Use of Binomial Group Testing in Tests of Hypotheses for Classification or Quantitative Covariables

Abstract

In group testing, the test unit consists of a group of individuals. If the group test is positive, then one or more individuals in the group are assumed to be positive. A group observation in binomial group testing can be, say, the test result (positive or negative) for a pool of blood samples that come from several different individuals. It has been shown that, when the proportion (p) of infected individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of those infected. We extend the potential applications of group testing to hypothesis-testing problems wherein one wants to test for a relationship between p and a classification or quantitative covariable. Asymptotic relative efficiencies (AREs) of tests based on group testing versus the usual individual testing are obtained. The Pitman ARE strongly favors group testing in many cases. Small-sample results from simulation studies are given and are consistent with the large-sample (asymptotic) findings. We illustrate the potential advantages of group testing in hypothesis testing using HIV-1 seroprevalence data.

More Powerful Likelihood Ratio Tests for Isotonic Binomial Proportions

“…Using the randomization method of Gastwirth and Hammick (1989), Kline et al (1989), and Hung and Swallow (2000), and using the observed proportion positive as an estimate of the true p i , we randomly assign individuals to groups within strata, thereby simulating group observations of size s ¼ 5 and s ¼ 10. The resulting numbers of tests also appear in Table 4.…”

Hypothesis Tests for and against a Simple Order among Proportions Estimated by Pooled Testing

“…However, by comparison, there has been little research incorporating covariate information into the estimation problem. Hung and Swallow (2000) investigate pooled testing in situations where the prevalence p is presumed to depend on a single categorical covariate with k > 2 levels and develop a procedure to test H 0 : p 1 ¼ p 2 ¼ Á Á Á ¼ p k versus an omnibus alternative which specifies that at least one of the p i is different. Tebbs and Swallow (2003a, b) extend this work to problems with inequality constrained parameter spaces by combining pooled testing with isotonic regression.…”

Nonparametric and Parametric Estimators of Prevalence From Group Testing Data With Aggregated Covariates

“…In group testing problems, it is often of interest to estimate the probability of contamination given a covariate X; that is, p(x) = P(Y = 1|X = x) (we use contamination as a generic term, which can represent contamination by a pollutant, the presence of a disease, evidence of genetic manipu- Chen and Swallow (1990), Farrington (1992), Hardwick et al (1998), Gastwirth and Johnson (1994) and Hung and Swallow (2000) for related work on estimation and inference about prevalence.…”