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.

The two-dimensional Monte Carlo: a new methodologic paradigm for dose reconstruction for epidemiological studies.

Retrospective dose estimation, particularly dose reconstruction that supports epidemiological investigations of health risk, relies on various strategies that include models of physical processes and exposure conditions with detail ranging from simple to complex. Quantification of dose uncertainty is an essential component of assessments for health risk studies since, as is well understood, it is impossible to retrospectively determine the true dose for each person. To address uncertainty in dose estimation, numerical simulation tools have become commonplace and there is now an increased understanding about the needs and what is required for models used to estimate cohort doses (in the absence of direct measurement) to evaluate dose response. It now appears that for dose-response algorithms to derive the best, unbiased estimate of health risk, we need to understand the type, magnitude and interrelationships of the uncertainties of model assumptions, parameters and input data used in the associated dose estimation models. Heretofore, uncertainty analysis of dose estimates did not always properly distinguish between categories of errors, e.g., uncertainty that is specific to each subject (i.e., unshared error), and uncertainty of doses from a lack of understanding and knowledge about parameter values that are shared to varying degrees by numbers of subsets of the cohort. While mathematical propagation of errors by Monte Carlo simulation methods has been used for years to estimate the uncertainty of an individual subject's dose, it was almost always conducted without consideration of dependencies between subjects. In retrospect, these types of simple analyses are not suitable for studies with complex dose models, particularly when important input data are missing or otherwise not available. The dose estimation strategy presented here is a simulation method that corrects the previous deficiencies of analytical or simple Monte Carlo error propagation methods and is termed, due to its capability to maintain separation between shared and unshared errors, the two-dimensional Monte Carlo (2DMC) procedure. Simply put, the 2DMC method simulates alternative, possibly true, sets (or vectors) of doses for an entire cohort rather than a single set that emerges when each individual's dose is estimated independently from other subjects. Moreover, estimated doses within each simulated vector maintain proper inter-relationships such that the estimated doses for members of a cohort subgroup that share common lifestyle attributes and sources of uncertainty are properly correlated. The 2DMC procedure simulates inter-individual variability of possibly true doses within each dose vector and captures the influence of uncertainty in the values of dosimetric parameters across multiple realizations of possibly true vectors of cohort doses. The primary characteristic of the 2DMC approach, as well as its strength, are defined by the proper separation between uncertainties shared by members of the entire cohort or members of defined cohort subsets, and uncertainties that are individual-specific and therefore unshared.

How to account for uncertainty due to measurement errors in an uncertainty analysis using Monte Carlo simulation.

Two kinds of error are considered, namely Berkson and classical measurement error. The true values of the measurands will never be known. Possibly true sets of values are generated by the Monte Carlo simulation of the uncertainty analysis. This is straightforward for Berkson errors but requires the modeling of statistical dependence between measured values and errors in the classical case. A method is presented that enables this dependence modeling as part of the uncertainty analysis. Practical examples demonstrate the applicability of the method. Two "quick fixes" are also discussed together with their shortcomings. The uncertainty analysis of the application of a small computer model from the area of dose reconstruction illustrates, by example, the effect both kinds of error can have on model results like individual dose values and mean value and standard deviation of the population dose distribution.

Hypothesis testing, statistical power, and confidence limits in the presence of epistemic uncertainty.

Hypothesis testing, statistical power, and confidence limits are concepts from classical statistics that require data from observations. In some important recent applications some of the data are not observational but are reconstructed by computer models. There is generally epistemic uncertainty in model formulations, as well as in parameter and input values. The resulting epistemic uncertainty of the reconstructed data is determined by an uncertainty analysis and is expressed by subjective probability distributions. Sometimes only the mean or median values of the distributions are used in the concepts mentioned above, which hides the uncertainty of the data thereby rendering misleading results. Misleading results are also obtained if the epistemic uncertainty of the data is combined incorrectly with the stochastic variability of the outcome of the actual random complex concerned. This paper argues that an uncertainty analysis of the application of classical statistical concepts is essentially the correct way of dealing with the epistemic uncertainty of the data. A practical example serves as an illustration.