, but the extent of conservatism imparted by the various
choices is usually unclear. As with the issue of variability, this makes it difficult or impossible for the
risk assessor to effectively convey the inherent conservatism associated with the risk estimate.
Probabilistic risk assessment is an alternative approach that can address the shortcomings of
deterministic calculations in terms of variability and uncertainty. In probabilistic risk assessment, input
variables are entered as probability density functions (PDFs) instead of single values. For example,
instead of using a single body weight of 70 kg in the risk calculation, a distribution of body weights
would be entered that reflects the variability in body weight of the exposed population. PDFs might
also be entered for other variables such as inhalation rate, skin surface area, and frequency of contact
with contaminated media—anything that would be expected to vary from one individual to another.
These PDFs are then combined in such a way as to yield a risk distribution, representing the range and
frequency of risks anticipated to exist in the exposed population. Although there are several ways to
combine PDFs, one of the most commonly used techniques is Monte Carlo simulation. With Monte
Carlo simulation, a computer program in essence creates a simulated population designed to resemble
the exposed population in every key respect. For each risk calculation, it takes a value from each input
PDF and calculates a numerical risk. This process is repeated, usually thousands of times, and the
resulting range of risk values is tallied in the form of a distribution. This distribution represents the
risk distribution for the population. From this distribution, the variability in risk among individuals
can be visualized and the risk level at various percentiles of the population determined (see Figure
18.7).
Probabilistic risk assessment can also provide quantitative representation of the uncertainties in the
risk calculation. For each input or model, some estimate of the uncertainty is entered. For example,
the concentration of chemical X for which a risk estimate is desired is assumed to be 100, but could
be as low as 50 or as high as 200. In this case, the chemical concentration could be entered as a
distribution of values, with 100 as the most likely estimate, but with a range extending from 50 to 200.
As with variability, the uncertainty associated with various inputs can be combined to produce a PDF
showing boundaries of uncertainty associated with a risk estimate. An additional benefit of this
approach is that a sensitivity analysis can be used to rank the various sources of uncertainty in terms
of their relative contribution to overall uncertainty. If the uncertainty is unacceptably large, this can be
used to identify the best areas for further analysis or research to reduce uncertainty.
It is possible for a probabilistic risk assessment to address both variability and uncertainty
simultaneously. This requires the development of PDFs for both uncertainty and variability. For
example, a PDF might be used to portray variability in body weight in the exposed population, and a
separate PDF would be used to deal with any uncertainty that the body weight distribution selected
accurately reflects the actual body weight distribution of the population in question. (Note: This is not
an unreasonable uncertainty, since risk assessors almost never have the time and resources to actually
weigh everyone in an exposed population, and therefore must rely on published body weight data for
the general population to create their body weight PDF.) The variability and uncertainty PDFs are then
combined separately to generate a risk distribution with confidence boundaries provided by the
uncertainty distributions. This is called a two-dimensional probabilistic risk assessment.
The principal advantage of a probabilistic risk assessment is that it provides much greater
information on variability and uncertainty associated with risk estimates. The manner in which risk is
distributed within the exposed population is transparent, and the magnitude of uncertainty associated
with the risk estimate is conveyed in quantitative terms. There are, however, a number of disadvantages
to probabilistic risk assessment, including the facts that (1) it is technically demanding, requiring much