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. ^

Mean corpuscular volume as a marker for adherence to antiretroviral therapy among HIV infected children and adolescents in Uganda

Mean corpuscular volume, which is an inexpensive and widely available measure to assess, increases in HIV infected individuals receiving zidovudine and stavudine raising the hypothesis that it could be used as a surrogate for adherence.^ The aim of this study was to examine the association between mean corpuscular volume and adherence to antiretroviral therapy among HIV infected children and adolescents aged 0–19 years in Uganda as well as the extent to which changes in mean corpuscular volume predict adherence as determined by virologic suppression.^ The investigator retrospectively reviewed and analyzed secondary data of 158 HIV infected children and adolescents aged 0–19 years who initiated antiretroviral therapy under an observational cohort at the Baylor College of Medicine Children's Foundation - Uganda. Viral suppression was used as the gold standard for monitoring adherence and defined as viral load of < 400 copies/ml at 24 and 48 weeks. ^ Patients were at least 48 weeks on therapy, age 0.2–18.4 years, 54.4% female, 82.3% on zidovudine based regimen, 92% WHO stage III at initiation of therapy, median pre therapy MCV 80.6 fl (70.3–98.3 fl), median CD4% 10.2% (0.3%–28.0%), and mean pre therapy viral load 407,712.9 ± 270,413.9 copies/ml. For both 24 and 48 weeks of antiretroviral therapy, patients with viral suppression had a greater mean percentage change in mean corpuscular volume (15.1% ± 8.4 vs. 11.1% ± 7.8 and 2.3% ± 13.2 vs. -2.7% ± 10.5 respectively). The mean percentage change in mean corpuscular volume was greater in the first 24 weeks of therapy for patients with and without viral suppression (15.1% ± 8.4 vs. 2.3% ± 13.2 and 11.1% ± 7.8 vs. -2.7% ± 10.5 respectively). In the multivariate logistic regression model, percentage change in mean corpuscular volume ≥ 20% was significantly associated with viral suppression (adjusted OR 4.0; CI 1.2–13.3; p value 0.02). The ability of percentage changes in MCV to correctly identify children and adolescents with viral suppression was higher at a cut off of ≥ 20% (90.7%; sensitivity, 31.7%) than at ≥ 9% (82.9%; sensitivity, 78.9%). Negative predictive value was lower at ≥ 20% change (25%; specificity, 84.8%) than at ≥ 9% change (33.3%; specificity, 39.4%).^ Mean corpuscular volume is a useful marker of adherence among children and adolescents with viral suppression. ^

Intensive care noise and mean arterial blood pressure in ELBW neonates

Objective. Loud noises in neonatal intensive care units (NICUs) may impede growth and development for extremely low birthweight (ELBW, < 1000 grams) newborns. The objective of this study was to measure the association between NICU sound levels and ELBW neonates' arterial blood pressure to determine whether these newborns experience noise-induced stress. ^ Methods. Noise and arterial blood pressure recordings were collected for 9 ELBW neonates during the first week of life. Sound levels were measured inside the incubator, and each subject's arterial blood pressures were simultaneously recorded for 15 minutes (at 1 sec intervals). Time series cross-correlation functions were calculated for NICU noise and mean arterial blood pressure (MABP) recordings for each subject. The grand mean noise-MABP cross-correlation was calculated for all subjects and for lower and higher birthweight groups for comparison. ^ Results. The grand mean noise-MABP cross-correlation for all subjects was mostly negative (through 300 sec lag time) and nearly reached significance at the 95% level at 111 sec lag (mean r = -0.062). Lower birthweight newborns (454-709 g) experienced significant decreases in blood pressure with increasing NICU noise after 145 sec lag (peak r = -0.074). Higher birthweight newborns had an immediate negative correlation with NICU sound levels (at 3 sec lag, r = -0.071), but arterial blood pressures increased to a positive correlation with noise levels at 197 sec lag (r = 0.075). ^ Conclusions. ELBW newborns' arterial blood pressure was influenced by NICU noise levels during the first week of life. Lower birthweight newborns may have experienced an orienting reflex to NICU sounds. Higher birthweight newborns experienced an immediate orienting reflex to increasing sound levels, but arterial blood pressure increased approximately 3 minutes after increases in noise levels. Increases in arterial blood pressure following increased NICU sound levels may result from a stress response to noise. ^

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^