Optimal Additive Dose Distributions for Minimizing Dose Estimate Error in Retrospective and Emergency Dosimetry with Heteroscedastic Effects

In retrospective and emergency dosimetry with additive dose methods, the extrapolated dose estimate uncertainty has been shown to relate to the selection of the applied dose distribution, but under the ideal assumptions of constant variance or homoscedastic effects. This work looks at the case when the assumptions of constant variance are violated and instead the case of when heteroscedastic effects are present. With these heteroscedastic effects, this work investigates any consequential results on the optimal dose distributions previously established. Using Monte Carlo simulations and linear least-squares regression, the relative uncertainty of the extrapolated dose estimate was calculated and compared under homoscedastic and heteroscedastic conditions. From this research, mild heteroscedastic effects were found to not significantly impact the previously established optimal dose distributions, while more extreme heteroscedastic effects, having variance increasing with dose responses, showed a difference. In the more extreme heteroscedastic cases, optimal dose distributions favored taking more dose points at the low (0 added initial dose) and high (maximum additive dose) extremes of the dose distribution. For example, the single high point (SHP) distribution showed the least dose estimate error in the cases of the extreme heteroscedastic effects for small reconstructed doses in comparison to other dose distributions. As the name implies, the SHP distribution involves taking one single “high” dose point at the maximum applied laboratory dose and the remaining dose points taken at the lowest applied dose point (i.e, zero). Further extreme dose distributions generally remained optimal in the extreme heteroscedastic case such as the two high point (TwoHP) and three high point (ThreeHP) distributions. These extreme dose distributions showed less dose estimate error than the more common and labor-intensive constant, evenly spaced additive dose distribution that is more frequently employed. For the applicability of these more extreme distributions (SHP, TwoHP, ThreeHP), an intersection of their optimal suitability was found in both heteroscedastic and homoscedastic cases, as long as the initial dose estimate was at most 20% of the maximum applied dose or less. Therefore, adapting dose distributions to assumed variance structures can help reduce the uncertainty of the initial dose estimate for higher-quality radiation dosimetry extrapolations in electron paramagnetic resonance, optically stimulated luminescence, and thermoluminescence applications.