U.S. Environmental Protection Agency


Date of this Version



Published in Uncertainty Modeling in Dose Response: Bench Testing Environmental Toxicity (2009) 197-205.


In animal bioassays, tumors are often observed at multiple sites. Unit risk estimates calculated on the basis of tumor incidence at only one of these sites may underestimate the carcinogenic potential of a chemical (NRC 1994 ). Furthermore the National Research Council (NRC, 1994 ) and Bogen (1990) concluded that an approach based on counts of animals with one or more tumors (counts of “ tumor - bearing animals ” ) would tend to underestimate overall risk when tumors occur independently across sites. On independence of tumors, NRC (1994) stated: “ … a general assumption of statistical independence of tumor - type occurrences within animals is not likely to introduce substantial error in assessing carcinogenic potency. ” Also application of a single dose – response model to pooled tumor incidences (i.e., counts of tumor - bearing animals) does not reflect possible differences in dose – response relationships across sites. Therefore the NRC (1994) and Bogen (1990) concluded that an approach that is based on well - established principles of probability and statistics should be used to calculate composite risk for multiple tumors. Bogen (1990) also recommended a re - sampling approach, as it provides a distribution of the combined potency. Both NRC (1994) and Guidelines for Carcinogen Risk Assessment (US EPA 2005 ) recommend that a statistically appropriate upper bound on composite risk be estimated in order to gain some understanding of the uncertainty in the composite risk across multiple tumor sites.

This chapter presents a Markov chain Monte Carlo (MCMC) computational approach to calculating the dose associated with a specified composite risk and a lower confidence bound on this dose, after the tumor sites of interest (those believed to be biologically relevant) have been identified and suitable dose – response models (all employing the same dose metric) have been selected for each tumor site. These methods can also be used to calculate a composite risk for a specified dose and the associated upper bound on this risk. For uncertainty characterization, MCMC methods have the advantage of providing information about the full distribution of risk and/or benchmark dose. This distribution, in addition to its utility in generating a confidence bound, provides expected values of risks that are useful for economic analyses.

The methods presented here are specific to the multistage model with nonnegative coefficients fitted to tumor incidence counts (i.e., summary data rather than data on individual animals, as in the nectorine example; if data on individual animals are available, other approaches are possible), and they assume that tumors in an animal occur independently across sites. The nectorine example is used to illustrate proposed methodology and compare it with the current approach.