  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 surface smoothing. The resulting posterior distribution is
sampled by Markov Chain Monte Carlo. 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.
