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. ^

"Gangsterism," HIV, and "tik:" An exploration of Cape Town youth

Since early 2000, the Western Cape of South Africa has been documented as an area for monitoring the spread of HIV. The majority of HIV cases occur within individuals between the ages of 15-49 years, and the epidemic is believed to be complicated by the increased use of crystal methamphetamine (CM), or “tik.” Eighty percent of current CM users in Cape Town are under the age of 21 years, and almost 18% of current HIV cases are in individuals under the age of 24 years. Gang membership in youth may also be complicating the HIV problem as gangs feed the social acceptability of “tik” and encourage sexual violence. With almost half the population of Cape Town in their mid-twenties, the threat of a new HIV epidemic complicated by CM use has become a concern in the young adults of the city. Research into the relationships between gang membership and drugs/violence has been extensively studied in the Cape Flats. Yet, few have examined the role of gangs in the perpetuation of HIV. Therefore, the purpose of this investigation was exploratory in nature. Key informant interviews from Cape Town youth were used as case illustrations to generate potential hypotheses on the interrelationships between “gangsterism,” “tik” use, and HIV. Such awareness is important if effective efforts to reduce HIV incidence in Cape Town (and Sub-Saharan Africa) are to transpire. If the problem of CM is not addressed quickly, the Cape Flats may find itself with a higher rate of an already uncontrollable HIV epidemic. ^