Regression models of antibiotic disk diffusion assays and the Eagle Effect

We analyse dose-response data from disk-diffusion antibiotic susceptibility tests (ddASTs) that quantify a pathogen's susceptibility to antibiotics. In this assay, an antibiotic diffuses from a central source across an agar plate, producing a zone of inhibition (ZoI) where pathogen growth is suppressed. ZoI size is used to estimate the key pharmacological quantity, namely the minimal inhibitory concentration (MIC), defined as the lowest dose that prevents pathogen growth. In clinical practice, MICs can be estimated from ddAST data using regression relationships between ZoI size and MIC that are curated by regulatory bodies. Motivated by this, we use diffusion theory to derive new regression models for dose-response data and compare them with log-linear regressions that remain in use. These nonlinear regressions can provide accurate descriptions of data and often, but not always, yield mutually consistent MIC estimates whose uncertainty we quantify using Bayesian regression. To test model robustness with challenging datasets, we generate synthetic dose-response data using a spatial population-genetics model that (i) illustrate how the regressions can fail and (ii) helps explain why some antibiotics exhibit an Eagle effect.