Assessing the drivers of syphilis among men who have sex with men in Switzerland reveals a key impact of testing frequency: A modelling study

Background: Over the last decade, syphilis diagnoses among men-who-have-sex-with-men (MSM) have strongly increased in Europe. Understanding the drivers of the ongoing epidemic may aid to curb transmissions. Methods and Findings: We set up an epidemiological model to assess the drivers of syphilis in MSM in Switzerland between 2006 and 2017. We stratified the model by syphilis stage, HIV-diagnosis, and behavioral factors to account for syphilis infectiousness and risk for transmission. In the main model, we used 'reported non-steady partners' (nsP) as the main proxy for sexual risk. We parameterized the model using data from the Swiss HIV Cohort Study, Swiss Voluntary Counselling and Testing center, cross-sectional surveys among the Swiss MSM population, and published syphilis notifications from the Federal Office of Public Health. The main model reproduced the increase in syphilis diagnoses from 168 cases in 2006 to 418 cases in 2017. It estimated that between 2006 and 2017, MSM with HIV diagnosis had 45.9 times the median syphilis incidence of MSM without HIV diagnosis. Defining risk as condomless anal intercourse with nsP decreased model accuracy (sum of squared weighted residuals, 378.8 vs 148.3). Counterfactual scenarios suggested that increasing screening of MSM without HIV diagnosis and with nsP from once every two-years to twice per year may reduce syphilis incidence (at most 12.8% reduction by 2017). Whereas, increasing screening among MSM with HIV diagnosis and with nsP from once per year to twice per year may substantially reduce syphilis incidence over time (at least 63.5% reduction by 2017). Conclusions: The model suggests that reporting nsP regardless of condom use is suitable for risk stratification when modelling syphilis transmission. More frequent screening of MSM with HIV diagnosis, particularly those with nsP may aid to curb syphilis transmission.

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Methods 89
We used data from the SHCS and cross-sectional surveys among the Swiss MSM population 90 to estimate the transmission risk of syphilis. These temporal trends were used to 91 parameterize a mathematical model, which was then used to assess the impact of different 92 screening strategies via counterfactual scenarios (see Figure 1 for Step 1: Establish the transmission model structure Step 2: Parameterization of the model Step 3: Fit the transmission model to SHCS and syphilis notification data Step 4: Test counterfactual scenarios Step 5: Perform sensitivity analyses to assess the robustness of the model Cohort Study (SHCS) [13,14]. The SHCS is a prospective multicenter cohort study, which 105 systematically collects epidemiological and clinical data for more than 20000 HIV-diagnosed  (Table S1). In a sensitivity analysis, we also fitted the 175 model through maximization of the likelihood by assuming Poisson distributed incident 176 cases of syphilis and compared the model fits. 177

Counterfactual scenarios 178
We compared the incidence of syphilis obtained with the main model fit with that simulated 179 when assuming the following two alternative scenarios. Firstly, we considered the impact of 180 The key demographic characteristics of MSMwHD in the SHCS is summarized in Table 1  Alcohol consumption more than once a month for at instead of once a year, respectively. Red and black lines in panel b) represent incidence rate 285 of syphilis that obtained for the counterfactual scenarios when MSM without HIV diagnosis 286 were screened for syphilis every 6 and 3 months instead of once every 2 years, respectively. 287 The shaded regions represent the 95% quantile for the respective incidence rates. 288

Sensitivity analysis 289
To test the robustness of the model and possible inconsistencies in data, we recalibrated 290 the model and determined the corresponding change in the incidence rate of syphilis, the 291 fitted parameters, and the goodness of fit (sum of squared weighted residuals) (Table S4). 292 Firstly, we considered alternative criteria to stratify transmission risk ( Figure S13 MSMw/oHD. In the main model we had to assume different transmission rates, because of an 299 apparent discrepancy in the data: despite similar frequency of reported nsP among MSMwHD 300 and MSMw/oHD, we observed much higher incidence of syphilis among MSMwHD than 301 MSMw/oHD even when taking serosorting into account (Table S2). To resolve this 302 contradiction, in the main model, we assumed different transmission rates of syphilis (beta) 303 in MSMwHD and MSMw/oHD in our model (Table S1). In the absence of this assumption, the 304 model was unable to reproduce the syphilis epidemic in Switzerland and led to either large 305 overestimation of syphilis incidence in MSMw/oHD or large underestimation in MSMwHD 306 ( Figure S14). As an alternative approach to capture the discrepancy in the data, we fitted a 307 model assuming that there is no difference in transmission rate of syphilis among MSMwHD 308 and MSMw/oHD but instead including a parameter to account for possible underreporting of 309 syphilis cases to FOPH among MSMw/oHD ( Figure S15). However, the goodness of fit for this 310 model was worse than for the main model (sum of squared weighted residuals, 206.6 vs 311 148.3) and required the assumption of an unrealistically high underreporting factor (40.8). 312 Thirdly, we investigated the impact of a possible overestimation of transmission risk among 313 MSMw/oHD. We fitted models assuming the proportion of MSMw/oHD with nsP to be 25%, 314 50%, and 75% lower than the proportion of MSMw/oHD with nsP estimated from data 315 incidence assuming the infectiousness of syphilis in the latent stage to 1% and 10% of that in 336 primary and secondary stage of syphilis, respectively; MSM -men who have sex with men; 337 nsP -non-steady partners; py -person-years; Blue lines represent incidence rate of syphilis 338 in the base model (initial model fit). Red and black lines represent incidence rate of syphilis 339 that obtained for the counterfactual scenarios when MSM with HIV diagnosis were screened 340 for syphilis every 6 and 3 months instead of once a year, respectively. The shaded regions 341 represent the 95% quantile for the respective incidence rates. 342 Finally, we tested the effect of using an alternative fitting procedure. Instead of fitting the 343 model through minimization of the sum of squared weighted residuals, we fitted the model 344 through maximization of the likelihood by assuming Poisson distributed incident cases of 345 b) Impact of syphilis screening frequency for assuming 10% infectiousness in latent stage of that in primary and secondary stage of syphilis a) Impact of syphilis screening frequency for assuming 1% infectiousness in latent stage of that in primary and secondary stage of syphilis syphilis. We obtained similar median incidence rate and model fit as obtained by the main 346 approach ( Figure S18). 347 Discussion 348 The transmission model presented here could accurately reproduce the syphilis epidemic in 349 Switzerland. Our study outlines the much higher incidence Alternatively, this difference may also be due to unadjusted transmission risk of syphilis 371 such as number of partners and frequency of contacts, which we did not model explicitly. 372 To explore alternative distributions of risk, we stratified the structure of transmission risk in 373 our model based on reported condomless anal intercourse with non-steady partners (versus 374 just reported non-steady partners). The model fit was worse than that in the main analysis. 375 This might be because syphilis could be transmitted through oral sex, and using condoms for 376 anal intercourses is not completely protective against syphilis [20]. In an alternative 377 approach, we assumed no difference in transmission rate of syphilis among MSMwHD and 378 MSMw/oHD and allowed the model to account for possible underreporting of syphilis cases to 379 FOPH among MSMw/oHD to explain the apparent difference in the incidence rate among 380 MSMwHD and MSMw/oHD. We estimated the incidence of syphilis in MSMw/oHD to be 40. and estimated similar incidence rates compared to the main model fit. By means of 408 counterfactual scenarios, we further assessed the impact of infectiousness of syphilis in 409 latent stage on the dependency between the screening frequency and the syphilis 410 incidence. We found that the estimated reduction in syphilis incidence due to increase in 411 screening frequency decreases when assuming residual infectiousness during the latent 412 stage. Infectiousness during the latent stage of syphilis warrants further investigation as it 413 may have an impact on the effectiveness of different screening strategies. However, even 414 when we assumed infectiousness during the latent stage to be as high as 10% of that in 415 primary and secondary stage, we observed 63.5% reduction in syphilis incidence in 2017 416 when screening of syphilis was performed twice per year instead of once per year in 417 MSMwHD with nsP. Our study results thus robustly indicate that frequent screening of MSM 418 with HIV diagnosis and with nsP is required to curb syphilis transmission. This supports the 419 EACS guidelines which recommend to "consider more frequent than annual screening if at 420 risk" [26]. 421 As mentioned before, we observed that the proportion of MSMw/oHD with non-steady 422 partners is higher than the proportion of MSMwHD with non-steady partners. On one hand, One of the main limitations of our study is the uncertainty regarding the representativeness 451 of the data used for MSMw/oHD. This resulted in model assumptions which required critical 452 sensitivity analyses to assess the robustness of our findings. Our study has however a 453 substantial strength with regard to HIVwHD: the use of routine serological screening in a 454 representative population over many years. Estimation of transmission risk of syphilis in 455 MSMwHD were based on the SHCS data. As the SHCS is highly representative for MSMwHD in 456 care in Switzerland, we expect these data to provide accurate estimates. In contrast, 457 estimation of transmission risk in MSMw/oHD was based on cross-sectional studies which 458 might have led to more uncertainty in results. The degree of mixing between MSMwHD and 459 MSMw/oHD were based on the estimated frequency of HIV discordant status in the data 460 collected from VCT checkpoints across Switzerland where people can get spontaneously 461 tested for sexually transmitted infections in a fully anonymized way. As bias towards testing 462 upon transmission risk is expected, representativeness cannot be warranted. We stratified 463 based on reported non-steady partners and condomless anal intercourse with non-steady 464 partners as the transmission risk of syphilis. Although the available data in the SHCS did not 465 allow us to account for the effect of other risk factors such as number of partners and 466 frequency of sexual acts, the goodness of fit suggests reported non-steady partner to be a 467 good proxy for risk stratification to model syphilis transmission. 468 In conclusion, our model reconstructed the syphilis epidemic among MSM in Switzerland