Comparative bias associated with various estimates of dose to maximally exposed individuals

Protection of the environment from anthropogenic radiation is a resurging international interest. The paradigm currently in use argues that the population is adequately protected if dose rates to the maximally exposed individuals are below a certain limit. Based on data sampled from natural populations, resource managers need to be able to test the hypothesis that dose rates to the maximally exposed individuals are acceptable. Recognizing the difficulty of sampling the maximally exposed individual within a contaminated environment, risk assessors have used various alternative approaches that vary from changing the paradigm and applying recommended dose rate limits to representatively, rather than maximally, exposed individuals, to using the 95th percentile of the sample mean as an estimator of the population maximum. To determine the effectiveness of numerous proposed alternatives, we used computer simulation techniques to generate a "population" of doses with known distributional qualities and then mathematically "sampled" the population to compare the ability of the various statistics at estimating the known population maximum. The simulation procedure was repeated 1000 times using Monte Carlo techniques, each time producing a measure of the distance between the estimate and the true value. We were thus able to quantify the bias associated with several approaches used to determine compliance with dose rate criteria established by the Department of Energy for protecting biota. The 95th quantile of the sample mean, and the sample maximum underestimated the population maximum by as much as 72 and 44%, respectively. The maximum likelihood estimate (MLE) of the 99.99th percentile was found to be the best predictor of the population maximum, even for small sample sizes of 20 and for both normally and lognormally distributed populations. However, bias associated with the MLE increased significantly if the population's distribution was incorrectly identified. We suggest shifting the regulatory criterion appropriately to argue that if the top 1% (as opposed to the maximum) of the population has a dose rate less than or equal to the regulatory limit then the population is adequately protected, and then using the MLE of the 99th percentile as the least biased sample statistic. Results of this study are also relevant when estimating dose to critical sub-groups of humans whose lifestyles are such that their doses are among the maximum for the population.