A Bayesian Regression Methodology for Correlating Noisy Hazard and Structural Alert Parameters of Nanomaterials

Exposure to ENMs may have associated health risks, but accurate measurement of these risks is difficult due to overwhelming methodological limitations and epistemic uncertainties. This is especially the case for ENM physiochemical and toxicity measurements. A common example of controlling such risks in workplace environments where these materials are produced and used is control banding. It offers a useful framework to categorize health risk but is presently limited by existing quantitative data that is susceptible to ambiguity. With an aim to addressing these issues, this chapter develops a Bayesian regression or QSAR (Quantitative Structure Activity Relationship) model that relates hazard levels (dependent) to physical and chemical attributes (independent) but crucially takes full account of uncertainty in both the dependent and independent data sets. The developed model is applied to recover the marginal probability density distribution of a varied set of physical attribute measurements of cerium oxide nanoparticles that were supplied from a common batch. Each of the measurements in the set was carried out by one of several disparate institutions. It is in the author’s opinion that this model is successful because in principle it is able to exploit and objectively incorporate seemingly conflicting data points to produce meaningful regression fits. This is something that is not possible using conventional regression techniques that typically rely on subjective judgments to resolve such conflicts prior to analysis. The danger of the conventional approach is that potentially useful information, usually interpreted as ‘statistical outliers’, may be disregarded as a result of experimenter bias.