Bayesian Group Testing Regression with a Shape-Free Dilution Curve
Group testing pools specimens to cut the cost of screening, but pooling positive specimens with negative ones lowers assay sensitivity, so that the sensitivity of a pooled test depends on how many of its members are positive. Regression models for group testing accommodate this dilution effect through submodels that fix a one-parameter shape for that dependence. We propose BADGER (Bayesian Analysis of Dilution in Group tEsting Regression), a regression model incorporating a shape-free dilution curve. The pooled sensitivity is modeled as a nondecreasing function represented by nonnegative increments with a Dirichlet prior, so that the parametric submodels become special cases. By an appropriate augmentation, every full conditional of BADGER is in closed form and inference is carried out by an exact Gibbs sampler. The evidence for dilution is measured by a Bayes factor computed from the posterior draws. We validate the BADGER model through simulation studies across different dilution shapes, prevalences and pool sizes. We further illustrate the method on hepatitis E serology from a national health survey.