Semi-parametric Benchmark Dose Analysis with Monotone Additive Models

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.