Continuous model averaging for benchmark dose analysis: Averaging over distributional forms

When estimating a benchmark dose (BMD) from chemical toxicity experiments, model averaging is recommended by the National Institute for Occupational Safety and Health, World Health Organization and European Food Safety Authority. Though numerous studies exist for model average BMD estimation using dichotomous responses, fewer studies investigate it for BMD estimation using continuous response. In this setting, model averaging a BMD poses additional problems as the assumed distribution is essential to many BMD definitions, and distributional uncertainty is underestimated when one error distribution is chosen a priori. As model averaging combines full models, there is no reason one cannot include multiple error distributions. Consequently, we define a continuous model averaging approach over distributional models and show that it is superior to single distribution model averaging. To show the superiority of the approach, we apply the method to simulated and experimental response data.