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. ^

Evaluating statistical methods used to estimate the number of postsynaptic receptors.

Calcium levels in spines play a significant role in determining the sign and magnitude of synaptic plasticity. The magnitude of calcium influx into spines is highly dependent on influx through N-methyl D-aspartate (NMDA) receptors, and therefore depends on the number of postsynaptic NMDA receptors in each spine. We have calculated previously how the number of postsynaptic NMDA receptors determines the mean and variance of calcium transients in the postsynaptic density, and how this alters the shape of plasticity curves. However, the number of postsynaptic NMDA receptors in the postsynaptic density is not well known. Anatomical methods for estimating the number of NMDA receptors produce estimates that are very different than those produced by physiological techniques. The physiological techniques are based on the statistics of synaptic transmission and it is difficult to experimentally estimate their precision. In this paper we use stochastic simulations in order to test the validity of a physiological estimation technique based on failure analysis. We find that the method is likely to underestimate the number of postsynaptic NMDA receptors, explain the source of the error, and re-derive a more precise estimation technique. We also show that the original failure analysis as well as our improved formulas are not robust to small estimation errors in key parameters.

Multiple imputation for missing continuous and dichotomous data: The effects of patterns of missingness and variable correlations on type I error with small samples

The purpose of this study is to investigate the effects of predictor variable correlations and patterns of missingness with dichotomous and/or continuous data in small samples when missing data is multiply imputed. Missing data of predictor variables is multiply imputed under three different multivariate models: the multivariate normal model for continuous data, the multinomial model for dichotomous data and the general location model for mixed dichotomous and continuous data. Subsequent to the multiple imputation process, Type I error rates of the regression coefficients obtained with logistic regression analysis are estimated under various conditions of correlation structure, sample size, type of data and patterns of missing data. The distributional properties of average mean, variance and correlations among the predictor variables are assessed after the multiple imputation process. ^ For continuous predictor data under the multivariate normal model, Type I error rates are generally within the nominal values with samples of size n = 100. Smaller samples of size n = 50 resulted in more conservative estimates (i.e., lower than the nominal value). Correlation and variance estimates of the original data are retained after multiple imputation with less than 50% missing continuous predictor data. For dichotomous predictor data under the multinomial model, Type I error rates are generally conservative, which in part is due to the sparseness of the data. The correlation structure for the predictor variables is not well retained on multiply-imputed data from small samples with more than 50% missing data with this model. For mixed continuous and dichotomous predictor data, the results are similar to those found under the multivariate normal model for continuous data and under the multinomial model for dichotomous data. With all data types, a fully-observed variable included with variables subject to missingness in the multiple imputation process and subsequent statistical analysis provided liberal (larger than nominal values) Type I error rates under a specific pattern of missing data. It is suggested that future studies focus on the effects of multiple imputation in multivariate settings with more realistic data characteristics and a variety of multivariate analyses, assessing both Type I error and power. ^

Assessing homogeneity in workplace exposure under stationary and non-stationary scenarios

In most epidemiological studies, historical monitoring data are scant and must be pooled to identify occupational groups with homogeneous exposures. Homogeneity of exposure is generally assessed in a group of workers who share a common job title or work in a common area. While published results suggest that the degree of homogeneity varies widely across job groups, less is known whether such variation differs across industrial sectors, classes of contaminants, or in the methods used to group workers. Relying upon a compilation of results presented in the literature, patterns of homogeneity among nearly 500 occupational groups of workers were evaluated on the basis of type of industry and agent. Additionally, effects of the characteristics of the sampling strategy on estimated indicators of homogeneity of exposure were assessed. ^ Exposure profiles for occupational groups of workers have typically been assessed under the assumption of stationarity, i.e., the mean exposure level and variance of the distribution that describes the underlying population of exposures are constant over time. Yet, the literature has shown that occupational exposures have declined in the last decades. This renders traditional methods for the description of exposure profiles inadequate. Thus, work was needed to develop appropriate methods to assess homogeneity for groups of workers whose exposures have changed over time. A study was carried out applying mixed effects models with a term for temporal trend to appropriately describe exposure profiles of groups of workers in the nickel-producing industry over a 20-year period. Using a sub-set of groups of nickel-exposed workers, another study was conducted to develop and apply a framework to evaluate the assumption of stationarity of the variances in the presence of systematic changes in exposure levels over time. ^

Inherited and noninherited sources of variation in metastasis and the growth rate of tumors: Implications for tumor evolution and therapy

I have undertaken measurements of the genetic (or inherited) and nongenetic (or noninherited) components of the variability of metastasis formation and tumor diameter doubling time in more than 100 metastatic lines from each of three murine tumors (sarcoma SANH, sarcoma SA4020, and hepatocarcinoma HCA-I) syngeneic to C3Hf/Kam mice. These lines were isolated twice from lung metastases and analysed immediately thereafter to obtain the variance to spontaneous lung metastasis and tumor diameter doubling time. Additional studies utilized cells obtained from within 4 passages of isolation. Under the assumption that no genetic differences in metastasis formation or diameter doubling time existed among the cells of a given line, the variance within a line would estimate nongenetic variation. The variability derived from differences between lines would represent genetic origin. The estimates of the genetic contribution to the variation of metastasis and tumor diameter doubling time were significantly greater than zero, but only in the metastatic lines of tumor SANH was genetic variation the major source of metastatic variability (contributing 53% of the variability). In the tumor cell lines of SA4020 and HCA-I, however, the contribution of nongenetic factors predominated over genetic factors in the variability of the number of metastasis and tumor diameter doubling time. A number of other parameters examined, such as DNA content, karyotype, and selection and variance analysis with passage in vivo, indicated that genetic differences existed within the cell lines and that these differences were probably created by genetic instability. The mean metastatic propensity of the lines may have increased somewhat during their isolation and isotransplantation, but the variance was only slightly affected, if at all. Analysis of the DNA profiles of the metastatic lines of SA4020 and HCA-I revealed differences between these lines and their primary parent tumors, but not among the SANH lines and their parent tumor. Furthermore, there was a direct correlation between the extent of genetic influence on metastasis formation and the ability of the tumor cells to develop resistance to cisplatinum. Thus although nongenetic factors might predominate in contributing to metastasis formation, it is probably genetic variation and genetic instability that cause the progression of tumor cells to a more metastatic phenotype and leads to the emergence of drug resistance. ^

Racial disparities in CD4 counts at initial HIV-1 diagnosis: Analysis of the Adult Spectrum of HIV disease dataset and public health implications

Introduction. The HIV/AIDS disease burden disproportionately affects minority populations, specifically African Americans. While sexual risk behaviors play a role in the observed HIV burden, other factors including gender, age, socioeconomics, and barriers to healthcare access may also be contributory. The goal of this study was to determine how far down the HIV/AIDS disease process people of different ethnicities first present for healthcare. The study specifically analyzed the differences in CD4 cell counts at the initial HIV-1 diagnosis with respect to ethnicity. The study also analyzed racial differences in HIV/AIDS risk factors. ^ Methods. This is a retrospective study using data from the Adult Spectrum of HIV Disease (ASD), collected by the City of Houston Department of Health. The ASD database contains information on newly reported HIV cases in the Harris County District Hospitals between 1989 and 2000. Each patient had an initial and a follow-up report. The extracted variables of interest from the ASD data set were CD4 counts at the initial HIV diagnosis, race, gender, age at HIV diagnosis and behavioral risk factors. One-way ANOVA was used to examine differences in baseline CD4 counts at HIV diagnosis between racial/ethnic groups. Chi square was used to analyze racial differences in risk factors. ^ Results. The analyzed study sample was 4767. The study population was 47% Black, 37% White and 16% Hispanic [p<0.05]. The mean and median CD4 counts at diagnosis were 254 and 193 cells per ml, respectively. At the initial HIV diagnosis Blacks had the highest average CD4 counts (285), followed by Whites (233) and Hispanics (212) [p<0.001 ]. These statistical differences, however, were only observed with CD4 counts above 350 [p<0.001], even when adjusted for age at diagnosis and gender [p<0.05]. Looking at risk factors, Blacks were mostly affected by intravenous drug use (IVDU) and heterosexuality, whereas Whites and Hispanics were more affected by male homosexuality [ p<0.05]. ^ Conclusion. (1) There were statistical differences in CD4 counts with respect to ethnicity, but these differences only existed for CD4 counts above 350. These differences however do not appear to have clinical significance. Antithetically, Blacks had the highest CD4 counts followed by Whites and Hispanics. (2) 50% of this study group clinically had AIDS at their initial HIV diagnosis (median=193), irrespective of ethnicity. It was not clear from data analysis if these observations were due to failure of early HIV surveillance, HIV testing policies or healthcare access. More studies need to be done to address this question. (3) Homosexuality and bisexuality were the biggest risk factors for Whites and Hispanics, whereas for Blacks were mostly affected by heterosexuality and IVDU, implying a need for different public health intervention strategies for these racial groups. ^

Obesity during pregnancy on vagal tone, hemoglobin A1c, oxygenation, and perinatal outcomes

Purpose: To examine the effect of obesity and gestational weight gain on heart rate variability (HRV), oxygenation (HbO 2 and SpO2), hemoglobin A1c (HbA1c) and the frequency of pregnancy complications in obese (O) and non-obese (NO) women.^ Design: The study was an observational comparison study with a repeated measures design. ^ Setting: The setting was a low risk prenatal, university clinic located in a large southeastern metropolitan city. ^ Sample: The sample consisted of a volunteer group of 41 pregnant women who were observed at the three time points of 20, 28, and 36 weeks gestation. ^ Analysis: Analysis included general linear modeling with repeated measures to test for group differences with changes over time on vagal response, HbA1c, and oxygenation. Odds ratios were computed to compare the frequency of birth outcomes. ^ Findings: The interaction effect of time between O and NO women on HbO2 was significant. The mean HP, RSA, and HbO2 changed significantly over time within the NO women. The mean HbA 1c increased significantly over time within the O women. Women with excess gestational weight gain had significantly lower heart period than women with weight gain within the IOM recommendations. Obese women were more likely to have Group B streptococcal infections, gestational hypertension, give birth by cesarean or instrument assistance, and have at least one postnatal event. ^ Conclusions: Monitoring HRV, oxygenation, and HbA1c using minimally invasive measures may permit early identification of alterations in autonomic response. Implementation of interventions to promote vagal tone may help to reduce risks for adverse perinatal outcomes related to obesity. Future studies should examine the effect of obesity on the vagal response and perinatal outcomes. ^

Improving disclosure of medical errors: Including patients and family members in the disclosure process

Over the last decade, adverse events and medical errors have become a main focus of interest for the standards of quality and safety in the U.S. healthcare system (Weinstein & Henderson, 2009). Particularly when a medical error occurs, the disclosure of medical errors and its practices have become a focal point of the healthcare process. Patients and family members who have experienced a medical error might be able to provide knowledge and insight on how to improve the disclose process. However, patient and family member are not typically involved in the disclosure process, thus their experiences go unnoticed. ^ The purpose of this research was to explore how best to include patients and family members in the disclosure process regarding a medical error. The research consisted of 28 qualitative interviews from three stakeholder groups: Hospital Administrators, Clinical Service Providers, and Patients and Family Members. They were asked for their ideas and suggestions on how best to include patients and family members in the disclosure process. Framework Analysis was used to analyze this data and find prevalent themes based on the primary research question. A secondary aim was to index categories created based on the interviews that were collected. Data was used from the Texas Disclosure and Compensation Study with Dr. Eric Thomas as the Principal Investigator. Full acknowledgement of access to this data is given to Dr. Thomas. ^ The themes from the research revealed that each stakeholder group was interested and open to including patients and family members in the disclosure process and that the disclosure process should not be a "one-way" avenue. The themes gave many suggestions regarding how to best include patients and family members in the disclosure process of a medical error. Secondary aims revealed several ways to assess the ideas and suggestion given by the stakeholders. Overall, acceptability of getting the perspective of patients and family members was the most common theme. Comparison of each stakeholder group revealed that including patients and family members would be beneficial to improving hospital disclosure practices. ^ Conclusions included a list of recommendations and measureable appropriate strategies that could provide hospital with key stakeholders insights on how to improve their disclosure process. Sharing patients and family members experience with healthcare providers can encourage a shift in culture where patients are valued and active in participating in hospital practices. To my knowledge, this research is the very first of its kind and moves the disclosure process conversation forward in a patient-family member inclusion direction that will assist in improving disclosure practices. Future research should implement and evaluate the success of the various inclusion strategies.^