Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests

Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur

A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence

A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality

The Kinetics of Rotating Biological Contactors Treating Domestic Wastewater

Four, four-stage, laboratory scale rotating biological contactor (RBC) units were employed to develop kinetic models for the RBC process when treating domestic wastewater. The study was conducted at three different temperatures of 5 degrees C, 15 degrees C, and 20 degrees C. Each unit operated at a different constant organic loading rate taht ranged from 4 qCOD/m^2/d to 14 gCOD/m^2/d and at a constand detention time of 2 hours. Carbonaceous substrate removals measured as COD cencentrations with the four-stage RBC\u27s were 80, 85, and 90 percent for 5 degrees C, 15 degrees C, and 20 degrees C, respectively. The major part of the removal occurred in the first stages. The overall precentage removals of ammonia nitrogen were 87 to 98 percent at 15 degrees C from 91 to 99 percent at 20 degrees C depending upon the influent organic loading rate. At 5 degrees C there was no ammonia nitrogen removal. Kinetic models were devloped and kinetic constants were determined for COD and ammonia nitrogen removal in the first and succeeding stages of the RBC units. Biomass yeild, biomass stabilization, and ammonia nitrogen removal were also evaluated. Monod growth kinetics were used in the development of the models for carbonaceous substrate removal in the first stages and for ammonia nitrogen removal in the system. The temeprature dependency of each kindetic constant was determined for the range of 5 degrees C to 20 Degrees C. Steady-state kinetic models were developed, and kinetic constants were determined as a function of temperature to provide a rational design approach for the RBC process treating domestic wastewater

Final Report: Buffalo National River Ecosystems

The objective of this study was to sample the Buffalo River on a seasonal basis for a year, in order to determine whether any potential water quality problems existed

Factor copula models for item response data

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data

Secondary Mathematics Teachers’ Planned Approaches For Teaching Standard Deviation

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers to teach in alignment with prior learning experiences, despite professional development. Implications for teacher education and curricular development are offered

Effect of Temperature on Algal Removal by Alum Coagulation

Questions about the effect of temperature on algal cell coagulation and the relationships between algae removal and temperature, alum dosage, paddle speed, flocculation time, and settling time are answered. The investigations consisted of two series of tests: Studies on algae cultured under laboratory control, and algae in wastewater stabilization ponds. The jar-test technique was used for the coagulation of algal suspensions by alum. Coagulation of algae is caused mainly by the insoluble flocs of aluminum hydroxide. Other aluminum species also have coagulative properties but are far less effective. The destabilization of algal colloids results from enmeshment within the hydroxide precipitates, or by adsorption of coagulant species. Neutralization of the pH-dependent charges of algal cells is not necessary for coagulation, but does aid coagulation. Analyses of variance of the variables and their interactions showed significantly the effect of all variables ad most of their interactions. Step-wise multiple regression technique was used for the development of mathematical models for the estimation of algal removal. Increased temperatures adversely affected the percentage removal of algal cells by alum coagulation. The effect of temperature on the removal of algae grown in the wastewater stabilization pond effluent was more pronounced than that found for the algae cultured in the laboratory. Alum was effective in removing algae from Logan wastewater stabilization ponds. However, high alum dosages are required which may not be justified economically. It also was found that at low concentrations of algal cells the straight line portion of the Langmuir isotherm describes the removal of algae with alum