Christopher R. Bilder

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.

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.

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.

Modeling Association Between Two or More Categorical Variables that Allow for Multiple Category Choices

Multiple-response (or pick any/c) categorical variables summarize responses to survey questions that ask “pick any” from a set of item responses. Extensions to loglinear model methodology are proposed to model associations between these variables across all their items simultaneously. Because individual item responses to a multiple-response categorical variable are likely to be correlated, the usual chi-square distributional approximations for model-comparison statistics are not appropriate. Adjusted statistics and a new bootstrap procedure are developed to facilitate distributional approximations. Odds ratio and standardized Pearson residual measures are also developed to estimate specific associations and examine deviations from a specified model.

Pooled‐testing procedures for screening high volume clinical specimens in heterogeneous populations

Pooled testing is a procedure commonly used to reduce the cost of screening a large number of individuals for infectious diseases. In its simplest form, pooled testing works by compositing a set of individual specimens (e.g., blood or urine) into a common pool. If the pool tests negative, all individuals within it are diagnosed as negative. If the pool tests positive, retesting is needed to decode the positive individuals from the negative individuals. Traditionally, pooled testing has assumed that each individual has the same probability of being positive. However, this assumption is often unrealistic, especially when known risk factors can be used to measure distinct probabilities of positivity for each individual. In this paper, we investigate new pooled-testing algorithms that exploit the heterogeneity among individual probabilities and subsequently reduce the total number of tests needed, while maintaining accuracy levels similar to standard algorithms that do not account for heterogeneity. We apply these algorithms to data from the Infertility Prevention Project, a nationally implemented program supported by the Centers for Disease Control and Prevention.

Regression analysis for multiple-disease group testing data

Group testing, where individual specimens are composited into groups to test for the presence of a disease (or other binary characteristic), is a procedure commonly used to reduce the costs of screening a large number of individuals. Group testing data are unique in that only group responses may be available, but inferences are needed at the individual level. A further methodological challenge arises when individuals are tested in groups for multiple diseases simultaneously, because unobserved individual disease statuses are likely correlated. In this paper, we propose new regression techniques for multiple-disease group testing data. We develop an expectation-solution based algorithm that provides consistent parameter estimates and natural large-sample inference procedures. We apply our proposed methodology to chlamydia and gonorrhea screening data collected in Nebraska as part of the Infertility Prevention Project and to prenatal infectious disease screening data from Kenya.

Estimating the prevalence of multiple diseases from two-stage hierarchical pooling.

Testing protocols in large-scale sexually transmitted disease screening applications often involve pooling biospecimens (e.g., blood, urine, and swabs) to lower costs and to increase the number of individuals who can be tested. With the recent development of assays that detect multiple diseases, it is now common to test biospecimen pools for multiple infections simultaneously. Recent work has developed an expectation-maximization algorithm to estimate the prevalence of two infections using a two-stage, Dorfman-type testing algorithm motivated by current screening practices for chlamydia and gonorrhea in the USA. In this article, we have the same goal but instead take a more flexible Bayesian approach. Doing so allows us to incorporate information about assay uncertainty during the testing process, which involves testing both pools and individuals, and also to update information as individuals are tested. Overall, our approach provides reliable inference for disease probabilities and accurately estimates assay sensitivity and specificity even when little or no information is provided in the prior distributions. We illustrate the performance of our estimation methods using simulation and by applying them to chlamydia and gonorrhea data collected in Nebraska. Copyright