Title: Estimating the susceptible component of a zone diameter distribution
Authors: Bettina Gruen - WU (Vienna University of Economics and Business) (Austria) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Thomas Petzoldt - Technische Universitaet Dresden (Germany)
Abstract: Disk diffusion tests are employed in diagnostic laboratories to determine the susceptibility of bacteria to antibiotics. The bacteria, as well as the antibiotics, are administered to an agar plate and the zone diameter (ZD) of inhibition is measured. ZD data have restricted support and usually, only rounded values are observed. Previous work suggested using a composite model of a parametric distribution covering the range of observations from the susceptible component combined with a non-parametric distribution capturing the range of observations containing also resistant observations when modeling the minimum inhibitory concentration that separates the susceptible from the resistant bacterial sub-population. We investigate the use of this model for ZD data and consider in addition a two-component mixture model of a parametric distribution capturing the susceptible observations and a non-parametric distribution for the resistant observations. We present maximum likelihood estimation of both models, the composite as well as the mixture model, for arbitrary parametric distributions taking the restricted support and the rounding of the data into account and outline the computational tools required for implementing the estimation as well as additional inference methods for model selection, visualization and estimation of a data-driven epidemiological cut-off.