Benchmark analysis is a general risk estimation strategy for identifying the benchmark dose (BMD) past which the risk of exhibiting an adverse environmental response exceeds a fixed, target value of benchmark response. Estimation of BMD and of its lower confidence limit (BMDL) is well understood for the case of an adverse response to a single stimulus. In many environmental settings, however, one or more additional, secondary, qualitative factor(s) may collude to affect the adverse outcome, such that the risk changes with differential levels of the secondary factor. This article extends the single-dose BMD paradigm to a mixed-factor setting with a secondary qualitative factor possessing two levels. With focus on quantal-response data and using a generalized linear model with a complementary-log link function, we derive expressions for BMD and BMDL. We study the operating characteristics of six different multiplicity-adjusted approaches to calculate the BMDL, using Monte Carlo evaluations. We illustrate the calculations via an example dataset from environmental carcinogenicity testing.

中文翻译：

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环境风险评估中混合因子量化数据的基准剂量风险分析

基准分析是一种通用风险估计策略，用于确定基准剂量 (BMD)，超过该基准剂量，表现出不利环境响应的风险将超过基准响应的固定目标值。对于对单一刺激的不良反应的情况，BMD 及其置信下限 (BMDL) 的估计是很好理解的。然而，在许多环境设置中，一个或多个附加的次要定性因素可能共同影响不良结果，使得风险随着次要因素的不同水平而变化。本文将单剂量 BMD 范式扩展到具有两个水平的次要定性因素的混合因素设置。通过关注量子响应数据并使用具有互补对数链接函数的广义线性模型，我们推导了 BMD 和 BMDL 的表达式。我们使用蒙特卡洛评估研究了六种不同的多重调整方法的操作特性来计算 BMDL。我们通过环境致癌性测试的示例数据集来说明计算结果。