Quantifying uncertainty in dose–response screenings of nanoparticles: a Bayesian data analysis

Fitting theoretical models to experimental data for dose–response screenings of nanoparticles yields values of several hazard metrics that can support risk management. In this paper, we describe a Bayesian approach to the analysis of dose–response data for nanoparticles that takes into account multiple sources of uncertainty. Specifically, we develop a Bayesian model for the analysis of data for the cytotoxicity of ZnO nanoparticles that follow the log-logistic equation. This model reproduces the unequal variance across doses observed in the experimental data, incorporates information about the sensitivity of the cytotoxicity assay used (i.e. resazurin), and complements experimental data with historical information about the system. The model determines probability distributions for multiple values of toxicity potency (EC50), and exponential decay (the slope s); these distributions provide a direct measure of uncertainty in terms of probabilistic credibility intervals. By substituting these distributions in the log-logistic equation, we determine upper and lower limits of the benchmark dose (BMD), corresponding to upper and lower limits of credibility intervals with 95% probability given the experimental data, multiple sources of uncertainty, and historical information. In view of a reduction of costs and time of dose–response screenings, we use the Bayesian model for the cytotoxicity of ZnO nanoparticles to identify the experimental design that uses the minimum number of data while reducing uncertainty in the estimation of both fitting parameters and BMD.