Dose-response Analysis in the Presence of Shared and Unshared Uncertainties of the Dose Values

The dose values used in dose-response analyses are often the result of a computer model. Epistemic uncertainties of the model application make it necessary to perform an uncertainty analysis. Such uncertainties are model parameters, model formulations, and input data subject to either classical or Berkson additive or multiplicative measurement error. Epistemic uncertainties are often shared among the computed dose values of all individuals in a cohort or among groups thereof. The effect of these uncertainties on the estimate of the dose-response parameter in least-squares linear regression is difficult to judge. Additive classical error is known to bias the estimate towards lower values (attenuation). The method suggested in this paper is applicable in situations where any combination of uncertainties mentioned above is involved. All it requires is a random sample of dose vectors taken from their joint subjective probability distribution. Such a sample is the output of a Monte Carlo uncertainty analysis of the model application. The covariance matrix of the vectors is used in the computation of correction factors that are possibly true, given the dose vector used in the estimation of the dose-response parameter. The efficiency of the method is demonstrated with five cases. They differ by the combination of uncertainties involved in the uncertainty analysis of a small illustrative dose reconstruction model.