Bayesian estimation of multivariate normal mixtures with covariate-dependent mixing weights, with an application in antimicrobial resistance monitoring.

Bacteria with a reduced susceptibility against antimicrobials pose a major threat to public health. Therefore, large programs have been set up to collect minimum inhibition concentration (MIC) values. These values can be used to monitor the distribution of the nonsusceptible isolates in the general population. Data are collected within several countries and over a number of years. In addition, the sampled bacterial isolates were not tested for susceptibility against one antimicrobial, but rather against an entire range of substances. Interest is therefore in the analysis of the joint distribution of MIC data on two or more antimicrobials, while accounting for a possible effect of covariates. In this regard, we present a Bayesian semiparametric density estimation routine, based on multivariate Gaussian mixtures. The mixing weights are allowed to depend on certain covariates, thereby allowing the user to detect certain changes over, for example, time. The new approach was applied to data collected in Europe in 2010, 2012, and 2013. We investigated the susceptibility of Escherichia coli isolates against ampicillin and trimethoprim, where we found that there seems to be a significant increase in the proportion of nonsusceptible isolates. In addition, a simulation study was carried out, showing the promising behavior of the proposed method in the field of antimicrobial resistance.