Discrete Bayesian Dose-response Analysis under Dose Uncertainty

Establishing a relationship between disease and dose requires each individual in the population under investigation to be known by disease status and by the value of the dose received. Frequently, the dose values are reconstructed using a dose assessment model containing imprecisely known parameter values, model formulations, and input data (epistemic uncertainties). As a consequence, the state of knowledge of the assessed dose values needs to be expressed by a joint subjective probability distribution thereby accounting for state of knowledge dependence due to uncertainties shared by the assessed dose values of several individuals. Dose-response analysis must apply this joint state of knowledge in obtaining a subjective probability distribution for the parameters of the dose-response model. This is achieved by drawing a random sample of dose vectors according to the joint distribution, by applying Bayes' theorem for each vector, and by averaging the posterior parameter distributions (Bayesian model averaging). If the dose response is quantified by a binary variable, a logistic regression model is embedded in the likelihood function. This paper presents a new, computationally efficient Bayesian model averaging method that operates over the discretized parameter space and thereby does away with the computational complexities of Bayesian methods. It corrects for the attenuation effect that is due to the application of dose vectors other than the true vector. Results obtained for a sample of dose vectors are compared to those obtained with the standard discrete Bayesian method using the true dose vector.