Statistical models for genetic susceptibility in toxicological and epidemiological investigations

Models are presented for use in assessing genetic susceptibility to cancer (or other diseases) with animal or human data. Observations are assumed to be in the form of proportions, hence a binomial sampling distribution is considered. Generalized linear models are employed to model the response as a function of the genetic component; these include logistic and complementary log forms. Susceptibility is measured via odds ratios of response, relative to a background genetic group. Significance tests and confidence intervals for these odds ratios are based on maximum likelihood estimates of the regression parameters. Additional consideration is given to the problem of gene-environment interactions and to testing whether certain genetic identifiers/categories may be collapsed into a smaller set of categories. The collapsibility hypothesis provides an example of a mechanistic context wherein nonhierarchical models for the linear predictor can sometimes make sense.