Bayesian inference of infected patients in group testing with prevalence estimation
This work addresses group testing for disease screening, offering practical guidance for implementation, but it appears incremental as it builds on existing Bayesian methods.
The paper tackles the problem of identifying infected patients in group testing with imperfect tests by proposing Bayesian inference and belief propagation algorithms, showing that the true-positive rate improves by considering credible intervals and estimating prevalence and error probabilities.
Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and a corresponding belief propagation (BP) algorithm to identify the infected patients from the results of tests performed on the pool. We show that the true-positive rate is improved by taking into account the credible interval of a point estimate of each patient. Further, the prevalence and the error probability in the test are estimated by combining an expectation-maximization method with the BP algorithm. As another approach, we introduce a hierarchical Bayes model to identify the infected patients and estimate the prevalence. By comparing these methods, we formulate a guide for practical usage.