Benchmark Dose Profiles for Joint‐Action Quantal Data in Quantitative Risk Assessment

Abstract

Summary 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 pre-specified 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-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.

Benchmark dose profiles for joint‐action continuous data in quantitative risk assessment

“…Expanding upon earlier work for quantal joint-action data in the form of proportions (Deutsch and Piegorsch, 2012), we develop an approach for continuous data that estimates a joint BMP of points, past which dual exposure to a pair of hazardous agents may produce unacceptable risks. Corresponding lower confidence limits (BMPLs) are derived, based on the functional form of the BMP.…”

“…If finite upper bounds are known to exist on the individual doses x j ( j = 1, 2), a Monte Carlo-based method due to Liu (2010) provides the necessary simultaneous critical point to account for this. We described use of Liu's critical points for the quantal-response setting in Deutsch and Piegorsch (2012); see that article for more detail. Applied to nonquantal data as seen herein, however, we discovered via preliminary simulations that implementations of Liu's simulated critical points provided no improvement over the Cox and Ma BMPLs.…”

“…When applied to our dual-exposure setting, however, the concept requires modification. Adapting our previously developed framework for joint-action benchmark analysis with quantal data (Deutsch and Piegorsch, 2012) to the case of nonquantal data, we can define a natural extension for the joint additional risk:…”

“…Due to the profile's multivariable nature, however, finding lower confidence limits on exposure is tantamount to constructing a lower confidence band on the BMP: the BMP (lower) limit, BMPL, as we introduced previously (Deutsch and Piegorsch, 2012). In the next subsection, we propose a suitable methodology for building a BMPL with nonquantal data.…”

“…Zhu (2005) developed BMD estimators for quantal data with two factors modeled in tandem, but where one of these factors was taken specifically as time and viewed as a secondary, nuisance variate. We (Deutsch and Piegorsch, 2012) were able to expand on Zhu's approach to build benchmark inferences for any two hazardous stimuli, but like Zhu we only considered the quantal data setting. Herein, we extend our previous results and describe a strategy for conducting full benchmark analysis with dual-exposure, nonquantal data.…”