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. 2020 Apr 3;17(4):e1003077. doi: 10.1371/journal.pmed.1003077

Adaptive guidelines for the treatment of gonorrhea to increase the effective life span of antibiotics among men who have sex with men in the United States: A mathematical modeling study

Reza Yaesoubi 1,*, Ted Cohen 2, Katherine Hsu 3, Thomas L Gift 4, Harrell Chesson 4, Joshua A Salomon 5, Yonatan H Grad 6
Editor: Nicola Low7
PMCID: PMC7122693  PMID: 32243443

Abstract

Background

The rise of gonococcal antimicrobial resistance highlights the need for strategies that extend the clinically useful life span of antibiotics. Because there is limited evidence to support the current practice of switching empiric first-line antibiotic when resistance exceeds 5% in the population, our objective was to compare the impact of alternative strategies on the effective life spans of antibiotics and the overall burden of gonorrhea.

Methods and findings

We developed and calibrated a mathematical model of gonorrhea transmission among men who have sex with men (MSM) in the United States. We calibrated the model to the estimated prevalence of gonorrhea, the rate of gonorrhea cases, and the proportion of cases presenting symptoms among MSM in the US. We used this model to project the effective life span of antibiotics and the number of gonorrhea cases expected under current and alternative surveillance strategies over a 50-year simulation period. We demonstrate that compared to the current practice, a strategy that uses quarterly (as opposed to yearly) surveillance estimates and incorporates both the estimated prevalence of resistance and the trend in the prevalence of resistance to determine treatment guidelines could extend the effective life span of antibiotics by 0.83 years. This is equivalent to successfully treating an additional 80.1 (95% uncertainty interval: [47.7, 111.9]) gonorrhea cases per 100,000 MSM population each year with the first-line antibiotics without worsening the burden of gonorrhea. If the annual number of isolates tested for drug susceptibility is doubled, this strategy could increase the effective life span of antibiotics by 0.94 years, which is equivalent to successfully treating an additional 91.1 (54.3, 127.3) gonorrhea cases per 100,000 MSM population each year without increasing the incidence of gonorrhea. Study limitations include that our conclusions might not be generalizable to other settings because our model describes the transmission of gonorrhea among the US MSM population, and, to better capture uncertainty in the characteristics of current and future antibiotics, we chose to model hypothetical drugs with characteristics similar to the antibiotics commonly used in gonorrhea treatment.

Conclusions

Our results suggest that use of data from surveillance programs could be expanded to prolong the clinical effectiveness of antibiotics without increasing the burden of the disease. This highlights the importance of maintaining effective surveillance systems and the engagement of policy makers to turn surveillance findings into timely and effective decisions.

Reza Yaesoubi and colleagues study possible approaches to delaying the appearance of antimicrobial resistance in treatment of gonorrhea.

Author summary

Why was this study done?

  • Gonorrhea is the second most common notifiable disease in the United States and has developed resistance to all first-line antibiotics.

  • The selection of antibiotics used for gonorrhea treatment is almost always empiric and based on guideline recommendations.

  • There is limited evidence to support the current practice of switching the first-line antibiotic after resistance to it exceeds 5% in annual surveillance estimates.

  • Our objective was to project how alternative strategies to inform the first-line treatment recommendations impact the life span of antibiotics and the overall burden of gonorrhea.

What did the researchers do and find?

  • We developed a mathematical model that describes the key characteristics of gonorrhea transmission among men who have sex with men (MSM) in the United States.

  • Our model estimates the life span of antibiotics and the incidence of gonorrhea under current and alternative strategies for changing first-line empiric antibiotic treatment.

  • We found that compared to the current practice, a strategy that 1) uses quarterly surveillance estimates and 2) incorporates both the estimated prevalence of resistance and the trend in the prevalence of resistance to determine treatment guidelines could extend the effective life span of antibiotics without worsening the burden of gonorrhea.

What do these findings mean?

  • This work suggests an opportunity to optimize the use of surveillance systems to slow the spread of antibiotic-resistant strains and control the burden of gonorrhea.

  • This requires enhancing the surveillance systems (e.g., by allowing for more frequent reporting of estimates and a larger number of observations) and the engagement of policy makers to turn surveillance findings into timely decisions.

  • Further studies are needed to investigate the generalizability of these conclusions.

Introduction

Gonorrhea remains a globally significant sexually transmitted infection (550,000 reported cases in 2017 in the United States [1] and an estimated 87 million cases worldwide in 2016 [2]), and the recent descriptions of resistance to standard treatments has raised concern about the global emergence of untreatable infections [3,4]. The threat of spread of untreatable gonococcal infections highlights the need for strategies to maximize the life span of existing antibiotics while providing effective treatment for infected individuals.

The selection of antibiotics used for gonorrhea treatment is almost always empiric and based on guideline recommendations because the diagnosis is usually made by nucleic acid amplification test, which does not inform on antibiotic susceptibility [5–7]. Even when culture is available, patients likely receive first-line empiric antibiotic treatment while awaiting drug-susceptibility results. In the US, current treatment guidelines are based on the prevalence of antimicrobial resistance estimated by the Gonococcal Isolate Surveillance Project (GISP) [8], a sentinel surveillance system that monitors trends in antimicrobial susceptibilities of gonococcal strains in the US [9].

Once the point estimate for prevalence of resistance to the first-line antibiotic exceeds 5% [8,10], the WHO guideline recommends switching to another antibiotic for empiric treatment [10]. However, there is limited evidence to support this 5% threshold. Increasing the threshold may extend the life span of second-line antibiotics by minimizing the use of these agents but at the cost of decreasing the probability that any given individual with gonorrhea receives effective first-line therapy. This could be associated with greater individual morbidity and may also lead to longer durations of infectiousness, facilitating further transmission of gonorrhea. In contrast, decreasing the switching threshold may increase the probability that each individual receives effective first-line therapy but also would lead to earlier and more extensive use of second-line regimens, which would be expected to shorten their life span. Beyond the cross-sectional resistance proportion, other easily observed features of resistance emergence, such as tempo of change, could also be considered in designing optimal switching policy. A rapid rise in resistance proportion, e.g., might prompt an earlier switch in recommended antibiotics than a slow increase [11].

In this study, we used a transmission dynamic model to compare the performance of different decision rules that could inform the recommendations for the first-line therapy of gonococcal infections. Specifically, we considered whether the current switching strategy based on the 5% threshold from annually reported surveillance efforts is outperformed by policies that i) use different thresholds for the percentage of isolates that are resistant, ii) incorporate information on the trend in the percentage of isolates that are resistant, and iii) increase the frequency and/or size of drug resistance surveys.

Methods

Treatment of gonococcal infections

We considered a scenario in which 3 antibiotic drugs (drug A, drug B, and drug M) are available for treatment of gonorrhea. Drug A represents first-line therapy, such as ceftriaxone or azithromycin [12], and drug B represents an alternative antibiotic that may be suitable for the first-line treatment of gonorrhea, such as zoliflodacin [13] or gepotidacin [14], both of which have been over 95% effective against urogenital gonococcal infections in phase 2 trials. Drug M represents the last-line antibiotic for gonorrhea.

We assumed that drug B would be initially reserved for treatment of cases that fail treatment with drug A. The selective pressure for resistance to drug A increases as more cases of gonorrhea are treated with this drug. Following the current strategy [8,10], one would remove drug A from clinical use and replace it with drug B once a specific threshold for resistance to drug A is exceeded. Subsequently, those who fail first-line treatment with drug B will be retreated with drug M. Likewise, when the prevalence of resistance to drug B reaches a predefined threshold, drug B will be removed from the first-line therapy, and drug M will be used for both first-line and second-line therapy.

Adaptive guidelines to inform first-line treatment recommendations

An efficient strategy to guide the first-line treatment recommendations strikes a balance between the need to maximize the effective lives of drugs A and B with the goal of treating gonococcal infections with the most effective drug available. An adaptive guideline identifies the first-line therapy drug based on cumulative observations on the resistance characteristics of the ongoing gonorrhea epidemic. In this study, we compared the performance of 4 types of adaptive guidelines in terms of their ability to prolong the effective life of drugs A and B and to prevent gonorrhea (Table 1).

Table 1. Adaptive guidelines to inform first-line treatment recommendations for gonorrhea.

Strategies Frequency of Decision-Making Annual Number of Tests for Resistance Epidemiolocal Estimates Used for Decision-Making Policy Examples
Threshold—annual Annually 5,000 Estimate of resistance prevalence Switch to a new first-line drug when the point estimate of the proportion of resistant isolates exceeds τ%.
Threshold—quarterly Quarterly 5,000 Same as Threshold Same as Threshold.
Threshold + trend Annually 5,000 Estimate of resistance prevalence and change in the estimate of resistance prevalence Switch to a new first-line drug when point estimate of the proportion of resistant isolates exceeds τ% or the change in the estimate of resistance since the last decision point exceeds θ percentage point.
Enhanced threshold + trend Quarterly 10,000 Same as “Threshold + trend” Same as “Threshold + trend.”
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The strategies “Threshold—annual” and “Threshold—quarterly” represent the guidelines that recommend switching to a new first-line drug once the resistance prevalence passes a certain threshold (e.g., 5%) [8,10]. They differ in how frequently the estimates of resistance prevalence are obtained and treatment recommendations are updated. The strategy “Threshold—annual” with a value of 5% represents the current practice because the estimates of resistance prevalence from surveillance systems (such as GISP in the US) become available on a yearly basis. The “Threshold—quarterly” policy relies on the same annual number of susceptibility tests as in “Threshold—annual,” but it distributes them over 4 quarters. Therefore, it might be able to detect trends in resistance more quickly but at the expense of lowering the precision in the estimates of resistance prevalence.

The strategy “Threshold + trend” seeks to detect the emergence of resistance to the first-line drug more proactively by using both estimates of resistance prevalence and the change in the resistance prevalence since the last year. An example of this strategy may recommend switching to a new first-line drug when point estimate of the proportion of resistant isolates exceeds 5% or the change in the estimate of resistance since the last decision point exceeds 1 percentage point. By accounting for the temporal change in resistance, this strategy is more responsive to the rapid spread of resistant gonococcal infection.

The strategy “Enhanced threshold + trend” is the same as strategy “Threshold + trend,” except that the evaluation of resistance prevalence is performed quarterly, with twice as many annual susceptibility tests as in the strategy “Threshold + trend.” Compared to the “Threshold + trend” strategy, the “Enhanced threshold + trend” strategy benefits from more frequent and a larger number of observations, which might facilitate the detection of statistically significant trends.

A gonorrhea transmission dynamic model

To evaluate the impact of these strategies on the overall burden of gonorrhea and antibiotic life spans, we developed a stochastic compartmental model that describes the transmission of Neisseria gonorrhoeae among men who have sex with men (MSM) in the US (Fig 1). About 42% of gonorrhea cases in 2017 were among MSM, and the emergence of resistance among this population is of particular concern [1,5]. The model is adapted from Tuite and colleagues [15], with additional details necessary to evaluate the strategies described in Table 1.

Fig 1. A stochastic gonorrhea transmission model.

Fig 1

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Dotted arrows represent new infection, and red arrows represent resistance acquisition while under treatment. S represents susceptibles, I0 represents drug-susceptible infections, and IA, IB, and IAB represent infections resistant to drug A, drug B, and both. Tx A, Tx B, and Tx M denote treatment with drugs A, B, and M. The expanded model structure is displayed in S1 Fig in S1 Text. The model is adapted from [15], with additional details necessary to evaluate the strategies in Table 1.

In our model, susceptible individuals are at risk of infection with gonorrhea, and this risk varies by the prevalence of infection. Infected cases can be symptomatic or asymptomatic (Fig 1A). Infected individuals are further divided to represent the resistance profile of the infecting strain: drug-susceptible infection (I0), infection resistant to drug A (IA), infection resistant to drug B (IB), and infection resistant to both drugs A and B (IAB) (Fig 1B). Asymptomatic cases do not seek treatment and remain infectious until they recover spontaneously or get detected through active screening (Fig 1A). All symptomatic cases are assumed to seek treatment with some delay. Cases who seek treatment or are detected through screening will receive treatment with drug A, B, or M, depending on the current recommendation for the first-line therapy. If treated with an antibiotic to which the infecting strain is susceptible, the individual returns to the susceptible state. A portion of symptomatic individuals who fail the first-line treatment (because of receiving ineffective treatment or developing resistance) will seek retreatment with some delay. As soon as effective treatment is initiated, we assume that infected individuals no longer contribute to the force of infection (because of either negligible infectiousness and/or reduced sexual activity).

Resistance may arise while an individual receives antibiotic treatment (Fig 1B). To account for the fitness cost associated with resistance, we assumed that compared to susceptible strains, resistant strains are less transmissible [15], at least initially. Data from GISP indicate that despite the decrease in the use of tetracycline, penicillin, ciprofloxacin, cefixime, ceftriaxone, and azithromycin in recent years, the prevalence of resistance to these antibiotics has been fairly stable [1]. To produce simulated trajectories that allow for this persistence despite reduced use of these antibiotics, we allow the fitness cost of resistance to gradually decrease, consistent with the idea that the fitness costs may be compensated (see S1.3 of S1 Text) [16]. Additional details about the model are provided in S1 Text.

Model calibration and validation

We used a Bayesian approach to calibrate our model against estimates of gonorrhea prevalence, the rate of reported gonorrhea cases in 2017, and the proportion of gonorrhea cases with symptoms. This calibration approach seeks to estimate the probability distributions of unknown parameters that result in simulated trajectories with good fit to the available epidemiological data [17]. We chose prior parameter distributions based on the available data, estimates and plausible ranges extracted from the literature, and expert opinion when estimates were unavailable (see S1 Text for additional details).

Comparing the performance of guidelines to inform first-line treatment recommendations

We compare the performance of strategies to inform the first-line treatment recommendations (Table 1) based on the number of gonorrhea cases that could be averted with respect to the status quo (the “Threshold—annual” strategy in Table 1 with 5% switch threshold) and the increase in the effective life of drugs A and B. To measure the effective life of antibiotics, we note that the consumption of drug M is inversely related to the effective life span of drugs A and B. If resistance to drugs A and B rises quickly, implying a short effective life span for these drugs, all future cases of gonorrhea will be treated with drug M. We therefore defined the effective life span of drugs A and B as the area under the curve of the annual percentage of gonorrhea cases that are successfully treated with drugs A or B over 50 years of simulation (i.e., ∑t=150NA(t)+NB(t)NA(t)+NB(t)+NM(t), where NA(t), NB(t), and NM(t) are the number of gonorrhea cases treated successfully with drugs A, B, or M in simulation year t).

If a strategy extends the effective life span of drugs A and B by ΔL years, we estimate the number of additional cases of gonorrhea that would be treated successfully with first-line antibiotics under this strategy with S0ΔLL0, where S0 is the number of cases successfully treated with drugs A or B and L0 is the effective life span of drugs A and B under the status quo.

The simulation window of 50 years was selected to ensure enough time for the resistance to emerge against drug A and drug B (in a sensitivity analysis, we set the simulation window at 25 years). We summarized results using the mean and 95% uncertainty interval (i.e., the interval between 2.5th and 97.5th percentiles of realizations) across 500 simulated trajectories. For the “Threshold + trend” and “Enhanced threshold + trend” strategies (Table 1), the 2 thresholds used to inform switching (i.e., threshold for resistance prevalence and the threshold for change in the resistance prevalence) are determined using the optimization algorithm described in S4 of S1 Text.

Results

We fitted our model against gonorrhea prevalence, the rate of reported gonorrhea cases in 2017, and the proportion of gonorrhea cases with symptoms and estimated the proportion of cases resistant to drugs A, B, or both when 5,000 annual gonorrhea cases are tested for drug resistance during each simulation (Fig 2). We used 5,000 annual cases based on how many N. gonorrhoeae isolates were collected and tested through GISP in 2014 (5,093 isolates) [5].

Fig 2. Displaying 100 simulated trajectories from the calibrated model.

Fig 2

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The green dots in panels A–C represent the data or estimates the model is calibrated against: gonorrhea prevalence (2.0% [1.2%, 2.8%] [18,19] of MSM), the estimated rate of gonorrhea cases in 2017 (5,241.8 cases per 100,000 MSM [1]), and the proportion of gonorrhea cases among MSM that are symptomatic (67.9% [64.4%–71.4%] [20]). In these simulated trajectories, the first-line treatment is changed when more than 5% of the annual gonorrhea cases are resistant to the first-line drug. MSM, men who have sex with men.

In Fig 3A, we report the tradeoff between increasing the effective life span of antibiotics and reducing the annual incidence of gonorrhea. The origin in this figure represents the status quo, in which switching policies are triggered when greater than 5% of the isolates tested are resistant [8,10]. Increasing this resistance-prevalence threshold for switching to new antibiotic drugs (moving toward the top-right corner of Fig 3A) increases the effective life span of drugs A and B by using the existing drugs for a longer period. Increasing this switching threshold, however, leads to increases in the expected number of annual gonorrhea cases because delaying the switch to a new antibiotic drug lowers the probability of receiving an effective first-line therapy, thereby extending the expected duration of infectiousness while these cases await detection of treatment failure and treatment with effective second-line therapy. The blue curve in Fig 3A has a slope of 15.3 at the origin. This implies that the 5% switch threshold represents a sacrifice of the effective life span of drugs A and B by 1 year to avert an additional 15.3 gonorrhea cases per 100,000 MSM population per year.

Fig 3. Comparing the performance of policies in Table 1 with respect to the current policy.

Fig 3

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The origins in these figures reflect the current policy that recommends switching the antibiotic used for empiric treatment once the estimated resistance prevalence exceeds 5% [8,10]. The numbers on the curves of “Threshold—annual” and “Threshold—quarterly” strategies represent the threshold of resistance prevalence to switch the first-line therapy of gonorrhea, and the 2 numbers on the curves of “Threshold + trend” and “Enhanced threshold + Trend” strategies represent the 2 thresholds used to inform switching: resistance prevalence (first %) and percentage point change in the resistance prevalence (second %). S6 Fig in S1 Text shows that the comparative performance of these strategies is maintained when the simulation length is reduced from 50 years to 25 years. MSM, men who have sex with men.

Fig 3A also demonstrates that increasing the frequency at which first-line therapy recommendations are revisited could lead to a substantial increase in the effective life span of drugs A and B without increasing the number of gonorrhea cases. Compared to the current policy, the “Threshold—quarterly” strategy could increase the effective life span of drugs A and B by 0.82 years without increasing the number of gonorrhea cases (this is measured as the horizontal distance between the points where the curves in Fig 3A crosses the x-axis). This is equivalent to successfully treating an additional 79.6 (47.4, 111.2) gonorrhea cases per 100,000 MSM population each year with drugs A and B without worsening the burden of gonorrhea.

Fig 3B shows that the “Threshold + trend” strategy, which uses both the resistance prevalence and the change in resistance prevalence since the last year, outperforms the “Threshold—annual” strategy. Compared to the status quo, the “Threshold + trend” strategy could increase the effective life span of drugs A and B by 0.83 years (which is equivalent to successfully treating an additional 80.1 (47.7, 111.9) gonorrhea cases per 100,000 MSM population each year with drugs A and B) without increasing the incidence of gonorrhea. Specifically, the “Threshold + trend” strategy, which removes an antibiotic from the first-line therapy either when the resistance prevalence exceeds 10.1% or when the increase in the resistance prevalence from last year is greater than 1.6 percentage points, is expected to increase the effective life of drugs A and B while preventing gonorrhea cases compared with the status quo.

Fig 3C demonstrates that the benefits of the “Threshold + trend” strategy can be enhanced when the evaluation of resistance prevalence is performed quarterly, and the annual number of gonorrhea cases tested for drug susceptibility is doubled. Compared to the current approach, the “Enhanced threshold + trend” strategy could increase the effective life span of drugs A and B by 0.94 years (which is equivalent to successfully treating an additional 91.1 (54.3, 127.3) gonorrhea cases per 100,000 MSM population each year with drugs A and B) without worsening the burden of gonorrhea.

Discussion

We used a mathematical model of gonorrhea transmission to evaluate how different strategies to inform recommendations for the first-line treatment of gonorrhea would impact the effective life span of antibiotics and the incidence of gonorrhea in the US MSM population. We used a Bayesian approach to calibrate the model to the estimated prevalence of gonorrhea, the rate of gonorrhea cases, and the proportion of cases presenting symptoms among MSM in the US. We examined alternative strategies to inform the timing of shifts in first-line treatment regimen. These strategies respond to the data from surveillance systems 1) by revisiting the treatment guidelines more frequently (quarterly versus annually) or 2) by considering not only the current resistance prevalence but also the increase in resistance prevalence since the last decision point to inform the first-line treatment recommendations. Our analysis showed that these adaptive strategies could extend the effective life spans of existing antibiotics for the treatment of gonorrhea without exacerbating the burden of gonorrhea.

In the absence of rapid drug-susceptibility testing to determine the resistance profile of a gonococcal infection, the treatment of gonorrhea remains empiric and based on population surveillance. Historically, once the estimated resistance prevalence for the recommended first-line antibiotic exceeds 5%, it is replaced in the guidelines by a regimen with lower levels of population-wide resistance [8,10]. Our analysis suggests that the optimal choice of this threshold requires a tradeoff between the effective life span of antibiotics and the incidence of gonorrhea. Increasing this switch threshold would increase the effective life span of existing antibiotics but could also increase the burden of gonorrhea; conversely, decreasing this switch threshold would prevent more gonorrhea cases but at the expense of reducing the effective life span of existing antibiotics. Using our mathematical model, we estimated that the 5% switch threshold currently used represents a tradeoff of forgoing a year of the effective life of existing antibiotics to avert an additional 15.3 cases of gonorrhea per year per 100,000 MSM population. Different decision rules could improve this relationship.

Our analysis has a number of limitations. Our mathematical model describes the transmission of N. gonorrhoeae only among MSM in the US. The burden of gonorrhea and drug-resistant gonorrhea is particularly high in this subpopulation [1,5], and hence, our conclusions might not be generalizable. For populations with lower burden of the disease, the benefits of adaptive strategies might diminish as the consequences of making suboptimal decisions would be less severe. While data from surveillance systems indicate an upward trend in the rate of gonorrhea cases among MSM [1], we assumed that the incidence and prevalence of gonorrhea among this population are expected to be relatively stable around the 2017 estimates (Fig 3). We did not model specific antibiotics and instead chose to model hypothetical drugs with characteristics similar to the antibiotics commonly used in treatment of gonorrhea. This allowed us to better capture the uncertainty in the characteristics of current and future antibiotics drugs (e.g., probability of resistance from treatment).

Current US Centers for Disease Control and Prevention (CDC) treatment guidelines for gonorrhea recommend dual therapy with ceftriaxone and azithromycin, but our decision model assumes that first-line therapy consists of only one antibiotic, such as the guidelines now in place in the United Kingdom [21]. Although our approach considers single antibiotic treatment for clarity, it can be extended to scenarios in which combination therapy is the first-line gonorrhea treatment. We assumed that once an antibiotic treatment for gonorrhea is abandoned because of the level of resistance, it will not be reintroduced. However, alternative stewardship and diagnostic strategies (e.g., the use of sequence-based diagnostics to identify the resistance profile [22]) suggest the possibility of reintroduction of these antibiotics; e.g., a recent modeling study suggests that cefixime, which had previously been removed from clinical use because of increasing levels of resistance, could be reintroduced to treat a minority of cases, assuming that cefixime resistance incurs a fixed fitness cost [23].

Our model did not account for site-specific infections, although the percent of infections that are asymptomatic varies by anatomic sites [24–26]. While we assumed that estimates of resistance prevalence calculated from GISP data are representative of the MSM population, GISP includes isolates from the first 25 men (not only MSM) who have been diagnosed with urethral gonorrhea after attending sexually transmitted disease clinics in select US cities. Our model assumes complete adherence to the first-line treatment guidelines. While the actual treatment regimens used in the population may differ from the recommended guidelines, recent studies estimate the adherence to the CDC guideline for the treatment of gonorrhea to be around 80% [27]. Relaxing these assumptions could improve the accuracy of projections made by our model, but it is not expected to significantly affect the comparative evaluation of strategies considered here.

Enhancing surveillance systems to enable more frequent reporting and evaluation of more gonococcal isolates would increase the cost of surveillance. While the cost effectiveness of these proposed changes needs to be studied, the analysis presented here highlights the importance of maintaining effective surveillance systems and the engagement of policy makers to turn surveillance findings into timely decisions to better control the spread of drug-resistant gonorrhea [28]. In the future, decision support tools like the one we proposed in this paper could help policymakers to respond more efficiently to the rise of antibiotic-resistant gonorrhea in a way that could prolong the effective life span of existing antibiotics and control the burden of the disease.

While we await a breakthrough (new antimicrobial agents, novel molecular assays to determine susceptibility to antimicrobial agents, or a gonococcal vaccine), it is important to optimize the use of surveillance systems to minimize the burden of gonorrhea and to slow the spread of antibiotic-resistant strains. We demonstrated the potential for data from surveillance programs to be used in a more efficient and active way to prolong the effective life spans of existing antibiotics without increasing the burden of the disease.

Supporting information

S1 Text. Additional details on model structure, calibration procedure, and the algorithm to identify adaptive policies.

(PDF)

Click here for additional data file. (868.1KB, pdf)

Acknowledgments

Disclaimer: The findings and conclusions in this article are those of the authors and do not necessarily represent the official position of the Centers for Disease Control and Prevention or the U.S. Department of Health and Human Services.

Abbreviations

CDC

Centers for Disease Control and Prevention

GISP

Gonococcal Isolate Surveillance Project

MSM

men who have sex with men

Data Availability

The data underlying the results presented in the study are available from the Gonococcal Isolate Surveillance Project (https://www.cdc.gov/std/gisp/default.htm) and Sexually Transmitted Disease Surveillance 2018 (https://www.cdc.gov/std/stats18/).

Funding Statement

This work was supported by the U.S. Centers for Disease Control and Prevention (CDC), National Center for HIV, Viral Hepatitis, STD, and TB Prevention Epidemiologic and Economic Modeling Agreement (5NU38PS004644, https://www.cdc.gov/nchhstp/neema) to JAS. The Centers for Disease Control and Prevention contributed to study design and preparation of the manuscript. RY was supported by 1K01AI119603, YHG by R01 AI132606, and TC by R01 AI112438, all from the National Institute of Allergy and Infectious Diseases (https://www.niaid.nih.gov/). The National Institute of Allergy and Infectious Diseases had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Decision Letter 0

Thomas J McBride

27 Sep 2019

Dear Dr. Yaesoubi,

Thank you very much for submitting your manuscript "Adaptive guidelines for the treatment of gonorrhea to increase the effective lifespan of antibiotics: A mathematical modeling study" (PMEDICINE-D-19-02321) for consideration at PLOS Medicine.

Your paper was evaluated by a senior editor and discussed among all the editors here. It was also discussed with an academic editor with relevant expertise, and sent to three independent reviewers, including a statistical reviewer. The reviews are appended at the bottom of this email and any accompanying reviewer attachments can be seen via the link below:

[LINK]

In light of these reviews, I am afraid that we will not be able to accept the manuscript for publication in the journal in its current form, but we would like to consider a revised version that addresses the reviewers' and editors' comments. Obviously we cannot make any decision about publication until we have seen the revised manuscript and your response, and we plan to seek re-review by one or more of the reviewers.

In revising the manuscript for further consideration, your revisions should address the specific points made by each reviewer and the editors. Please also check the guidelines for revised papers at http://journals.plos.org/plosmedicine/s/revising-your-manuscript for any that apply to your paper. In your rebuttal letter you should indicate your response to the reviewers' and editors' comments, the changes you have made in the manuscript, and include either an excerpt of the revised text or the location (eg: page and line number) where each change can be found. Please submit a clean version of the paper as the main article file; a version with changes marked should be uploaded as a marked up manuscript.

In addition, we request that you upload any figures associated with your paper as individual TIF or EPS files with 300dpi resolution at resubmission; please read our figure guidelines for more information on our requirements: http://journals.plos.org/plosmedicine/s/figures. While revising your submission, please upload your figure files to the PACE digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at PLOSMedicine@plos.org.

We expect to receive your revised manuscript by Oct 18 2019 11:59PM. Please email us (plosmedicine@plos.org) if you have any questions or concerns.

***Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.***

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Please use the following link to submit the revised manuscript:

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Your article can be found in the "Submissions Needing Revision" folder.

Please ensure that the paper adheres to the PLOS Data Availability Policy (see http://journals.plos.org/plosmedicine/s/data-availability), which requires that all data underlying the study's findings be provided in a repository or as Supporting Information. For data residing with a third party, authors are required to provide instructions with contact information for obtaining the data. PLOS journals do not allow statements supported by "data not shown" or "unpublished results." For such statements, authors must provide supporting data or cite public sources that include it.

We look forward to receiving your revised manuscript.

Sincerely,

Thomas McBride, PhD

Senior Editor

PLOS Medicine

plosmedicine.org

-----------------------------------------------------------

Requests from the editors:

1- In the Abstract Methods and Findings section, please include a bit more information on the population and setting (i.e., the cohort from which you derive the inputs), the specific policy changes investigated, the timeframe simulated, and the main outcome measures.

2- Also in the Abstract Methods and Findings, please quantify the main results (with 95% UIs and p values where relevant).

3- At this stage, we ask that you include a short, non-technical Author Summary of your research to make findings accessible to a wide audience that includes both scientists and non-scientists. The Author Summary should immediately follow the Abstract in your revised manuscript. This text is subject to editorial change and should be distinct from the scientific abstract. Please see our author guidelines for more information: https://journals.plos.org/plosmedicine/s/revising-your-manuscript#loc-author-summary

4- In the first paragraph of the Discussion, please summarize what was done before describing the findings.

5- Please present and organize the Discussion as follows: a short, clear summary of the article's findings; what the study adds to existing research and where and why the results may differ from previous research; strengths and limitations of the study; implications and next steps for research, clinical practice, and/or public policy; one-paragraph conclusion.

Comments from the reviewers:

Reviewer #1: The manuscript by Yaesoubi and colleagues investigates a topical question in gonorrhea research, namely how to design optimal treatment strategies and guidelines. The authors compare a number of alternative strategies to the current practice of switching first-line antibiotics after the level of resistance exceeds 5%. The results suggest that some adaptations of the current surveillance programs would allow to extend the use of antibiotics and/or decrease the burden of disease.

From reading the manuscript, it becomes clear that the authors have clearly identified an interesting problem and propose a thoughtful approach to tackle it using a mathematical model. The modeling framework, a stochastic implementation of a previously published model, appears to be well-adapted.

While I think this is a really nice and important piece of work, the manuscript appears a little incomplete and might benefit from some further investigation. I have a number of suggestions that the authors could consider in a revised version of the manuscript which, I believe, would considerably help strengthen the overall conclusions:

1. Sensitivity analyses: My impression is that the results of the paper might heavily depend on a number of critical assumptions. For example, it is unclear to me why the authors chose a time window of 50 years. Also, increasing the number of additional antibiotics (C, D, ..., or N, K, ...) could result in quite some different results. I think some sensitivity analyses in that respect might be warranted.

2. Uncertainty: The authors write that they summarize results "using the mean and 95% confidence intervals across 500 simulated trajectories". However, I did not find any reporting on confidence intervals or any assessment of uncertainty. Fig. 3 is truly excellent and contains an incredible amount of information, but one wonders how much uncertainty is expected there. Table 1 could also be extended with some key results for the resistance thresholds of 5% and 10%, for example.

3. Methods: I found it a bit difficult to completely follow the modeling procedure. First, it is unclear why the authors chose the simulation approach described in S1.2 instead of the exact stochastic Gillespie algorithm. Did the authors opt for a fixed time step because of computational constraints? Second, it is also not clear how model calibration is performed. Apparently, the authors run 100,000 trajectories but it is not described how the posterior distributions are obtained based on the likelihood. Finally, I could not exactly follow what happens in the threshold-trend strategies described in S4. It appears the authors want to identify tau and theta, but I could not find any reporting of these values (at least not of theta) in the manuscript. Some additional details on this specific scenario and its results would be helpful.

Minor points:

1. Figure 2: It would help if the panels in this figure highlighted the median of all simulations, or an illustrative or typical simulation run.

2. Supplementary Information, p. 5, line 423: "estimated" should be "estimate".

Reviewer #2: The manuscript represents a valuable study into the potential impacts of both switching and optimising criteria for moving between first and second line and second and last line antibiotic therapies.

The study is almost entirely a simulation study. A detailed, yet realistic stochastic epidemic transmission model is established, which has a number of parameters as presented in Table 1. I have one query about the model:

1. In the SI, in Section 1.3, t_0 is defined to be the time at which the increase in the relative infectiousness of resistance profile i should occur. How is this time determined? It's not in the parameter list. Is γ_i(t) a constant before this time?

Model outputs are then related to three data points - two of which are extracted from published estimates and confidence intervals. For these data points an approximate likelihood is drawn up. The analysis of these data points is claimed to be Bayesian.

2. The likelihood is defined, but it is unclear how exactly it is used to produce the posterior distributions. The paper says that N = 100,000 epidemic trajectories are simulated using parameters sampled from the prior distributions. Some trajectories are not considered if they don't satisfy various feasibility constraints. On the remaining trajectories, what happens? Each will have an associated likelihood value, but it is not clear how these are used to produce the posterior distributions? Is MCMC used somehow? Are only a further proportion of the trajectories retained on the basis of their likelihood? This really isn't clear and left me rather confused. It looks like only four parameters have posterior distributions that are drastically different from their prior - which makes sense given there are only three data points. I think there has been a typo in the range of the priors and posteriors for the initial gonorrhea prevalence, as they are not consistent with each other. Also, minor point, but for parameters such as the probability of drug resistance, the prior specified is uniform, but it seems that the order of magnitude is uncertain. The current uniform prior places very little prior probability on this being 10^-5 or 10^-6, which is not the intention, I'm sure. It would make more sense to place the prior on the log-scale.

3. Does removing trajectories that never give a prevalence of resistance of 5% bias against strategies that use a thresholding rule <5%? Are the three criteria in lines 440-442 really so infeasible over the next 50 years?

4. There are many ways to calculate a confidence interval on the basis of binomial data. However, I don't think it is reasonable to be anticipating that the width of such an interval is based on the quantiles of a t-distribution. t-tests are used in cases where the variance of the data is unknown and has to be estimated separately to the mean. However, the estimate for variance of binomial data follows once the probability parameter has been estimated. Therefore, a z-statistic would be used. Can the authors justify their use of the t-distribution rather than the z? Given the likely sample sizes being estimated, this is very unlikely to make any real difference to the analyses, though does simplify the calculations. There's also a typo in the SI on line 420, it should be K hat, not S hat that is being estimated.

Of the retained trajectories, the impact of the four considered policies are assessed, with a detailed description of how each of the policies are optimised.

5. The Results section discusses some improvements that could be made given certain thresholds. It would be good to state explicitly (perhaps I missed it) if these thresholds are the ones found through the optimisation process outlined in the SI?

6. Have any values of ω been used previously? Also, there is no discussion of the anticipated costs of the enhanced surveillance ... are the improvements in the extension of the useful life of the antibiotics cost-efficient?

7. The final paragraph of the SI discusses ω_1, ω_2, ω_3 being drawn from the minimum, origin and maximum values from Fig. 3. I'm right in thinking these are not conventional minima and maxima, rather that they just come from the gradient at the largest and smallest values of the threshold that were considered?

8. Minor point, there are some typos in formulae:

- should there be a '-' in Equation (6) of the SI, rather than a '+'?

- in line 484, p_n approaches zero at a slower rate than p_n? I think the first should be ε_n.

- the equation in line 356 is confusing, if j is the index on the LHS, it shouldn't be used in the summations, which should be switched to k or some other letter.

- re-use of notation β in Section 3.3 of the SI. This is also used for the transmissibility. Could a different symbol be used?

Reviewer #3: This manuscript presents a transmission modelling study of innovative drug cycling strategies for the treatment of gonorrhea in the US MSM population. The ideas are intriguing and the ideas described here are important.

Unfortunately, I found it slightly too theoretical for PLOS Medicine.

There are only a few drugs used routinely around the world for treating this pathogen and their rates of acquiring resistance and their initial drop in fitness has been quantified. In a piece aimed at influencing policy, given these other findings are out there, it doesn't seem reasonable to drop back to a purely theoretical Drug A versus Drug B versus Drug N. The direction of effects of more rapid decisions or higher thresholds are reasonably intuitive (but still need pointing out). Readers of this style of article at PM will be looking for robust evidence that the strength of the effect has been accurately assessed - or if not accurately, at least as accurate as is possible with current data and approaches.

Although much of the language was clear and the charts were well designed. There were key aspects of the reporting that I couldn't appreciate even on careful reading. See comments about my ability to interpret magnitude for both the x and y axis of figure 3. I suspect that the value of this figure is higher than I was able to see, but it was quite opaque to me.

Given the call out to the UK policy in the discussion, it seemed strange to me that the authors were not influenced more by doi.org/10.1371/journal.pmed.1002416 in this journal. I don't know for sure, but I think this prior paper directly influenced the decision they mention.

Just to reiterate - there is genuine innovation here and a whole set of possible strategies not looked at before in the literature. But this presentation of the ideas did not seem to be specific enough to justify the strong statements to policy-making readers of the journal.

Detailed comments:

Line 34; The caveas in the results section seemed a little strange. Maybe in the conclusions instead?

42; Seems unusual not to have mentioned the modelling study by Whittles et al that appeared in this journal. They quantified relative fitness of different strains using a model, which seems highly relevant here.

99; Maybe call this threshold-annual

130; How much less transmissible. That seems like a key assumption that needs some discussion. Ref 15 doesn't seem to have any specific estimates of relative transmissibility

133; How exactly is this done and what are the approximate ranges for initial fitness cost and eventual costs.

141; A table of key parameter assumptions, prior distributions and posterior estimates would be very helpful here

148; please state the justification for the lifespan definition. It doesn't make sense to me. $T$ appears in the bounds of the summation and, I think, in the term itself. Couldn't understand this.

Fig 3: See comments about the lifespan definition. I couldn't understand what this was telling me at this point. Is the y axis absolute or some kind of relative percentage. If absolute, its tricky to interpret because I have to look back at the first figure.

168: So Fig 3 is per 100,000. COmparing this with Fug 2b, they seem to be very modest changes?

180; maybe a discussion of the accuracy with which the trend would need to be known is important. If not here then later. Accurately measuring small changes would not be wihtout costs.

202; this paragraph is a simple reststement of results. It doesn't quite make sense here in the discussion.

217; I'm pretty sure that the UK policy was influenced by the work by whittles et al in this journal that inferred fitness costs for specific drugs.

Any attachments provided with reviews can be seen via the following link:

[LINK]

Decision Letter 1

Thomas J McBride

4 Feb 2020

Dear Dr. Yaesoubi,

Thank you very much for re-submitting your manuscript "Adaptive guidelines for the treatment of gonorrhea to increase the effective lifespan of antibiotics: A mathematical modeling study" (PMEDICINE-D-19-02321R1) for review by PLOS Medicine.

I have discussed the paper with my colleagues and the academic editor and it was also seen again by 2 of the previous reviewers. I am pleased to say that provided the remaining editorial and production issues are dealt with we are planning to accept the paper for publication in the journal.

The remaining issues that need to be addressed are listed at the end of this email. Any accompanying reviewer attachments can be seen via the link below. Please take these into account before resubmitting your manuscript:

[LINK]

Our publications team (plosmedicine@plos.org) will be in touch shortly about the production requirements for your paper, and the link and deadline for resubmission. DO NOT RESUBMIT BEFORE YOU'VE RECEIVED THE PRODUCTION REQUIREMENTS.

***Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.***

In revising the manuscript for further consideration here, please ensure you address the specific points made by each reviewer and the editors. In your rebuttal letter you should indicate your response to the reviewers' and editors' comments and the changes you have made in the manuscript. Please submit a clean version of the paper as the main article file. A version with changes marked must also be uploaded as a marked up manuscript file.

Please also check the guidelines for revised papers at http://journals.plos.org/plosmedicine/s/revising-your-manuscript for any that apply to your paper. If you haven't already, we ask that you provide a short, non-technical Author Summary of your research to make findings accessible to a wide audience that includes both scientists and non-scientists. The Author Summary should immediately follow the Abstract in your revised manuscript. This text is subject to editorial change and should be distinct from the scientific abstract.

We expect to receive your revised manuscript within 1 week. Please email us (plosmedicine@plos.org) if you have any questions or concerns.

We ask every co-author listed on the manuscript to fill in a contributing author statement. If any of the co-authors have not filled in the statement, we will remind them to do so when the paper is revised. If all statements are not completed in a timely fashion this could hold up the re-review process. Should there be a problem getting one of your co-authors to fill in a statement we will be in contact. YOU MUST NOT ADD OR REMOVE AUTHORS UNLESS YOU HAVE ALERTED THE EDITOR HANDLING THE MANUSCRIPT TO THE CHANGE AND THEY SPECIFICALLY HAVE AGREED TO IT.

Please ensure that the paper adheres to the PLOS Data Availability Policy (see http://journals.plos.org/plosmedicine/s/data-availability), which requires that all data underlying the study's findings be provided in a repository or as Supporting Information. For data residing with a third party, authors are required to provide instructions with contact information for obtaining the data. PLOS journals do not allow statements supported by "data not shown" or "unpublished results." For such statements, authors must provide supporting data or cite public sources that include it.

If you have any questions in the meantime, please contact me or the journal staff on plosmedicine@plos.org.

We look forward to receiving the revised manuscript by Feb 11 2020 11:59PM.

Sincerely,

Thomas McBride, PhD

Senior Editor

PLOS Medicine

plosmedicine.org

------------------------------------------------------------

Requests from Editors:

Data link – the second one you provide is a broken link – please provide working URLs.

Please avoid the list in the abstract (remove 1 and 2)

Title – Please add the country setting and should MSM be added?

The abstract seems quite light on quantitative details – please add.

I think the manuscript would benefit from the description about the "threshold and trend" approach being in slightly more detail--as at line 224-5 (i.e., that the first- to second-line switch occurs at 10.1% prevalence of resistance, or when the prevalence increases by 1.6 percentage points year on year).

Comments from Reviewers:

Reviewer #1: I would like to thank the authors for adequately responding to my comments on their manuscript.

Reviewer #2: My main concern from the initial review was that the inferential processes were not clear. The authors have now added a significant amount of detail, making things much more explicit and I thank them for this.

The inferential procedure would appear to run according to:

1. Sample 100,000 parameter sets.

2. The likelihood of the three data points is dependent on initial conditions, therefore the likelihood is directly related to the parameters and not dependent on the projected epidemic trajectories... I think...

3. Each prior sample is given a weight according to its associated likelihood, and 500 parameter sets are resampled using weights proportional to the likelihood.

4. The retained 500 samples (and an associated trajectory) are then used as the basis for the assessments of the different antibiotic switching thresholds and surveillance schemes.

I feel a little uneasy about this as prior distributions are notoriously poor importance distributions to sample from. However, as there are only three data points, and most parameters have near identical priors and posteriors, this shouldn't matter unduly in this case. My second concern is a hope that when calculating the trajectories under different switching and surveillance policies, the same random seed is being used so that trajectories match until a particular threshold is reached. Apologies if this is made clear in the text and I have simply missed it.

Some further concerns amendments that are new or remain outstanding (where I'm referring to an item in the supplementary information, I will put an 'S' in front of the line number):

1. Line S437, I'm certain there shouldn't be a \\Delta t in the denominator.

2. Figure S1: Should the lines labelled 'Tx M' at the bottom of the figure be in green? A related point is the equation for S(t) in lines S443-8 - shouldn't this include contributions from those recovering from infection?

3. Section S2, line S467. There appears to be a mixture of \\hat y_t and the p_t that is introduced in the text. Can this be clarified?

4. Line S517: Are we talking about new or prevalent infections?

5. Each of the expressions for L_1, L_2, and L_3 (S484, S497, S509). Why do these have sums from 1 to 10? Are these general expressions for the first ten time periods? If so, then surely both \\hat s and \\hat S should also be indexed by t? I would suggest replacing the 10 with a general T and adding the index, .. or be explicit that you only have data at time t=1.

6. The z statistic has been switched in in Equation S502, but not in S486. Why? I think you need to redo using the z-statistic.

7. Figure 2 - there is clearly a trajectory that has prevalence >5%. Why has this one not been removed?

8. Lines 184: The use of S and L, it's a minor pedantic point, but could you use S_0 and L_0, to make it clear that these are values taken from a baseline analysis?

9. Lines S547, there is an inconsistency regarding the relationship between omega and the switching thresholds. I think you mean to say that lower switch thresholds correspond to higher \\omega.

10. Typos in caption to figure S4. 'Chaning' and 'threshod'.

11. Typo in lines S564-565. 'Values depend' or 'value depends'.

12. S538-540 - can we be clear whether q(\\tau,\\theta) and \\nu(\\tau.\\theta) are values unique to each trajectory or expected values, and whether this expectation is taken wrt to parameter uncertainty or just sampling uncertainty. In the many figures showing the impacts of different thresholds there are uncertainty intervals attached, I presume from looking at the 500 posterior samples for both parameters and trajectories.

13. Typo line S583 'optimzes'.

14. Step 5 of algorithm S2: f_n is not a realisation of f(x), it is an unbiased approximation of it.

Any attachments provided with reviews can be seen via the following link:

[LINK]

Decision Letter 2

Richard Turner

2 Mar 2020

Dear Dr. Yaesoubi,

On behalf of my colleagues and the academic editor, Dr. Nicola Low, I am delighted to inform you that your manuscript entitled "Adaptive guidelines for the treatment of gonorrhea to increase the effective lifespan of antibiotics among men who have sex with men in the United States: A mathematical modeling study" (PMEDICINE-D-19-02321R2) has been accepted for publication in PLOS Medicine.

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Thank you again for submitting the manuscript to PLOS Medicine. We look forward to publishing it.

Best wishes,

Richard Turner, PhD

Senior Editor

PLOS Medicine

plosmedicine.org

Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Supplementary Materials

    S1 Text. Additional details on model structure, calibration procedure, and the algorithm to identify adaptive policies.

    (PDF)

    Click here for additional data file. (868.1KB, pdf)
    Attachment

    Submitted filename: Response Letter.pdf

    Click here for additional data file. (197.7KB, pdf)

    Data Availability Statement

    The data underlying the results presented in the study are available from the Gonococcal Isolate Surveillance Project (https://www.cdc.gov/std/gisp/default.htm) and Sexually Transmitted Disease Surveillance 2018 (https://www.cdc.gov/std/stats18/).

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