Bayesian monotonic errors-in-variables models with applications to pathogen susceptibility testing

Drug dilution (MIC) and disk diffusion (DIA) are the two most common antimicrobial susceptibility assays used by hospitals and clinics to determine an unknown pathogen's susceptibility to various antibiotics. Since only one assay is commonly used, it is important that the two assays give similar results. Calibration of the DIA assay to the MIC assay is typically done using the error-rate bounded method, which selects DIA breakpoints that minimize the observed discrepancies between the two assays. In 2000, Craig proposed a model-based approach that specifically models the measurement error and rounding processes of each assay, the underlying pathogen distribution, and the true monotonic relationship between the two assays. The two assays are then calibrated by focusing on matching the probabilities of correct classification (susceptible, indeterminant, and resistant). This approach results in greater precision and accuracy for estimating DIA breakpoints. In this paper, we expand the flexibility of the model-based method by introducing a Bayesian four-parameter logistic model (extending Craig's original three-parameter model) as well as a Bayesian nonparametric spline model to describe the relationship between the two assays. We propose two ways to handle spline knot selection, considering many equally-spaced knots but restricting overfitting via a random walk prior and treating the number and location of knots as additional unknown parameters. We demonstrate the two approaches via a series of simulation studies and apply the methods to two real data sets.