We introduce a Bayesian multiple regression tree model to characterize relationships between physico-chemical properties of nanoparticles and their in-vitro toxicity over multiple doses and times of exposure. Unlike conventional models that rely on data summaries, our model solves the low sample size issue and avoids arbitrary loss of information by combining all measurements from a general exposure experiment across doses, times of exposure, and replicates. The proposed technique integrates Bayesian trees for modeling threshold effects and interactions, and penalized B-splines for dose and time-response surfaces smoothing. The resulting posterior distribution is sampled via a Markov Chain Monte Carlo algorithm. This method allows for inference on a number of quantities of potential interest to substantive nanotoxicology, such as the importance of physico-chemical properties and their marginal effect on toxicity. We illustrate the application of our method to the analysis of a library of 24 nano metal oxides.


Applied Statistics | Biostatistics | Multivariate Analysis | Statistical Methodology | Statistical Models