A dose response model for quantifying the infection risk of antibiotic-resistant bacteria

Quantifying the human health risk of microbial infection helps inform regulatory policies concerning pathogens, and the associated public health measures. Estimating the infection risk requires knowledge of the probability of a person being infected by a given quantity of pathogens, and this relationship is modeled using pathogen specific dose response models (DRMs). However, risk quantification for antibiotic-resistant bacteria (ARB) has been hindered by the absence of suitable DRMs for ARB. A new approach to DRMs is introduced to capture ARB and antibiotic-susceptible bacteria (ASB) dynamics as a stochastic simple death (SD) process. By bridging SD with data from bench experiments, we demonstrate methods to (1) account for the effect of antibiotic concentrations and horizontal gene transfer on risk; (2) compute total risk for samples containing multiple bacterial types (e.g., ASB, ARB); and (3) predict if illness is treatable with antibiotics. We present a case study of exposure to a mixed population of Gentamicin-susceptible and resistant Escherichia coli and predict the health outcomes for varying Gentamicin concentrations. Thus, this research establishes a new framework to quantify the risk posed by ARB and antibiotics.


Supplementary Materials
Datasets used in this study ID [Ref] Dose n ill n tot t fs (days)    Suppose we are interested in calculating the response for a pathogen. It is present in an exposure case with d = 1000, with 20% of the pathogen being resistant to an antibiotic, and the concentration of antibiotic is C = 0.025 × MIC (2 µg mL −1 ) = 0.05µg/mL.
• Identify dose-response data for the pathogen. This can be like DS1 or DS2 listed in Table S1.
• Identify t fs . This is the latest time at which some subject shows the rst symptom. Suppose t fs = 1 day • Identify E max and EC 50 for the antibiotic-pathogen combination of interest. Suppose E max = = 1224 day −1 and EC 50 = 9.93 mg L −1 = 9.93 µg mL −1 .
• Fit both exponential and β-Poisson models to this dataset and identify the best tting model, using methods outlined in [2].
• If best tting model is exponential, go to section titled "Using exponential DRM". If best tting model is β-Poisson, go to section titled "Using β-Poisson DRM".
Our sensitivity analyses indicate that getting approximate values for t fs are sucient to predict response. However, it's value is critical to accurately estimate death rate (µ) if using the exponential DRM.

Using exponential DRM
The exponential model is given by: Suppose the best t for r is given byr = 1.07 × 10 −8 .
• Compute µ by solving • Compute total response probability with P (d|f r , C) = 1 − P ext,s (d|f r , C)P ext,r (d|f r , C) ≈ 0.067241497 • If 1 − P ext,s (d, t|f r , C) P ext,r (d, t|f r , C) > (1 − P ext,r (d, t|f r , C)), illness is AB treatable. If not, illness is not AB treatable. In this case, this condition evaluates to False and hence the illness is likely not AB treatable.
Using β-Poisson DRM The β-Poisson DRM is given by Suppose the best t parameters areα ≈ 0.1615058 andβ = 1414958. Computing response probabilities is more involved and requires access to a function that can t a beta distribution, such as the fitdistrplus package in R ( [3]).
• From the values ofα,β, E max, EC 50 and C, compute α s and β s for the susceptible subpopulation. For this, use the algorithm outlined in the Methods section. We get α s = 0.1613020 and β s = 1.295420 × 10 13 .
• Compute extinction probabilities for the susceptible and resistant subpopulations using and P ext,r (d|f r , C) = 1 + d × f r β r −αr ≈ 0.999977202 • Compute total response probability with P (d|f r , C) = 1 − P ext,s (d|f r , C)P ext,r (d|f r , C) ≈ 2.28 × 10 −5 • If 1 − P ext,s (d, t|f r , C) P ext,r (d, t|f r , C) > (1 − P ext,r (d, t|f r , C)), illness is AB treatable. If not, illness is not AB treatable. In this case, this condition evaluates to False and hence the illness is likely AB untreatble.