Benchmark dose profiles for joint-action quantal data in quantitative risk assessment

Benchmark analysis is a widely used tool in public health risk analysis. 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 article demonstrates how the benchmark modeling paradigm can be expanded from the single-dose setting to joint-action, two-agent studies. Focus is on response outcomes expressed as proportions. 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 (BMP) - 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. The resulting, joint, low-dose guidelines can improve public health planning and risk regulation when dealing with low-level exposures to combinations of hazardous agents.