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

Abstract

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.

A hierarchical Bayesian latent class mixture model with censorship for detection of linear temporal changes in antibiotic resistance

“…Our proposed hierarchical Bayesian latent class mixture model with censoring and linear trend was implemented using the MCMC Gibbs sampling method. The Gibbs sampling algorithm was adapted for censorship in a finite mixture model [20] [21]. The algorithm of the Gibbs sampler is provided in S1 Appendix.…”

Overview of Quantitative Methodologies to Understand Antimicrobial Resistance via Minimum Inhibitory Concentration

“…A later iteration of this Bayesian approach by Jaspers et al enables the modeling of joint MIC distributions to explore relationships between resistance to multiple antimicrobials as a way to explore multidrug resistance patterns [67]. While this review will not cover Bayesian statistics extensively, the utility of a Bayesian framework for mixture distributions in this context is to take a prior estimate of the distribution and to update it using information from the observed MIC data and covariates to produce a posterior estimate of the parameters of the component distributions and the mixing weights [68].…”

A Bayesian latent class mixture model with censoring for correlation analysis in antimicrobial resistance across populations

“…Further analysis on the mean MIC creep was studied by Zhang et al [ 19 ] with a linear model in the susceptible component by a fully parametric Bayesian method. Jaspers et al[ 20 ] analyzed the joint distribution of MIC data on multiple antibiotics with Bayesian estimation of multivariate Gaussian mixtures, from which inference about the correlation between drug resistances within one year could be drawn. However, the multivariate means of MIC of each component were assumed as fixed from year to year, which ignores the potential for changes in the mean MIC for the components.…”