• Benchmark analysis;
  • Benchmark dose approach;
  • Benchmark profile;
  • Joint-action model;
  • Nonquantal data;
  • Risk analysis

Benchmark analysis is a widely used tool in biomedical and environmental risk assessment. Therein, estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a prespecified benchmark response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This paper demonstrates how the benchmark modeling paradigm can be expanded from the single-agent setting to joint-action, two-agent studies. Focus is on continuous response outcomes. Extending the single-exposure setting, representations of risk are based on a joint-action dose–response model involving both agents. Based on such a model, the concept of a benchmark profile—a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR—is defined for use in quantitative risk characterization and assessment.