  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.
