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. ^

DEVELOPMENT AND IMPLEMENTATION OF A REMOTE AUDIT TOOL FOR HIGH DOSE RATE (HDR) 192IR BRACHYTHERAPY USING OPTICALLY STIMULATED LUMINESCENCE DOSIMETRY

This work aimed to create a mailable and OSLD-based phantom with accuracy suitable for RPC audits of HDR brachytherapy sources at institutions participating in NCI-funded cooperative clinical trials. An 8 × 8 × 10 cm3 prototype with two slots capable of holding nanoDot Al2O3:C OSL dosimeters (Landauer, Glenwood, IL) was designed and built. The phantom has a single channel capable of accepting all 192Ir HDR brachytherapy sources in current clinical use in the United States. Irradiations were performed with an 192Ir HDR source to determine correction factors for linearity with dose, dose rate, and the combined effect of irradiation energy and phantom construction. The uncertainties introduced by source positioning in the phantom and timer resolution limitations were also investigated. It was found that the linearity correction factor was where dose is in cGy, which differed from that determined by the RPC for the same batch of dosimeters under 60Co irradiation. There was no significant dose rate effect. Separate energy+block correction factors were determined for both models of 192Ir sources currently in clinical use and these vendor-specific correction factors differed by almost 2.6%. For Nucletron sources, this correction factor was 1.026±0.004 (99% Confidence Interval) and for Varian sources it was 1.000±0.007 (99% CI). Reasonable deviations in source positioning within the phantom and the limited resolution of the source timer had insignificant effects on the ability to measure dose. Overall measurement uncertainty of the system was estimated to be ±2.5% for both Nucletron and Varian source audits (95% CI). This uncertainty was sufficient to establish a ±5% acceptance criterion for source strength audits under a formal RPC audit program. Trial audits of eight participating institutions resulted in an average RPC-to-institution dose ratio of 1.000 with a standard deviation of 0.011.