How local antibiotic use, carriage duration, resistance costs and international travel shape resistance frequency in E. coli in France

Reviewer #1 (Public review):

Summary:

The authors used a large dataset evaluating gut carriage of Enterobacterales and ESBL organisms from children aged 6-24 months as the basis for a modeling study to investigate what factors are most important for determining the prevalence of ESBL resistance. The modeling incorporated travel, a simple model of carriage duration (short and long), fitness cost of resistance on transmission and clearance, and antibiotic use. They found that antibiotic use is the primary driver of resistance prevalence, with transmissibility of resistant strains also important for setting the prevalence. Travel, while important when prevalence is very low, plays less of a role in maintaining prevalence once it is established (in keeping with other recent work). They estimated the fitness cost of resistance (terming a reduction of 14% on the rate of transmission and an increase of 23% on the rate of clearance as "low"). While the extent of assumptions and simplifications makes me skeptical of the quantitative conclusions, the qualitative ones seem reasonable and reinforce the long-held principles of the field--reducing antibiotic pressure and interrupting transmission--and highlight the importance of understanding the biological factors that shape the duration of carriage and the likelihood of colonization.

Strengths:

This study incorporates many of the factors that might influence the carriage prevalence of ESBL Enterobacterales. This builds on the work led by this group, both in primary data collection and in theory. Overall, it's such a tough problem that I commend the authors for trying to tackle it. The authors take a thoughtful, rigorous approach, acknowledging simplifications and assumptions where they need to, so as to evaluate the various factors shaping ESBL prevalence.

Weaknesses:

Part of the reason it's such a tough problem is that we have limited data to structure and parameterize a complex model.

(1) The data are not sufficiently described.

The primary data source for this modeling exercise comes from a study of 6-24-month-old children who underwent rectal swabs and evaluation of the carriage prevalence of Enterobacterales, and then whether these Enterobacterales were ESBL; moreover, the study included data on travel and on antibiotic use. Could the authors please direct us to these primary data? Could the authors also justify the parameters in their models from these data--for example, could they please provide the distribution of antibiotic use and the associated timing? Could they also explain why they decided to treat all Enterobacterales as if they were E. coli (line 307)? Is there evidence that all Enterobacterales occupy the same niche and compete with each other?

(2) The model should be more fully described and the limitations explored/explained.

- The authors should point to the code and the ODEs.
- I understand the focus on the pediatric population; the authors argue that this is reasonable because ESBL colonization is similar across age groups. But presumably, antibiotic use differs across age groups, and there is colonization pressure from within households.
- The authors only consider resistance to extended-spectrum beta-lactams and use of beta-lactam antibiotics, but ESBL Enterobacterales are often resistant to other antibiotics as well. How much does the use of other antibiotics also select for Enterbacterales that happen to carry ESBL resistance? "One bug/one drug" modeling, as done here, neglects the complexities of the actual patterns of resistance and range of antibiotic use.
- Do the data support the T3 or S3 compartments, which, if I understand correctly, means no exposure to antibiotics can happen during three months after either treatment or travel? What do the data say about the patterns of antibiotic use? I'd imagine that the likelihood of antibiotic use is not homogenous, but instead, there are some who use repeated rounds of antibiotics.
- Why do the authors exclude individuals who used antibiotics in the prior 7 days? What justifies that cutoff? The authors speculate that the impact of excluding these individuals is likely to be minimal; why exclude them, then? Did the authors evaluate the results if they were included?
- What is the basis of "niche differentiation", as described starting on line 221? Why should clearance of one strain be slower when the strain co-occurs in a host with a strain of another type?

Reviewer #2 (Public review):

Overview:

This study integrates several datasets into a unified modeling framework that incorporates several mechanisms thought to impact the spread of ESBL-resistant bacterial strains. The model accounts for tradeoffs between persistor and colonizer strains, travel rates, antibiotic treatment and strain clearance, direct competitive interactions, and, most importantly, a series of distinct costs associated with the carriage of ESBL resistance. The resulting 75-compartment model is internally consistent and structurally neutral. However, the parameter estimation is flawed in many ways, compromising the interpretations of the model.

On the usage of the Swedish infant data set to estimate colonization and persistence:

First, while other papers have taken similar approaches, the Swedish infant data set is fundamentally inadequate to estimate colonization and persistence rates. This is because very few colonies were typed per sampling event (2 to 6 colonies per event). The original authors themselves argued that strains of indistinguishable morphology would not be able to be differentiated by this method. They also provided data showing that strain identity was not directly related to colony morphology (same strain often displaying distinct morphologies).

The consequence of this is that strains present in low abundance would be missed with a high likelihood. However, if they were to be stochastically sampled, this would count as a "colonization" event, and if they were missed in subsequent samplings, this would count as a "loss" event. In other words, the statistical methods described conflate within-host dynamics (which might lead to distinct within-host abundances) with between-host dynamics (colonization and loss).

Beyond this conceptual issue, some technical aspects aren't particularly sound. The mean of the inferred posterior for the lambda and mu parameters are then used to calculate the beta, gamma, d, and epsilon parameters through a linear regression. The more technically correct way of doing this would be to directly infer these parameters from the data and obtain a full posterior for these parameters.

This highlights another issue: these parameters are passed down to the next statistical model as point estimates, with no associated uncertainty. This artificially inflates the (already low) confidence of the estimates for the cost parameters.

Finally, when this procedure generated parameters that were inconsistent with their expectations (clearance is too high to explain prevalence in France), they adjusted the parameters by discarding and recalculating their beta parameters to artificially enforce neutrality between their strains and enforce the expected prevalence. This is problematic because beta and gamma were jointly estimated, and there is no particular reason why some of them should be discarded. The more natural interpretation would be that parameters inferred from Swedish infants do not translate well to French adults, which should preclude their usage in this context.

On the estimation of costs of ESBL resistance:

The core of the second statistical model is to use prevalence data, travel data, and treatment data in conjunction with the previously inferred colonization and loss parameters to infer the costs of carrying antibiotic resistance. Therefore, the accuracy of this section is contingent on an accurate estimation of the previous parameters. However, these colonization and loss parameters are inherited with no uncertainty (just point estimates are passed down), which, as previously mentioned, generates an artificially precise posterior distribution for the resistance parameters.

However, the most severe issue with the statistics lies in the choice of priors for the cost parameters. All of them are uniform in a positive range that implies a positive cost. Importantly, the average over a positive range will always be positive; therefore, this method will ALWAYS estimate a positive mean for the costs. Note that the posterior distribution of some cost parameters seems to peak around zero and abruptly decays with no mass to the left of zero. This is caused by the choice of prior. Had delta been allowed to be negative (i.e., antibiotic resistance carried a benefit, having the prior be uniform between -1 and 1), the posterior distribution would likely be much more symmetrical, and the confidence interval would have included 0.

Restating, because the prior is a continuous function between 0 and 1, it contains infinitely more mass in the region that represents there being a cost (delta>0) than in the region representing no cost (delta=0). This means that it is a mathematical impossibility for this model to infer the absence of a cost.

Therefore, the main finding of the paper ("We found that resistance is costly") is a mathematical artifact of the prior choice and of the model structure.

Reviewer #3 (Public review):

Cotto and colleagues integrated data analysis with mathematical modeling to examine extended-spectrum beta-lactamase (ESBL)-producing E. coli in France. While ESBL prevalence has risen globally, it has stabilized at approximately 6-8% across Europe. Established risk factors for ESBL carriage include prior antibiotic exposure and travel to high-prevalence regions, most notably South-East Asia. The dataset incorporated information on ESBL-producing E. coli and travel history in young children, and the model was calibrated to ECDC surveillance data on ESBL across Europe, supplemented by literature-derived parameters on antibiotic use, E. coli biology, and transmission dynamics. The authors report that ESBL-carrying strains exhibit a 14% fitness cost in community transmission relative to susceptible bacteria, yet are cleared 23% less frequently. ESBL carriage was strongly associated with factors that prolong gut colonization. Both antibiotic treatment rates and transmission efficiency were identified as key determinants of community-level ESBL prevalence.

Strengths:

The study addresses a clinically and epidemiologically important topic. The integrated modeling approach is methodologically sound and well-suited to disentangling the relative contributions of transmission and antibiotic selection pressure.

Weaknesses:

Several concerns regarding the data used in this study warrant consideration. First, model calibration relied on ECDC surveillance data pooled across multiple European countries, several of which have substantially lower antibiotic consumption than France (ECDC ESAC-Net Annual Epidemiological Report, 2024). Given that antibiotic use is a primary driver of ESBL selection, ESBL prevalence is likely to be heterogeneous across these settings. Calibrating to a geographically diverse dataset risks introducing systematic bias into parameter estimates that may not be representative of the French context. The authors should repeat the analysis using France-specific data, or, where this is not feasible, restrict the calibration dataset to countries with comparable antibiotic consumption profiles. Second, the travel exposure data may be insufficient to adequately capture importation dynamics from South-East Asia, as the cohort consisted exclusively of young children, a demographic less likely to travel to high-prevalence regions than older age groups. This may result in an underestimation of travel-associated importation as a contributor to community ESBL prevalence, and the generalizability of these findings to the broader population should be interpreted with caution.

Author Response:

We thank you for this assessment of our work and the positive assessment of the overall theoretical framework. We can fully answer the concerns, in particular regarding data quality, and will provide detailed answers in the following directions:

“insufficient description of the data”: We will describe the data as much as possible and will share the data and the analysis code.

“lack of included equations and code”:  We will share the mathematical equations in the supplementary material, and the full code on an online repository. The reason why our data repository (10.5281/zenodo.18480481) is not yet public is that it cannot be changed after publication. For the review process, we provide a github link to data and code here https://github.com/oliviercotto/eLife_epidR. We will ultimately share the link to the final version of the files on Zenodo.

“definitions of antibiotic use that are not complete”: We will complete the definition of antibiotic use, which is the use of any antibiotic between 7 days and 3 months before sampling. Children who used any antibiotic 7 days before sampling were not included in the study. The type of antibiotic used is given in supplementary material S1: 93% of the antibiotics prescribed are beta-lactams (amoxicillin, amoxicillin/clavunalate, oral 3rd generation cephalosporins).

“low sensitivity of assays for carriage”: the carriage study conducted in Sweden is used to get plausible estimates of carriage duration parameters in infants.

• Strain definition is based mainly on randomly amplified polymorphic DNA (RAPD), not colony morphology. Strains with distinct morphology but the same RAPD profile are considered one strain. Conversely, it was checked that strains of the same timepoint with the same morphology most often had the same RAPD profile.

• We did check that these data are not much affected by imperfect sampling: observations of a strain ‘disappearing’ from sampling then ‘reappearing’  at later timepoints are rare (14 out of 273 strains). This is why we did not correct these occurrences in the previous version of the analysis. In the revised version, we will add a description of these occurrences and correct them. This correction did not significantly alter the inferred parameters in our preliminary analyses.

• At a broad level, the fact that E. coli clades vary in their carriage duration is very well established across multiple independent datasets; the precise value of carriage duration difference for “persistent” vs. “transient” that we inferred here (a two-fold difference, supplementary material S3) is actually relatively conservative, in the sense that other studies have detected more important differences. We will create a table summarising available evidence on colonization parameters of E. coli to show that the insights from the Swedish data are qualitatively robust.

• Yet, we will conduct a range of sensitivity analyses to see how the inferred costs of ESBL resistance vary when varying differences in carriage durations, competition and niche differentiation.

“technical issues with statistical prior selection and parameter identification”: We disagree there is a “technical issue” with prior selection: The fact that resistance is costly, hence that our priors are left-bounded at 0 for the cost parameters, is a prior expectation based on the observation that resistances do not go to fixation. If resistances only conferred an advantage in treatment, but zero cost, then they would quickly evolve to 100% frequency–contrary to what is observed in virtually all epidemiological studies of resistance. That said, we will relax the definition of these priors to test that the data is also compatible with a strong cost on some traits, and no cost or a “negative cost” on other traits.

Regarding parameter identification and the specific comments on the inference of colonisation parameters: we re-inferred all colonisation parameters with direct inference assuming specific functional forms. This does not alter much the final colonisation parameters that we then use for our main inference. We will also conduct sensitivity analyses to examine how changing some of the colonisation parameters (carriage duration, competition and niche differentiation)  would alter the main inference.

“application of non-regional ECDC surveillance data to France”: We will clarify our text, as there is a misunderstanding here: we do not use non-regional ECDC surveillance data for inference. We use ECDC data (i) for illustrative purposes, to show that trends in ESBL in France in this surveillance system are very similar to those observed in France in our focal dataset, thus showing the consistency and representativeness of our data. (ii) to give an overview of the weak and inconsistent association of ESBL with age across Europe, thus supporting the relevance of our approach even if our data concerns infants and children. We will make sure this is clarified in the updated version of the manuscript.