Benchmark dose analysis aims to estimate the level of exposure to a toxin that results in a clinically-significant adverse outcome and quantifies uncertainty using the lower limit of a confidence interval for this level. We develop a novel framework for benchmark dose analysis based on monotone additive dose-response models. We first introduce a flexible approach for fitting monotone additive models via penalized B-splines and Laplace-approximate marginal likelihood. A reflective Newton method is then developed that employs de Boor's algorithm for computing splines and their derivatives for efficient estimation of the benchmark dose. Finally, we develop and assess three approaches for calculating benchmark dose lower limits: a naive one based on asymptotic normality of the estimator, one based on an approximate pivot, and one using a Bayesian parametric bootstrap. The latter approaches improve upon the naive method in terms of accuracy and are guaranteed to return a positive lower limit; the approach based on an approximate pivot is typically an order of magnitude faster than the bootstrap, although they are both practically feasible to compute. We apply the new methods to make inferences about the level of prenatal alcohol exposure associated with clinically significant cognitive defects in children using data from an NIH-funded longitudinal study. Software to reproduce the results in this paper is available at https://github.com/awstringer1/bmd-paper-code.

翻译：摘要：基准剂量分析旨在估计导致临床显著不良结果的毒素暴露水平，并通过该水平的置信区间下限量化不确定性。我们基于单调加性剂量-响应模型，提出了一种全新的基准剂量分析框架。首先，引入一种通过惩罚B样条和拉普拉斯近似边际似然来拟合单调加性模型的灵活方法。随后，开发了一种反射牛顿方法，利用德布尔算法计算样条及其导数，以实现基准剂量的高效估计。最后，我们提出并评估了三种计算基准剂量下限的方法：一种基于估计量渐近正态性的朴素方法，一种基于近似枢轴量的方法，以及一种使用贝叶斯参数自助法的方法。后两种方法在准确性上优于朴素方法，并能保证返回正的下限；尽管两种方法在计算上均可行，但基于近似枢轴量的方法通常比自助法快一个数量级。我们利用美国国立卫生研究院资助的纵向研究数据，将新方法应用于推断与儿童临床显著认知缺陷相关的产前酒精暴露水平。本文结果的可复现软件可在https://github.com/awstringer1/bmd-paper-code获取。