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.