Revisiting Nested Group Testing Procedures: New Results, Comparisons, and Robustness

Group testing regression analysis with covariates and specimens subject to missingness

We develop parametric estimators of a conditional prevalence in the group testing context. Group testing is applied when a binary outcome variable, often a disease indicator, is assessed by testing a specimen for the presence of the disease. Instead of testing all individual specimens separately, these are pooled in groups and the grouped specimens are tested for the disease, which permits to significantly reduce the number of tests to be performed. Various techniques have been developed in the literature for estimating a conditional prevalence from group testing data, but most of them are not valid when the data are subject to missingness. We consider this problem in the case where the specimen and the covariates are subject to nonmonotone missingness. We propose parametric estimators of the conditional prevalence, establish identifiability conditions for a logistic missing not at random model, and introduce an ignorable missing at random model. In theory, our estimators could be applied with multiple covariates missing, but in practice, they face numerical challenges when more than one covariate is missing for given individuals. We illustrate the method on simulated data and on a dataset from the Demographics and Health Survey.

Using group testing in a two-phase epidemiologic design to identify the effects of a large number of antibody reactions on disease risk

BACKGROUND

The role of immunological responses to exposed bacteria on disease incidence is increasingly under investigation. With many bacterial species, and many potential antibody reactions to a particular species, the large number of assays required for this type of discovery can make it prohibitively expensive. We propose a two-phase group testing design to more efficiently screen numerous antibody effects in a case-control setting.

METHODS

Phase 1 uses group testing to select antibodies that are differentially expressed between cases and controls. The selected antibodies go on to Phase 2 individual testing.

RESULTS

We evaluate the two-phase group testing design through simulations and example data and find that it substantially reduces the number of assays required relative to standard case-control and group testing designs, while maintaining similar statistical properties.

CONCLUSION

The proposed two-phase group testing design can dramatically reduce the number of assays required, while providing comparable results to a case-control design.

The efficient design of Nested Group Testing algorithms for disease identification in clustered data

Group testing study designs have been used since the 1940s to reduce screening costs for uncommon diseases; for rare diseases, all cases are identifiable with substantially fewer tests than the population size. Substantial research has identified efficient designs under this paradigm. However, little work has focused on the important problem of disease screening among clustered data, such as geographic heterogeneity in HIV prevalence. We evaluated designs where we first estimate disease prevalence and then apply efficient group testing algorithms using these estimates. Specifically, we evaluate prevalence using individual testing on a fixed-size subset of each cluster and use these prevalence estimates to choose group sizes that minimize the corresponding estimated average number of tests per subject. We compare designs where we estimate cluster-specific prevalences as well as a common prevalence across clusters, use different group testing algorithms, construct groups from individuals within and in different clusters, and consider misclassification. For diseases with low prevalence, our results suggest that accounting for clustering is unnecessary. However, for diseases with higher prevalence and sizeable between-cluster heterogeneity, accounting for clustering in study design and implementation improves efficiency. We consider the practical aspects of our design recommendations with two examples with strong clustering effects: (1) Identification of HIV carriers in the US population and (2) Laboratory screening of anti-cancer compounds using cell lines.

Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies

Background: Due to the ongoing COVID-19 pandemic, demand for diagnostic testing has increased drastically, resulting in shortages of necessary materials to conduct the tests and overwhelming the capacity of testing laboratories. The supply scarcity and capacity limits affect test administration: priority must be given to hospitalized patients and symptomatic individuals, which can prevent the identification of asymptomatic and presymptomatic individuals and hence effective tracking and tracing policies. We describe optimized group testing strategies applicable to SARS-CoV-2 tests in scenarios tailored to the current COVID-19 pandemic and assess significant gains compared to individual testing. Methods: We account for biochemically realistic scenarios in the context of dilution effects on SARS-CoV-2 samples and consider evidence on specificity and sensitivity of PCR-based tests for the novel coronavirus. Because of the current uncertainty and the temporal and spatial changes in the prevalence regime, we provide analysis for several realistic scenarios and propose fast and reliable strategies for massive testing procedures. Key Findings: We find significant efficiency gaps between different group testing strategies in realistic scenarios for SARS-CoV-2 testing, highlighting the need for an informed decision of the pooling protocol depending on estimated prevalence, target specificity, and high- vs. low-risk population. For example, using one of the presented methods, all 1.47 million inhabitants of Munich, Germany, could be tested using only around 141 thousand tests if the infection rate is below 0.4% is assumed. Using 1 million tests, the 6.69 million inhabitants from the city of Rio de Janeiro, Brazil, could be tested as long as the infection rate does not exceed 1%. Moreover, we provide an interactive web application, available at www.grouptexting.com, for visualizing the different strategies and designing pooling schemes according to specific prevalence scenarios and test configurations. Interpretation: Altogether, this work may help provide a basis for an efficient upscaling of current testing procedures, which takes the population heterogeneity into account and is fine-grained towards the desired study populations, e.g., mild/asymptomatic individuals vs. symptomatic ones but also mixtures thereof. Funding: German Science Foundation (DFG), German Federal Ministry of Education and Research (BMBF), Chan Zuckerberg Initiative DAF, and Austrian Science Fund (FWF).