Bayesian Calibration to Address the Challenge of Antimicrobial Resistance: A Review

Abstract

Antimicrobial resistance (AMR) emerges when disease-causing microorganisms develop the ability to withstand the effects of antimicrobial therapy. This phenomenon is often fueled by the human-to-human transmission of pathogens and the overuse of antibiotics. Over the past 50 years, increased computational power has facilitated the application of Bayesian inference algorithms. In this comprehensive review, the basic theory of Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods are explained. These inference algorithms are instrumental in calibrating complex statistical models to the vast amounts of AMR-related data. Popular statistical models include hierarchical and mixture models as well as discrete and stochastic epidemiological compartmental and agent based models. Studies encompassed multi-drug resistance, economic implications of vaccines, and modeling AMR in vitro as well as within specific populations. We describe how combining these topics in a coherent framework can result in an effective antimicrobial stewardship. We also outline recent advancements in the methodology of Bayesian inference algorithms and provide insights into their prospective applicability for modeling AMR in the future.

Keywords: Antimicrobial resistance; Bayesian inference; Markov chain Monte Carlo; antimicrobial stewardship; approximate Bayesian computation; epidemiology; sequential Monte Carlo.

Figure 1

Two Markov chains with different initial starting points when sampling from a 𝒩(0, 1) when using (a) σ = 0.15, (b) σ = 1.5 and σ = 15 in the proposal distribution. The horizontal dashed red line is the true value. The average acceptance rate for both chains in subplots (a), (b) and (c) are 0.906, 0.602 and 0.084, respectively.

Figure 2

Sampling a 2-dimensional Gaussian distribution with Gibbs with 0 means for θ₁ and θ₂ for 50 MCMC iterations. The solid black lines show the trajectory between two successive accepted samples represented by the red dots.

Figure 3

HMC analogy: The starting position of the left most puck (red) in a frictionless bowl (black solid line) will have potential energy but no kinetic energy. As the puck follows the trajectory of the arrows, potential energy is changed to kinetic energy.

Figure 4

Sampling a 2-dimensional Gaussian distribution with HMC when (a) changing ϵ and L = 5 and (b) changing parameter L with ϵ = 0.1 for 10 MCMC iterations.

Figure 5. Toy example of using approximate Bayesian computation to estimate the parameters governing the linear relationship between antibiotic concentration and bacterial growth inhibition.

(a) The blue and red points are the accepted and rejected values, respectively. (b) Is the contour plot of the accepted values with the true set of values indicated by the red dot.

Figure 6

Two simulations of the discrete time approximation of the ODEs in (22) and (23) when β = 0.4, γ = 0.15 (dashed/dot lines) and β = 0.3, γ = 0.2 (solid lines).

Figure 7

Simulation of the discrete time approximation of the ODEs in (22) and (23). Hand hygiene by health-care workers is introduced at t = 80 (black dashed vertical line) with β = 0.3 and β = 0.1 pre and post hand hygiene intervention, respectively.