Joshua M. Tebbs

An Introduction to Categorical Data Analysis

Bilder and Tebbs review An Introduction to Categorical Data Analysis (2nd ed.) by Alan Agresti.

Group Testing Regression Models with Fixed and Random Effects

Group testing, where subjects are tested in pools rather than individually, has a long history of successful application in infectious disease screening. In this article, we develop group testing regression models to include covariate effects that are best regarded as random. We present approaches to fit mixed effects models using maximum likelihood, investigate likelihood ratio and score tests for variance components, and evaluate small sample performance using simulation. We illustrate our methods using chlamydia and gonorrhea data collected by the state of Nebraska as part of the Infertility Prevention Project.

Confidence Interval Procedures for the Probability of Disease Transmission in Multiple-Vector-Transfer Designs

In plant pathology, group testing has been widely used in vector-transfer designs to study factors affecting the spread of disease by insect vectors. In such contexts, vectors are tested in groups rather than individually. However, the goal is still to estimate p, the probability of disease transmissi on by a single vector. The purpose of this article is to provide a thorough comparison of new and established interval estimators for p in terms of coverage probability and mean length. We ill ustrate our methods using data from an Argentinean study in volving the Mal Rio Cuarto virus and its transmission by the Delphacodes kuscheli planthopper.

Regression models for group testing data with pool dilution effects

Group testing is widely used to reduce the cost of screening individuals for infectious diseases. There is an extensive literature on group testing, most of which traditionally has focused on estimating the probability of infection in a homogeneous population. More recently, this research area has shifted towards estimating individual-specific probabilities in a regression context. However, existing regression approaches have assumed that the sensitivity and specificity of pooled biospecimens are constant and do not depend on the pool sizes. For those applications, where this assumption may not be realistic, these existing approaches can lead to inaccurate inference, especially when pool sizes are large. Our new approach, which exploits the information readily available from underlying continuous biomarker distributions, provides reliable inference in settings where pooling would be most beneficial and does so even for larger pool sizes. We illustrate our methodology using hepatitis B data from a study involving Irish prisoners.

Regression analysis for current status data using the EM algorithm

We propose new expectation-maximization algorithms to analyze current status data under two popular semiparametric regression models: the proportional hazards (PH) model and the proportional odds (PO) model. Monotone splines are used to model the baseline cumulative hazard function in the PH model and the baseline odds function in the PO model. The proposed algorithms are derived by exploiting a data augmentation based on Poisson latent variables. Unlike previous regression work with current status data, our PH and PO model fitting methods are fast, flexible, easy to implement, and provide variance estimates in closed form. These techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy.

Bias, efficiency, and agreement for group-testing regression models

Group testing involves pooling individual items together and testing them simultaneously for a rare binary trait. Whether the goal is to estimate the prevalence of the trait or to identify those individuals that possess it, group testing can provide substantial benefits when compared with testing subjects individually. Recently, group-testing regression models have been proposed as a way to incorporate covariates when estimating trait prevalence. In this paper, we examine these models by comparing fits obtained from individual and group testing samples. Relative bias and efficiency measures are used to assess the accuracy and precision of the resulting estimates using different grouping strategies. We also investigate the agreement of individual and group-testing regression estimates for various grouping strategies and the effects of group size selection. Depending on how groups are formed, our results show that group-testing regression models can perform very well when compared with the analogous models based on individual observations. However, different grouping strategies can provide very different results in finite samples.

There Is No Relationship between Academic Achievement and Body Mass Index among Fourth-Grade, Predominantly African-American Children

School-based initiatives to combat childhood obesity may use academic performance to measure success. This cross-sectional study investigated the relationship between academic achievement and body mass index percentile, socioeconomic status (SES), and race by linking existing datasets that are not routinely linked. Data from a school-based project (with National Institutes of Health funding) concerning dietary recall accuracy were linked with data from the states Department of Education through the states Office of Research and Statistics. Data were available on 1,504 fourth-grade, predominantly African-American children from 18 schools total in one district in South Carolina during the 2004-2005, 2005-2006, and 2006-2007 school years. School staff administered standardized tests in English, math, social studies, and science. Researchers measured childrens weight and height. Children were categorized as low-SES, medium-SES, or high-SES based on eligibility for free, reduced-price, or full-price school meals, respectively. Results from marginal regression analyses for each sex for the four academic subjects, separately and combined, showed that test scores were not related to body mass index percentile, but were positively related to SES (P values <0.0001), and were related to race, with lower scores for African-American children than children of other races (P values <0.0039). Cost-efficient opportunities exist to create longitudinal data sets to investigate relationships between academic performance and obesity across kindergarten through 12th-grade children. State agencies can house body mass index data in state-based central repositories where staff can use globally unique identifiers and link data across agencies. Results from such studies could potentially change the way school administrators view nutrition and physical education.

Two-stage hierarchical group testing for multiple infections with application to the infertility prevention project

Screening for sexually transmitted diseases (STDs) has benefited greatly from the use of group testing (pooled testing) to lower costs. With the development of assays that detect multiple infections, screening practices now involve testing pools of individuals for multiple infections simultaneously. Building on the research for single infection group testing procedures, we examine the performance of group testing for multiple infections. Our work is motivated by chlamydia and gonorrhea testing for the infertility prevention project (IPP), a national program in the United States. We consider a two-stage pooling algorithm currently used to perform testing for the IPP. We first derive the operating characteristics of this algorithm for classification purposes (e.g., expected number of tests, misclassification probabilities, etc.) and identify pool sizes that minimize the expected number of tests. We then develop an expectation-maximization (EM) algorithm to estimate probabilities of infection using both group and individual retest responses. Our research shows that group testing can offer large cost savings when classifying individuals for multiple infections and can provide prevalence estimates that are actually more efficient than those from individual testing.

An Empirical Bayes Group-Testing Approach to Estimating Small Proportions

Abstract Group testing has long been recognized as a safe and sensible alternative to one-at-a-time testing in applications wherein the prevalence rate p is small. In this article, we develop an empirical Bayes (EB) procedure to estimate p using a beta-type prior distribution and a squared-error loss function. We show that the EB estimator is preferred over the usual maximum likelihood estimator (MLE) for small group sizes and small p. In addition, we also discuss interval estimation and consider the use of other loss functions perhaps more appropriate in public health studies. The proposed methods are illustrated using group-testing data from a prospective hepatitis C virus study conducted in Xuzhou City, China.

On Latent-Variable Model Misspecification in Structural Measurement Error Models for Binary Response

We consider structural measurement error models for a binary response. We show that likelihood-based estimators obtained from fitting structural measurement error models with pooled binary responses can be far more robust to covariate measurement error in the presence of latent-variable model misspecification than the corresponding estimators from individual responses. Furthermore, despite the loss in information, pooling can provide improved parameter estimators in terms of mean-squared error. Based on these and other findings, we create a new diagnostic method to detect latent-variable model misspecification in structural measurement error models with individual binary response. We use simulation and data from the Framingham Heart Study to illustrate our methods.