Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Maternal ingestion of radon-222 in drinking water and the absorbed radiation dose to the embryo

Maternal ingestion of high concentrations of radon-222 (Rn-222) in drinking during pregnancy may pose a significant radiation hazard to the developing embryo. The effects of ionizing radiation to the embryo and fetus have been the subject of research, analyses, and the development of a number of radiation dosimetric models for a variety of radionuclides. Currently, essentially all of the biokinetic and dosimetric models that have been developed by national and international radiation protection agencies and organizations recommend calculating the dose to the mother's uterus as a surrogate for estimating the dose to the embryo. Heretofore, the traditional radiation dosimetry models have neither considered the embryo a distinct and rapidly developing entity, the fact that it is implanted in the endometrial layer of the uterus, nor the physiological interchanges that take place between maternal and embryonic cells following the implantation of the blastocyst in the endometrium. The purpose of this research was to propose a new approach and mathematical model for calculating the absorbed radiation dose to the embryo by utilizing a semiclassical treatment of alpha particle decay and subsequent scattering of energy deposition in uterine and embryonic tissue. The new approach and model were compared and contrasted with the currently recommended biokinetic and dosimetric models for estimating the radiation dose to the embryo. The results obtained in this research demonstrate that the estimated absorbed dose for an embryo implanted in the endometrial layer of the uterus during the fifth week of embryonic development is greater than the estimated absorbed dose for an embryo implanted in the uterine muscle on the last day of the eighth week of gestation. This research provides compelling evidence that the recommended methodologies and dosimetric models of the Nuclear Regulatory Commission and International Commission on Radiological Protection employed for calculating the radiation dose to the embryo from maternal intakes of radionuclides, including maternal ingestion of Rn-222 in drinking water would result in an underestimation of dose. ^