Group (pooled) testing is often used to reduce the total number of tests that are needed to screen a large number of individuals for an infectious disease or some other binary characteristic. ...Traditionally, research in group testing has assumed that each individual is independent with the same risk of positivity. More recently, there has been a growing set of literature generalizing previous work in group testing to include heterogeneous populations so that each individual has a different risk of positivity. We investigate the effect of acknowledging population heterogeneity on a commonly used group testing procedure which is known as 'halving'. For this procedure, positive groups are successively split into two equal-sized halves until all groups test negatively or until individual testing occurs. We show that heterogeneity does not affect the mean number of tests when individuals are randomly assigned to subgroups. However, when individuals are assigned to subgroups on the basis of their risk probabilities, we show that our proposed procedures reduce the number of tests by taking advantage of the heterogeneity. This is illustrated by using chlamydia and gonorrhoea screening data from the state of Nebraska.
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.
Questions that ask respondents to "choose all that apply" from a set of items occur frequently in surveys. Categorical variables that summarize this type of survey data are called both pick any/c ...variables and multiple-response categorical variables. It is often of interest to test for independence between two categorical variables. When both categorical variables can have multiple responses, traditional Pearson chi-square tests for independence should not be used because of the within-subject dependence among responses. An intuitively constructed version of the Pearson statistic is proposed to perform the test using bootstrap procedures to approximate its sampling distribution. First- and second-order adjustments to the proposed statistic are given in order to use a chi-square distribution approximation. A Bonferroni adjustment is proposed to perform the test when the joint set of responses for individual subjects is unavailable. Simulations show that the bootstrap procedures hold the correct size more consistently than the other procedures.
For the analysis of survey-weighted categorical data, one recommended method of analysis is a log-rate model. For each cell in a contingency table, the survey weights are averaged across subjects and ...incorporated into an offset for a loglinear model. Supposedly, one can then proceed with the analysis of unweighted observed cell counts. We provide theoretical and simulation-based evidence to show that the log-rate analysis is not an effective statistical analysis method and should not be used in general. The root of the problem is in its failure to properly account for variability in the individual weights within cells of a contingency table. This results in goodness-of-fit tests that have higher-than-nominal error rates and confidence intervals for odds ratios that have lower-than-nominal coverage.
Although "choose all that apply" questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are ...generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to "choose all that apply" questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. Quoique les questions du type « Sélectionner une ou plusieurs réponses » sont courantes dans les enquêtes modernes, les méthodes pour analyser les associations entre les réponses à de telles questions viennent seulement d'être développées. Ces méthodes sont habituellement valides uni-quement pour des échantillons aléatoires simples, mais ce genre de questions apparaissent souvent dans les enquêtes conduites sous des plans de sondage beaucoup plus complexes. Le but de cet article est de donner des méthodes d'analyse statistique pouvant être appliquées aux questions de type « Sélectionner une ou plusieurs réponses » dans des enquêtes utilisant des plans de sondage complexes. Des modèles loglinéaires sont développés permettant d'incorporer les réponses multiples inhérentes à ce type de questions. Des statistiques permettant de comparer les modèles et de mesu-rer l'association sont proposées et leurs distributions asymptotiques sont obtenues. Des simulations de Monte-Carlo montrent que les tests basés sur les statistiques de Pearson ajustées maintiennent généralement leur niveau lorsqu'ils sont utilisés pour comparer des modèles. Ces études montrent également que les niveaux des intervalles de confiance pour les rapports de cotes estimés à par-tir des modèles loglinéaires ont de bonnes propriétés de couverture tout en étant plus courts que ceux utilisant les estimations empiriques. De plus, il est montré que ces méthodes peuvent aussi êtres utilisées dans un contexte plus général de modélisation de l'association entre les éléments de deux ou plusieurs vecteurs binaires. Les méthodes d'analyse proposées sont appliquées à des données provenant de l'étude américaine « National Health and Nutrition Examination Survey » (NHANES).
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