MD Romain Carron

MD Caroline Gaudy-Marqueste

PhD Florent Amatore

MD Laetitia Padovani

MD Nausicaa Malissen

MD Anne Balossier

PhD Anderson Loundou

Nathalie Bonnet

MD Xavier Muracciole

MD Jean-Marie Régis

MD Jean-Jacques Grob
email: jean-jacques.grob@ap-hm.fr

Pr Jean

Jacques Grob

Stereotactic radiosurgery combined with anti-PD1 for the management of melanoma brain metastases: A retrospective study of safety and efficacy

Keywords: anti-PD1, brain metastases, melanoma, stereotactic radiosurgery

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

BACKGROUND

New systemic treatments have dramatically improved the course of metastatic melanoma (MM); however patients with brain metastases (BMs) still have a very poor prognosis [START_REF] Goyal | Clinical Management of Multiple Melanoma Brain Metastases: A Systematic Review[END_REF] . As these patients were generally excluded from clinical trials, data regarding check-point inhibitors efficacy in the treatment of BMs remains limited [START_REF] Ahmed | Clinical outcomes of melanoma brain metastases treated with stereotactic radiosurgery and anti-PD-1 therapy, anti-CTLA-4 therapy, BRAF/MEK inhibitors, BRAF inhibitor, or conventional chemotherapy[END_REF][START_REF] Ahmed | Clinical outcomes of melanoma brain metastases treated with stereotactic radiation and anti-PD-1 therapy[END_REF][START_REF] Choong | Survival of patients with melanoma brain metastasis treated with stereotactic radiosurgery and active systemic drug therapies[END_REF][START_REF] Nardin | Tolerance and outcomes of stereotactic radiosurgery combined with anti-programmed cell death-1 (pembrolizumab) for melanoma brain metastases[END_REF][START_REF] Parakh | Efficacy of anti-PD-1 therapy in patients with melanoma brain metastases[END_REF][START_REF] Tio | Survival and prognostic factors for patients with melanoma brain metastases in the era of modern systemic therapy[END_REF][START_REF] Minniti | Stereotactic radiosurgery combined with nivolumab or Ipilimumab for patients with melanoma brain metastases: evaluation of brain control and toxicity[END_REF][START_REF] Nordmann | Effect of Gamma Knife Radiosurgery and Programmed Cell Death 1 Receptor Antagonists on Metastatic Melanoma[END_REF][START_REF] Murphy | Concurrent Radiosurgery and Immune Checkpoint Inhibition: Improving Regional Intracranial Control for Patients With Metastatic Melanoma[END_REF] . Both ipilimumab and anti-PD1 have shown efficiency as single agent in phase 2 studies with response rates of 10-24 % for ipilimumab [START_REF] Margolin | Ipilimumab in patients with melanoma and brain metastases: an open-label, phase 2 trial[END_REF] , 20-22 % for anti-PD1 [START_REF] Goldberg | Pembrolizumab for patients with melanoma or non-small-cell lung cancer and untreated brain metastases: early analysis of a non-randomised, open-label, phase 2 trial[END_REF][START_REF] Kluger | Long-Term Survival of Patients With Melanoma With Active Brain Metastases Treated With Pembrolizumab on a Phase II Trial[END_REF][START_REF] Long | Combination nivolumab and ipilimumab or nivolumab alone in melanoma brain metastases: a multicentre randomised phase 2 study[END_REF] , and 46-57% for ipilimumab-nivolumab [START_REF] Long | Combination nivolumab and ipilimumab or nivolumab alone in melanoma brain metastases: a multicentre randomised phase 2 study[END_REF][START_REF] Tawbi | Efficacy and safety of Nivolumab plus ipilimumab in patients with melanoma metastatic to the brain: results of the phase II study checkmate 204. Combined Nivolumab and Ipilimumab in Melanoma Metastatic to the Brain[END_REF] . Stereotactic radiosurgery (SRS) has been increasingly used for the treatment of MM-BMs due to excellent local control rates, minimal invasiveness and possibility of repeated treatment in case of new BMs [START_REF] Gaudy-Marqueste | Survival of melanoma patients treated with targeted therapy and immunotherapy after systematic upfront control of brain metastases by radiosurgery[END_REF][START_REF] Lippitz | Stereotactic radiosurgery in the treatment of brain metastases: the current evidence[END_REF][START_REF] Marchan | Stereotactic radiosurgery of brain metastasis from melanoma[END_REF] . Preclinical and clinical data suggest a potential synergy with radiation therapy [START_REF] Demaria | Role of Local Radiation Therapy in Cancer Immunotherapy[END_REF][START_REF] Filippi | Radiotherapy and immune checkpoints inhibitors for advanced melanoma[END_REF] .

The combination of radiation therapy and check-point inhibitors is currently being tested prospectively (NCT03340129, NCT02978404, NCT02858869). A common concern is a possible increase of adverse radiation effects (ARE). This risk has been assessed differently in many series, most of them including different radiation modalities such as SRS and/or WBRT. In a recently-published meta-analysis focusing on the combination of SRS and immunotherapies the overall incidence of radionecrosis was 5.3% and all studies reporting radionecrosis involved the use of ipilimumab [START_REF] Lehrer | Treatment of brain metastases with stereotactic radiosurgery and immune checkpoint inhibitors: An international meta-analysis of individual patient data[END_REF] .

Our institutional strategy for the management of BMs is exclusively based on stereotactic radiosurgery (SRS) to all eligible patients, and excludes WBRT. We retrospectively assessed the efficacy and radiotoxicity of this stereotyped strategy in the setting of monotherapy by anti-PD1.

METHODS

Retrospective analysis of all consecutive patients with MM-BMs treated in our institution between Nov, 2013 and Dec, 2017. Inclusion criteria: 1: patients who received anti-PD1 concomitantly with SRS, i.e. ongoing at the time of SRS; or patients who started anti-PD1 no later than 3 months (m) after SRS; 2: patients who were treated at least one year before the analysis and 3: patients who maintained anti-PD1 treatment at least 3 m after SRS. SRS eligibility was discussed in the specific tumor board. regarded as inoperable. Patients with a single, large and symptomatic BM who underwent microsurgical resection were excluded. There was no change in practice over the period of the study.

All patients were treated with the Gamma-knife Perfexion (Elekta, Stockholm, Sweden) in the same unit within 4 weeks of the diagnosis of BMs.

All BMs were treated in a single framed-based session with a highly selective and conformal dose planning based on the appearance of the lesion on the contrast-enhanced 3D T1weighted stereotactic MRI scan. The selection of dosimetric parameters was made according to volume, location, and proximity of organs at risk. The marginal prescription dose ranged from 22 Gy to 26 Gy at the 50% isodose. This regimen of dose was deliberately high in order to optimize control rates but in line with published series [START_REF] Gaudy-Marqueste | Survival of melanoma patients treated with targeted therapy and immunotherapy after systematic upfront control of brain metastases by radiosurgery[END_REF][START_REF] Gaudy-Marqueste | Gamma-Knife radiosurgery in the management of melanoma patients with brain metastases: a series of 106 patients without whole-brain radiotherapy[END_REF] and took into consideration the fact that no patient had been submitted to any form of prior radiation therapy. SRS was repeated in case of new brain metastases on MRI follow-up scans according to an "ondemand "strategy. Whenever ongoing, anti-PD1s were not stopped for SRS. No patient received whole brain radiotherapy at any time.

All patients received monotherapy by anti-PD1 because the ipilimumab-nivolumab combination is not reimbursed in France.

Endpoints and Statistical analysis

Toxicity

The medical records were reviewed to assess neurological symptoms. Brain MRI-scans and full body CT-scans were performed every 3 months. A volumetric assessment of each BM was done with Leksell Gamma Plan version 10.1.1 software (LGP, Elekta, Stockholm, Sweden). The contouring was performed with the dedicated tool of LGP. The appearance or increase of preexisting edema as well as the occurrence of any hemorrhagic event within treatment volume were reported. The FU MRIs scans (3D post-contrast T1-weighted, Flair and T2-weighted axial acquisitions) were systematically imported and fused with the stereotactic images of treatment day with LGP software in order to allow reliable volumetric comparisons of each treated BM. All follow-up MRI scans were analyzed by a neuroradiologist and a neurosurgeon with expertise in SRS (RC) in order to determine whether the observed alterations within the treatment volume were suggestive of an ARE ("radionecrosis"), suggestive of a bleeding, or a progression (uncontrolled BMs defined as an increase in volume by more than 20%). The following criteria were used for the definition of ARE: a lesion showing a central area of low-signal with irregular, ill-defined, peripheral enhancement associated with a moderate increase in volume (up to 15%) and conspicuous augmentation of peritumoral edema on post-contrast T1-weighted acquisitions [START_REF] Dequesada | Can standard magnetic resonance imaging reliably distinguish recurrent tumor from radiation necrosis after radiosurgery for brain metastases? A radiographic-pathological study[END_REF][START_REF] Plowman | Stereotactic radiosurgery, VIII: the classification of postradiation reactions[END_REF] . An initial shrinkage and subsequent volumetric increase as well as a T1-T2 mismatch [START_REF] Kano | Differentiating radiation effect from tumor progression after stereotactic radiosurgery: T1/T2 matching[END_REF] were considered in favor of an ARE. Indeed it is still to date very difficult to demonstrate with certainty without pathological documentation that postoperative MRI alterations correspond clearly to an adverse radiation effect. As no irrefutable criterion exists, we considered any suspicious MRI alterations suggestive of an ARE unless proven otherwise.

Survival

Median follow up was calculated with a reverse Kaplan-Meier method [START_REF] Altman | Review of survival analyses published in cancer journals[END_REF] . Overall survival (OS) was calculated from the time of SRS (OSSRS). Brain-PFS was defined as the time between SRS and evidence of local or distant progression in the brain (Brain-PFSSRS). When patients underwent several SRS sessions in the setting of anti-PD1 treatment, survival rates were calculated from the date of the first SRS session. OS and brain-PFS curves were estimated by the Kaplan-Meier method and compared with the use of the log-rank test.

RESULTS

Patients'characteristics

Outcome of the whole cohort

Time to brain progression, survival from SRS, treatment exposure (SRS, duration of anti-PD1 treatment) and onset of suspected AREs are summarized in Fig 2

Toxicity

Eighteen patients (36%) presented neurological symptoms during the follow-up period: intracranial hypertension (n=5), headache (n=1), diplopia (n=1), proprioceptive ataxia (n=2), hemiparesis (n=6), hemiplegia (n=1), mental confusion (n=1) and sensory deficit (n=1). These events were related to SRS-treated BMs in 8 of the 18 patients (others were attributed to the appearance of new BMs or lepto-meningeal involvement).

Three patients required surgical resection of a BM later during their follow-up for SRS failure (n=1) or new symptomatic large BM (n=2).

In the 181 BMs treated by SRS, for which cerebral imaging was available, 11 (6.1%) cases of increased peritumoral edema (3 with a mass-effect) and 4 hemorrhages (2.2%) occurred in 13 patients. There were no significant differences as a function of the timing of SRS and anti-PD1 administration. Out of these 15 events, 9 events, given their neuro-imaging characteristics, were regarded as potential ARE by both neuroradiologists and SRS experts, being symptomatic in 6 patients (Fig 3 and Table S1 in supplemental data). In one patient, pathological documentation enabled to rule out an adverse radiation effect (pathological evidence of BM recurrence without foci of radionecrosis). Three of the 181 treated BMs recurred in 3 patients. Among these 3 patients only one developed new BMs in addition to the local recurrence (Table S2 in supplemental data). Twenty-three patients (46 %) developed new BMS and 10 (20%) underwent a new SRS session for new BMs.

Survival

At the time of the data analysis (Jan 2019), 18 patients were still alive. Six patients had stopped anti-PD1 for a complete response and 10 patients were still treated with anti-PD1.

Nine patients among the 50 received another systemic treatment after anti-PD1 including ipilimumab (n=1), dacarbazine (n=1), imatinib (n=1), vemurafenib (n=1), dabrafenibtrametinib (n=3) and vemurafenib-cobimetinib followed by ipilimumab (n=2).

The median OSSRS was 16.62 m (95% CI 7.33-34.4 m) and 1-year, 2 year and 3-year OSSRS rates were 60%, 40 % and 35% respectively (Fig 4). The median brain-PFSSRS was 13.25 m (95% CI 0-44.77 m) and 1-year, 2 year and 3-year brain-PFSSRS rates were 52.1, 49.7% and 49.7% respectively (Fig 5).

Baseline characteristics associated with a worse prognosis in univariate analysis were ECOG >1, total volume of BMS treated, number of extra cranial metastatic site, and previous treatment with a BRAF +/-MEK inhibitor for OSSRS (Table 2), and ECOG> 1 and total volume of BMS treated for brain-PFSSRS, respectively .

In multivariate analysis, gender, ECOG, number of extra cranial metastatic site and total volume of BMS treated remained significantly associated with OSSRS while ECOG, total volume of BMS treated and previous treatment with ipilimumab remained significantly associated with brain PFSSRS (Tables 2 and3). A high proportion of patients who died early (within 6 months of SRS) had numerous BMs (10/15 with ≥4 BMs), high tumor cumulated volume (13/15 with volume >1000 mm3), tumor located in the brainstem or posterior fossa (cerebellar) (11/15), leptomeningeal disease (LMD) 14/15), poor performance status (6/15 with ECOG >1) and resistance to a BRAF/MEK inhibitor (12/15).

DISCUSSION

This retrospective series of 50 real-world MM patients is meaningful since all patients were treated with the same strategy combining a homogeneous radiation procedure (upfront SRS without WBRT) and anti-PD1 monotherapy. Furthermore, the follow-up duration (median follow-up of 38.89 months) allows to address the question of ARES that are often delayed by 8-9 months. To our knowledge, in the current literature, there is no equivalent cohort of patients with the same characteristics (Table S3 in supplemental data highlights the main differences between series).

The combination of upfront SRS and anti-PD1 enables to achieve high survival rates, and brain-PFS, around 40% and 50% respectively at 2 years with 6 patients (12%) achieving a durable complete response allowing anti-PD1 discontinuation.

The local control rate in this cohort confirmed the high local efficacy of SRS, even in patients with a high number of BMs (1/3 d of patients with ≥4 BMs). The brain-PFS (49.7% at 2 years) suggests that anti-PD1 exerts some protective adjuvant effect on the development of new BMs, although this strategy is not completely protective as 46 % of the patients developed new BMS.

It is always difficult to compare different trials and especially retrospective and prospective ones. The interpretation must be very cautious but, due to the systematic and standardized practice in our tumor board, our results can be discussed in the context of prospective trials results (Table S4 in supplemental data). Keeping in mind there is an 80% intracranial progression rate at 6-months with anti-PD1 monotherapy alone reported in the ABC study [START_REF] Long | Combination nivolumab and ipilimumab or nivolumab alone in melanoma brain metastases: a multicentre randomised phase 2 study[END_REF] , the combination with SRS seems to yield much superior results in our analysis. The combined ipilimumab-nivolumab regimen is currently regarded as the most efficient systemic treatment for melanoma BMs [START_REF] Tawbi | Efficacy and safety of Nivolumab plus ipilimumab in patients with melanoma metastatic to the brain: results of the phase II study checkmate 204. Combined Nivolumab and Ipilimumab in Melanoma Metastatic to the Brain[END_REF] , despite high toxicity. In the largest phase 2 study published Checkmate 204 (94 patients), the intracranial progression rate was 33% with 6-m intra-cranial PFS and OS rates of 64.2 % and 92.3 % respectively, and a 12-m OS rate of 81.5.

The 60% 12-m OS rate obtained by combining systematic SRS with anti-PD1 proves quite comparable with the estimated 81.5% 12-m OS rate with the ipilimumab-nivolumab combination reported in the Checkmate 204 study, since our series included patients with more advanced disease and poorer prognosis. Indeed, solitary BM patients represent 52% of the trial population in the CheckMate 204 study [START_REF] Tawbi | Efficacy and safety of Nivolumab plus ipilimumab in patients with melanoma metastatic to the brain: results of the phase II study checkmate 204. Combined Nivolumab and Ipilimumab in Melanoma Metastatic to the Brain[END_REF] , versus 29.8% in our study. This results strongly support the rationale for a prospective comparison between the 2 strategies and a trial combining upfront SRS combination of ipilimumab-nivolumab, which is now ongoing (NCT03340129).

Despite biological data suggesting that radiotherapy may improve the response to check point inhibitors by increasing the immune infiltration of BMs [START_REF] Demaria | Role of Local Radiation Therapy in Cancer Immunotherapy[END_REF][START_REF] Pfannenstiel | Combination PD-1 blockade and irradiation of brain metastasis induces an effective abscopal effect in melanoma[END_REF] , there is only limited information about the efficacy of combined radiation and immune checkpoint inhibitors. These studies are usually small and highly heterogeneous regarding the systemic treatment, doses (single and multiple fraction) and type of radiation (SRS and WBRT) [2,-10,28] .

A meta-analysis of 17 studies) [START_REF] Lehrer | Treatment of brain metastases with stereotactic radiosurgery and immune checkpoint inhibitors: An international meta-analysis of individual patient data[END_REF] using SRS (Gamma-Knife, Cyberknife or Linac) and checkpoint inhibitors between 2013 and 2018 pooled together studies with different types of cancers (not only melanomas), heterogeneous regimen of immunotherapy (mostly ipilimumab) and limited follow-up (median 9 months). Our series is thus hardly comparable with these disparate studies. However the high local control rate, the rather long survival and the low rate of radionecrosis in this meta-analysis are in line with our results.

Increased rates of radionecrosis have been reported in 3 small series of patients treated with SRS and ipilimumab [START_REF] Diao | Combination ipilimumab and radiosurgery for brain metastases: tumor, edema, and adverse radiation effects[END_REF][START_REF] Four | Symptomatic Histologically Proven Necrosis of Brain following Stereotactic Radiation and Ipilimumab in Six Lesions in Four Melanoma Patients[END_REF][START_REF] Knisely | Radiosurgery for melanoma brain metastases in the ipilimumab era and the possibility of longer survival[END_REF] but this was not confirmed in larger cohorts [START_REF] Gerber | Ipilimumab and whole brain radiation therapy for melanoma brain metastases[END_REF][START_REF] Patel | Ipilimumab and Stereotactic Radiosurgery Versus Stereotactic Radiosurgery Alone for Newly Diagnosed Melanoma Brain Metastases[END_REF][START_REF] Mathew | Ipilimumab in melanoma with limited brain metastases treated with stereotactic radiosurgery[END_REF][START_REF] Silk | Ipilimumab and radiation therapy for melanoma brain metastases[END_REF] . Conversely the few reports on the combination of SRS and anti-PD1 do not suggest a high rate of ARE [START_REF] Ahmed | Clinical outcomes of melanoma brain metastases treated with stereotactic radiosurgery and anti-PD-1 therapy, anti-CTLA-4 therapy, BRAF/MEK inhibitors, BRAF inhibitor, or conventional chemotherapy[END_REF][START_REF] Ahmed | Clinical outcomes of melanoma brain metastases treated with stereotactic radiation and anti-PD-1 therapy[END_REF][START_REF] Choong | Survival of patients with melanoma brain metastasis treated with stereotactic radiosurgery and active systemic drug therapies[END_REF][START_REF] Nardin | Tolerance and outcomes of stereotactic radiosurgery combined with anti-programmed cell death-1 (pembrolizumab) for melanoma brain metastases[END_REF][START_REF] Parakh | Efficacy of anti-PD-1 therapy in patients with melanoma brain metastases[END_REF][START_REF] Tio | Survival and prognostic factors for patients with melanoma brain metastases in the era of modern systemic therapy[END_REF][START_REF] Minniti | Stereotactic radiosurgery combined with nivolumab or Ipilimumab for patients with melanoma brain metastases: evaluation of brain control and toxicity[END_REF][START_REF] Nordmann | Effect of Gamma Knife Radiosurgery and Programmed Cell Death 1 Receptor Antagonists on Metastatic Melanoma[END_REF][START_REF] Murphy | Concurrent Radiosurgery and Immune Checkpoint Inhibition: Improving Regional Intracranial Control for Patients With Metastatic Melanoma[END_REF][START_REF] Fang | Radiation necrosis with stereotactic radiosurgery combined with CTLA-4 blockade and PD-1 inhibition for treatment of intracranial disease in metastatic melanoma[END_REF] .

Despite a low number of available data, the overall summary estimate for radionecrosis was 5.3% in the largest meta-analysis [START_REF] Lehrer | Treatment of brain metastases with stereotactic radiosurgery and immune checkpoint inhibitors: An international meta-analysis of individual patient data[END_REF] . Our own series with a rather high number of patients and sufficient follow-up permits to address the question of radiotoxicity. Our data do not provide evidence that combining anti-PD1 therapy and SRS does increase radiotoxicity. The neurological symptoms observed during the follow-up period were related to SRS-treated BMs in only 7 patients. Despite the high number of patients with multiple BMs (66%), the 2.2 % bleeding rate, the 6 % rate of edema, and the 4.4% of ARE are within the expected figures of adverse events in a SRS-treated population. Indeed, there is a natural propensity of MM-BMs for bleeding [START_REF] Liew | Outcome predictors of Gamma Knife surgery for melanoma brain metastases. Clinical article[END_REF][START_REF] Raizer | Brain and leptomeningeal metastases from cutaneous melanoma: survival outcomes based on clinical features[END_REF] and it is not infrequent to observe ARE following radiosurgery for BM, particularly when large volume metastasis are treated [START_REF] Lippitz | Stereotactic radiosurgery in the treatment of brain metastases: the current evidence[END_REF][START_REF] Marchan | Stereotactic radiosurgery of brain metastasis from melanoma[END_REF] . One limitation of our study is that our 38.89 month median follow-up might not be long enough to rule out very late radiotoxicity. One must be aware that any strategy increasing survival of patients with BMs will naturally increase the rate of late AREs, since these events could not be captured before because of premature deaths by melanoma evolution.

Within the frame of this study OS and brain-PFS did not differ in patients already treated with anti-PD1 at the time of SRS and who started anti-PD1 just after SRS. Both can be considered as concurrent radio-immunotherapy in line with some series [START_REF] Chen | Concurrent Immune Checkpoint Inhibitors and Stereotactic Radiosurgery for Brain Metastases in Non-Small Cell Lung Cancer, Melanoma, and Renal Cell Carcinoma[END_REF][START_REF] Kiess | Stereotactic radiosurgery for melanoma brain metastases in patients receiving ipilimumab: safety profile and efficacy of combined treatment[END_REF][START_REF] Qian | Timing and type of immune checkpoint therapy affect the early radiographic response of melanoma brain metastases to stereotactic radiosurgery[END_REF][START_REF] Kotecha | The Impact of Sequencing PD-1/PD-L1 Inhibitors and Stereotactic Radiosurgery for Patients with Brain Metastasis[END_REF] and meta-analysis data [START_REF] Lehrer | Treatment of brain metastases with stereotactic radiosurgery and immune checkpoint inhibitors: An international meta-analysis of individual patient data[END_REF] suggesting that concurrent anti-PD1 and SRS achieves the best results. Looking for predictive markers of response, we found that the poor prognostic factors of BMs play a role in our cohort as expected (ECOG, number of extra cerebral metastatic site and total BM's volume).

It is noteworthy that having receive ipilimumab prior to SRS and antiPD1 seems to have a significant protective on brain PFS, although the low number of patients does not allow to draw reliable conclusions. We found no association between corticosteroids and survival.

A significant proportion (roughly 1/3 d ) of patients in our cohort died within 6 months of SRS. This may lead to discuss whether there is an actual indication of SRS +/-immunotherapy in patients cumulating poor prognosis factors such as very high cumulative volume (especially in the posterior fossa and brainstem) or associated LMD. Decision has to be made case by case in tumor boards since even these patients can have an immediate benefit from SRS without toxicity issue.

Although this study is retrospective, the systematic and standardized practice in our tumor board whose policy is to treat all BMs < 10cc, including multiple ones, with SRS at first BM diagnosis and anti-PD1 reduces the selection bias of this study, knowing however that large volume BMs are by definition not candidates for SRS. The best argument is that patients with severe disease were not excluded as 33% of patients had ≥4 BMs and 50% of patients had received prior targeted therapy with BRAF-MEK inhibitors.

Declaration of interest : none.

CONCLUSION

SRS combined with anti-PD1 achieves favorable outcomes without evidence of increased radiotoxicity in brain metastatic melanoma patients. Whether this benefit is due to the combination of local control and a systemic response or to an actual biological synergy between the 2 strategies is an open question. Given the excellent short term results recently obtained in BMs with the ipilimumab-nivolumab regimen [START_REF] Margolin | Ipilimumab in patients with melanoma and brain metastases: an open-label, phase 2 trial[END_REF] , a strategy combining SRS and this bi-therapy is now ongoing (NCT03340129).

Timing of index SRS and anti-PD1 administration

  Univariate and multivariate Cox proportional hazard regression models were performed on prognostic factors associated with OSSRS and brain-PFSSRS. The following variables were included in the model: age, gender, ECOG PS, BRAF mutation status, , total volume of BMs treated, number of extra-cranial metastatic sites, presence of neurological symptoms, use of corticosteroids at the time of SRS, type of systemic treatment received before anti-PD1 and timing of SRS and anti-PD1 administration. Variables with a p<.05 in univariate analysis or clinically relevant were kept in the multivariate model. Statistical analysis was performed using PASW Statistics version 17.02 (IBM SPSS Inc., Chicago, IL, USA). Continuous variables were expressed as means ±SD or as median with range (min, max), and categorical variables as count and percentages. Means values were compared by student t-test, and percentages by Chi-Square test (or Fisher's exact test, as appropriate). The results are reported as two-sided p values with 95 % confidence intervals (CI). All the tests were two-sided. The statistical significance was defined as p<.05. All statistical analyses were performed by AL from the department of public health and biostatistics.

  Among 125 patients treated by SRS at BM diagnosis over the study period, 50 fulfilled the inclusion criteria (concomitant SRS and anti-PD1 treatment) (Fig1). Detailed characteristics of the population are given in Table1.Overall, 188 BMs were treated during 50 SRS sessions in 50 patients. A solitary BM was targeted in 17 patients (34%), and multiple BMs in 33 patients (66%). The median number of BM treated per patient was 3 (min 1-max 21). The median aggregate metastases volume treated per patient was 366 mm[START_REF] Ahmed | Clinical outcomes of melanoma brain metastases treated with stereotactic radiation and anti-PD-1 therapy[END_REF] (min 15-max 21.570). Twenty-seven patients received Nivolumab and 23 patients received Pembrolizumab. Nine patients had neurological symptoms and 8 patients were under corticosteroids at the time of SRS. Twenty-six patients (52%) started anti-PD1 within 3 months after SRS (median time 0.79 m (min 0.10-max 3 m) and 24 patients (48%) were already under anti-PD1 at the time of SRS (median duration of anti-PD1 treatment at the time of SRS 3.28 m (min 0.2-max 22). Median clinical follow-up time after SRS was 38.89 months (IQR 24.43; 45.28). The neuroimaging evaluation was performed in 48 patients (2 patients died of highly disseminated disease before the first planned follow-up brain imaging).

Fig 1 :

 1 Fig 1: Retrospective selection of a cohort of patients homogeneously treated by SRS and anti-PD1 within 3 months, among consecutive patients with melanoma brain metastases

Fig 2 :

 2 Fig 2: Time to brain progression, survival from SRS, treatment exposure (SRS, duration of anti-PD1 treatment) and onset of suspected AREs in the 50 patients

Fig 3 :Fig 4 :Fig 5 :

 345 Fig 3: Assessment of toxicity among the 188 BMs treated by SRS Fig 4: OS from SRS Fig 5: Brain-PFS from SRS

Fig 1 :Fig 2 :

 12 Fig 1: "Retrospective selection of a cohort of patients homogeneously treated by SRS and anti-PD1 within 3 months, among consecutive patients with melanoma brain metastases"Fig 2: Time to brain progression, survival from SRS, treatment exposure (SRS, duration of anti-PD1 treatment) and onset of suspected AREs in the 50 patients

Fig 3 :Fig 4 :Fig 5 :

 345 Fig 3: Assessment of toxicity among the 188 BMs treated by SRS Fig 4: OS from SRS Fig 5: Brain-PFS from SRS

Table 1 : Patients' characteristics at SRS (n=50) 526Table 2 : Impact of patient and disease's characteristics at the time of SRS on the overall survival from SRS (OSSRS): univariate and multivariate analyses (n=50)

 12

	Univariate	Multivariate

.17 (3.01-27.92) <.001 20.99 (4.59-95.93) <.001 BRAF mutation

	1	11 (22)	0.22 (0.07-0.77)	0.017 0.38 (0.10-1.55)	0.178
	2	10 (20)	0.86 (0.36-2.08)	0.737 0.26 (0.07-0.93)	0.039
	≥3	22 (44)	1	1
	Total volume of BMs treated (cm 3 )
	<1 cm 3	19 (38)	1
	1-3 cm 3	12 (24)	5.07 (1.93-13.3)	0.001 8.52 (2.10-34.54) 0.003
	>3 cm 3	19 (38)	3.18 (1.26-8.02)	0.014 6.72 (1.64-27.5)	0.008
	Neurological symptoms at the time of SRS
	No	41 (82)	1
	Yes	9 (18)	1.74 (0.75-4.06)	0.201
	Corticosteroids at the time of SRS
	No	42 (84)	1	1
	Yes	8 (16)	1.04 (0.4-2.72)	0.932 0.35 (0.09-1.42)	0.141
	Systemic treatment before anti-PD1
	None	18 (36)	1	1
	BRAF+/-MEK inhibitor only	20 (40)	3.03 (1.30-7.05)	0.010 1.85 (0.61-5.57)	0.274
	Ipilimumab only	6 (12)	1.05 (0.28-3.98)	0.940 0.48 (0.11-2.06)	0.325
	Mutant BRAF+/-MEK inhibitor and Ipilimumab	29 (58) 5 (10)	1 1.23 (0.32-4.65)	0.762 1.43 (0.26-7.78)	0.681
	Wild-type Chemotherapy only	21 (42) 1 (2)	0.63 (0.30-1.32) NR	0.219 0.979 NR	0.983
	Number of EC metastatic sites Timing of index SRS and anti-PD1
	0 administration	7 (14)	0.72 (0.24-2.16)	0.560 0.28 (0.06-1.28)	0.101

Table 3 : Impact of patient and disease's characteristics at the time of SRS on the brain progression free survival from SRS (Brain- PFSSRS): univariate and multivariate analyses (analysis performed on 48 patients since 2 patients died before the first cerebral imaging)

 3

	Univariate	Multivariate

.15 (1.71-22.14) 0.006 14.43 (2.42-86.10) 0.003 BRAF mutation

	1-3 cm 3	10 (20.8)	4.62 (1.58-13.5)	0.005 8.84 (1.58-49.44) 0.013
	>3 cm 3	19 (39.6)	2.54 (0.92-7.03)	0.074 3.33 (0.81-13.64) 0.095
	Number of EC metastatic sites
	0	7 (14.6)	0.87 (0.24-3.15)	0.825 0.40 (0.08-2.10)	0.278
	1	11 (22.9)	0.53 (0.16-1.68)	0.278 0.98 (0.26-3.65)	0.972
	2	10 (20.8)	1.37 (0.52-3.61)	0.523 0.71 (0.20-2.49)	0.589
	≥3	20 (41.7)	1	1
	Neurological symptoms at the time of SRS
	No	39 (81.2)	1
	Yes	9 (18.8)	1.56 (0.62-3.95)	0.343
	Corticosteroids at the time of SRS
	No	40 (83.3)	1	1
	Yes	8 (16.7)	0.91 (0.31-2.66)	0.857 0.35 (0.10-1.55)	0.166
	Systemic treatment before anti-PD1
	None	18 (37.5)	1	1
	BRAF+/-MEK inhibitor only	19 (39.6)	2.10 (0.87-5.08)	0.101 0.67 (0.18-2.46)	0.541
	Ipilimumab only	5 (10.4)	0.33 (0.04-2.64)	0.296 0.08 (0.01-0.79)	0.031
	Mutant BRAF+/-MEK inhibitor and Ipilimumab	28 (58.3) 5 (10.4)	1 0.75 (0.16-3.56)	0.716 0.90 (0.16-5.18)	0.903
	Wild-type Chemotherapy only	20 (41.7) 1 (2.1)	0.607 (0.26-1.42) NR	0.250 0.982 NR	0.986
	Total volume of BMs treated
	<1 cm 3	19 (39.6)	1	1
			25

1 SRS under anti-PD1 24 (48) 0.77 (0.38-1.57) 0.472 EC: extra cerebral BM: brain metastases 1 SRS under anti-PD1 22 (45.8) 0.75 (0.33-1.70) 0.489 EC: extra cerebral BM: brain metastases

Patients' characteristics Number (%)

Age (year)

Median (min-max) (


Juliana De Oliveira Mota
email: juliana.de-oliveira@oniris-nantes.fr

Sandrine Guillou
email: sandrine.guillou@inrae.fr

Fabrice H F Pierre
email: fabrice.pierre@inrae.fr

Jeanne-Marie Membré
email: membre@oniris-nantes.fr

Juliana De

Oliveira Mota

Quantitative assessment of microbiological risks due to red meat consumption in France

Keywords: foodborne illnesses, risk ranking, public health, disability-adjusted life year, DALY

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In recent years, red meat consumption has become a public health concern in France and other western countries [START_REF] Casalonga | Quelles viandes manger? 60 millions de consommateurs[END_REF]. In addition, unprocessed red meat, including beef, pork, lamb and other small ruminants, is widely consumed in France. Indeed, in 2013, each adult consumed an average of 52.5 g/day of red meat, from which 31 g/day was beef and 11 g/day was pork [START_REF] Duchène | La consommation de viande en France[END_REF]. However, red meat has been classified by the World Cancer Research Found/Imperial College of London and the World Health Organization (WHO) as "probably carcinogenic to humans" for colorectal cancer [START_REF] Wcrf/Aicr | Diet, nutrition, physical activity and colorectal cancer[END_REF][START_REF] Bouvard | Carcinogenicity of consumption of red and processed meat[END_REF]. On this basis, there are dietary recommendations to limit red meat consumption to 500 g per week [START_REF] Anses | Avis et rapport relatifs à l'actualisation des repères du PNNS : révision des repères de consommation alimentaires[END_REF]. Red meat consumption was also associated with cardiovascular disease (CVD) mortality risk [START_REF] Abete | Association between total, processed, red and white meat consumption and all-cause, CVD and IHD mortality: a meta-analysis of cohort studies[END_REF] and suspected to increase the risk of breast cancer, advanced prostate cancer, stroke, coronary heart diseases and heart failure [START_REF] Wolk | Potential health hazards of eating red meat[END_REF][START_REF] Bechthold | Food groups and risk of coronary heart disease, stroke and heart failure: a systematic review and dose-response meta-analysis of prospective studies[END_REF].

Microbiological risks are also a major concern when preparing and consuming red meat. In 2017 in France, 10% of the total number of foodborne outbreaks declared to the Regional Health Agency and Departmental Directorate of Social Cohesion and Population Protection were due to red meat consumption. The main pathogens (confirmed or suspected) were Staphylococcus aureus (13%), Clostridium perfringens (11%) and Bacillus cereus (10%) [START_REF] Invs | Surveillance des toxi-infections alimentaires collectives -Données de la déclaration obligatoire[END_REF].

In Europe, the European Food Safety Authority (EFSA) and the European Centre for Disease Prevention and Control (ECDC) are in charge of evaluating the annual trends and sources of zoonoses, zoonotic agents and foodborne outbreaks. In 2017, they estimated that pork meat was responsible for 4.2% of the total outbreaks and 6.9% of the total cases for strongevidence outbreaks in Europe. Beef meat was responsible for 2% of total outbreaks and 3% of the total cases for strong-evidence outbreaks, with a reporting rate of 0.012 per 100,000 for both types of meat [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF].

Nevertheless, the number of confirmed cases was underestimated because notification is not mandatory for every pathogen (e.g. campylobacteriosis in France [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF]). Some studies have attempted to estimate the real number of cases. The WHO estimated the number of foodborne illness cases in 2010 by considering the effects of underestimation [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF]. In France, Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF] and Vaillant et al. [START_REF] Vaillant | Foodborne Infections in France[END_REF] performed this estimation for 2008-2013 and 1990-1999, respectively. Nevertheless, the number of cases provides an incomplete estimation of the health impacts of foodborne diseases. Indeed, the severity and duration of sequela vary according to the pathogenic species and the immune status of the consumer. For example, salmonella infection may cause diarrhoea, with a duration of 8 days, while Guillain-Barré syndrome-after campylobacteriosis-is assumed to last a lifetime [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF]. To overcome this limitation, the WHO has gone further than estimate the number of cases; it has used the disability-adjusted life year (DALY) metric [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF] to estimate the disability caused by foodborne diseases. The use of the composite DALY metric enables to consider morbidityencompassing the duration and the disability induced by the sequelae-and the number of years lost due to premature death [START_REF] Pires | Risk benefit assessment of foods: Key findings from an international workshop[END_REF][START_REF] Murray | Quantifying the burden of disease: The technical basis for disability-adjusted life years[END_REF]. The DALY metric was also used by ECDC through a software tool for the estimation of the infectious disease burden in Europe (BCoDE) [START_REF]ECDC BCoDE toolkit[END_REF].

Disease models were built for each microbiological hazard and country. Information about sequelae (health impact, death, proportion of people concerned, duration, etc.) were integrated, and the user had to complete the requested information per age group and gender Despite these substantial efforts, the burden of diseases induced by microbiological pathogens on health that is exclusively attributable to red meat consumption in France remains incomplete. In particular, the number of foodborne cases attributable to red meat consumption, and its corresponding DALY values, has not yet been estimated. Moreover, the uncertainty associated with the different types of data has not been aggregated into one model to deliver final estimates of disease burdens with confidence intervals. Thus, the objective of this study was to combine the available data in the literature to determine the main microbiological hazards when consuming red meat and to estimate the associated number of foodborne illness cases and deaths and the subsequent burden of diseases in France.

Moreover, this study aimed to estimate the burden of foodborne diseases attributable to red meat consumption to enable comparison and balancing with nutritional risks and benefits of red meat, expressed in DALYs, evaluated in recent publications [START_REF] Gold | oh my: Similarities and differences in summary measures of population health[END_REF][START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF].

Methods

Selection of the available data

The literature was searched using terms such as "foodborne disease(s)", "foodborne outbreak(s)", "foodborne illness(es)", "foodborne attribution" and "microbiological risk assessment" to select the main foodborne pathogens in France and to estimate the incidence and the associated burden of diseases when eating red meat (beef, pork and other small ruminants). Official reports from the WHO, the EFSA, the French Agency for Food, the Environmental and Occupational Health & Safety (ANSES), the ECDC and Santé Publique France were searched. PubMed and Google Scholar searches identified complementary data specific to the French population and the proportion of foodborne disease burden attributable to each type of red meat.

Determination of the main pathogens involved in foodborne outbreaks related to red meat consumption in France

To define the main foodborne pathogens of interest when eating red meat, three criteria were considered.

Incidence of foodborne illnesses in Europe and France for each pathogen, regardless of the source

To determine the hazards responsible for foodborne illness in Europe, a report from the WHO, which estimated the number of foodborne illness cases in 2010 in countries in the "EUR A" subregion, was used as a reference. It included Andorra, Austria, Belgium, Croatia, Cyprus, the Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Israel, Italy, Luxembourg, Malta, Monaco, Netherlands, Norway, Portugal, San Marino, Slovenia, Spain, Sweden, Switzerland and the United Kingdom [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF].

For the French incidence, the work of Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF] was considered. These authors estimated the number of French cases for the overall population. In order to make comparisons with future and other countries' estimations, the results were expressed per 100,000 population. The 2010 French population was considered to be 62,765,235 inhabitants (Table 1).

DALYs attributable to foodborne illnesses for each pathogen and for all sources

The WHO evaluated the disease burdens associated with foodborne illnesses in terms of DALYs [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF]. To estimate this measure, data on the incidence, clinical outcomes, duration of the health state, age distribution and mortality rate were collected for each hazard by the WHO. The study estimated the number of years lived with disability (YLD) attributable to the hazard health impact and multiplied it by the disability weight factor, which reflects the severity of the health state [START_REF] Gold | oh my: Similarities and differences in summary measures of population health[END_REF]. Subsequently, the number of years of life lost (YLL)-due to a premature death-was added [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF].

Our calculation considered the WHO's DALY estimations. For missing DALY values, the estimations from Havelaar et al. [START_REF] Fosse | Hiérarchiser les risques de zoonoses alimentaires : une approche quantitative. Application aux dangers bactériens transmis par les viandes porcine et bovine[END_REF], recently used by Mangen et al. [START_REF] Havelaar | Attribution of Foodborne Pathogens Using Structured Expert Elicitation[END_REF], were considered.

The proportion of foodborne illnesses attributable to red meat consumption for each pathogen

The burden that could be attributed to red meat consumption was mainly extracted from Hoffmann et al. [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF], the most recent study on the attribution fraction per pathogen for beef, pork and other small ruminant meat. When data about the attribution fraction was missing from this latter study [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF], attribution data from a French team was considered [START_REF] Fosse | Hiérarchiser les risques de zoonoses alimentaires : une approche quantitative. Application aux dangers bactériens transmis par les viandes porcine et bovine[END_REF]. However, that source only estimated the attributable fraction to beef and pork. Finally, for the remaining missing data, the attributable fraction estimated by a Dutch team was utilised [START_REF] Havelaar | Attribution of Foodborne Pathogens Using Structured Expert Elicitation[END_REF]. Attribution fractions per pathogen and type of meat is given in Table 1.

Incidence, death and disease burden of foodborne pathogens in Europe and

France associated with red meat consumption

The number of cases, deaths and disease burden attributable to red meat consumption were estimated. The number of illness cases were calculated as represented in Equation 1:

(

. = ∑ . × , × , 1)
-!" is the type of red meat (1: beef; 2: pork; and 3: other small ruminant meat). For norovirus, !" = 1 also included lamb;

-$ is the pathogen; - .
is the number of cases of foodborne illness attributable to red meat consumption per 100,000 individuals in France;

-. is the number of cases of foodborne illness caused by a specific pathogen in France from Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF];

- ,
is the proportion of foodborne illness cases attributable to a pathogen and a type of red meat. Campylobacter spp., non-typhoidal Salmonella enterica and shigatoxin producing Escherichia coli attribution fraction were extracted from Hoffmann et al. [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF]. The attribution fraction of hepatitis E and norovirus were extracted from

Havelaar et al. [START_REF] Havelaar | Attribution of Foodborne Pathogens Using Structured Expert Elicitation[END_REF] and Staphylococcus aureus, Clostridium perfringens and Toxoplama gondii were extracted from Fosse et al. [START_REF] Fosse | Hiérarchiser les risques de zoonoses alimentaires : une approche quantitative. Application aux dangers bactériens transmis par les viandes porcine et bovine[END_REF];

- %$ &
represents the 2010 population in France (62,765,235).

The number of deaths (Equation 2) was calculated by multiplying the number of foodborne illness cases per pathogen and red meat type by the proportion of deaths per pathogen-case. These latter values were obtained from the ratio between the number of deaths and the number of illness cases per pathogen from Van Cauteren et al [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF].

(2)

' (ℎ. = * . × 100,000 %$ & × , × -' (ℎ.
Where:

-' (ℎ.

is the number of deaths after of foodborne illness attributable to red meat consumption per 100,000 population in France;

--' (ℎ. is the ratio of deaths after a foodborne illness per pathogen-case from Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF].

DALYs issued from the WHO (2015) [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF] were considered in the estimation, except for C. perfringens, S. aureus, hepatitis E and norovirus. For those cases, DALY values attributable to foodborne diseases were not available in the WHO estimations. Therefore, DALYs per 1,000 cases from a Dutch study were used as reference [START_REF] Mangen | Cost-of-illness and disease burden of food-related pathogens in the Netherlands[END_REF]. DALYs were estimated as follows (Equation 3):

(3) >.?@AB,C@?D,EFAF,G.HIA@IJ × 100,000 %$ & × . /0. >.?@AB,C@?D,EFAF,G.HIA@IJ K, Where:

-. /0. is the number of DALYs caused by a specific pathogen and attributable to red meat consumption per 100,000 population in France;

-. /0. 23is the number of DALYs in the "EUR A" region due to the pathogen per 100,000 population from WHO [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF];

-. /0. is the number of DALYs in the Netherlands due to the pathogen per 1,000 cases;

- %$ &
is the 2010 population in France (62,765,235).

To compare the disease severity from any pathogen, considering the type of sequelae and their duration, the DALYs per case was estimated by dividing the number of DALYs by the number of cases.

Uncertainty propagated in the model

In literature and report, the data were expressed by their median values and corresponding 95% confidence intervals (CIs). Therefore, the probability distributions were re-built using these initial data, as explained hereafter:

-The number of foodborne disease cases was extracted from a previous study [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF],

specifically the median value of the estimations and the associated 95% CI. These data were integrated into our model with a lognormal distribution, which was the same distribution law used by Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF]. The latter study did not specify whether this confidence interval reflected uncertainty or variability. Therefore, it was considered to represent uncertainty. The mean was approximated by the median value reported (on a ln scale), the standard deviation was estimated by using the interval confidence bounds. As an example, for Campylobacter spp., the estimated median incidence from Van Cauteren et al. study [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF] was 392,177 with a confidence interval between 215,216 at the 5% limit and 862,747 at the 95% limit. The mean of the lognormal distribution was estimated to 12.88 and to match the confidence interval bounds, the standard deviation was approximated to 0. 375. This gave a lognormal distribution with a 5 th percentile of 12.27 and a 95 th percentile of 13.51. Once expressed in cell count, this interval was close to the one given in Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF].

-The attribution fraction of foodborne illnesses per pathogen and type of meat followed a beta distribution; the available mean or the median was used to estimate the beta distribution parameters. When the value of the attributable proportion was expressed by the mean, the parameters were estimated using the equation mean=α/(α+β). When the value of the attributable proportion was expressed by the median, the parameters were estimated using the equation median=(α-1/3)/(α+β-2/3). Therefore, the values of α and β were estimated by approximation. As an example, for Campylobacter spp., the median of the attributable fraction from beef was 0.16 with a confidence interval between 0 at the 5% limit, and 0.37 at the 95% limit [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF]. The best fit of α and β parameters were 3 and 14.3, respectively. This resulted to an estimation of beef Campylobacter spp. attribution by a beta distribution having a median of 0.16, a 5 th percentile of 0.05 and a 95 th percentile of 0.34, close to results given in Hoffmann et al. [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF].

-Finally, the probability distributions of DALY, acquired from the literature, were assumed to follow normal distributions.

The implementation of the inputs in the model are represented in Table 1. Our models used 10,000 iterations to capture the uncertainty. This action was performed using R software (version 3.6.2). To verify the stability of the outputs, three simulations were performed. The variation between these three simulations was less than 5% for the mean of the DALY whatever the pathogen and type of meat.

Results

Main microbiological hazards associated with red meat consumption

From our literature search, 16 foodborne pathogens were identified to be involved in foodborne diseases associated with red meat consumption:

- -Two parasites: Taenia saginata and Toxoplasma gondii.

Some of these pathogens were discarded according to the criteria described below.

-B. cereus, Shigella spp., Vibrio spp. and T. saginata were excluded due to the lack of data about the proportion attributable to red meat. Brucella spp. was excluded due to the lack of information about the number of French cases. C. botulinum was excluded due to the lack of quantified DALYs.

-Foodborne illnesses due to L. monocytogenes and Yersinia spp. were not considered because these pathogens were mostly associated with ready-to-eat foods [START_REF] Efsa/Ecdc | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF][START_REF] Anses | Information des consommateurs en matière de prévention des dangers biologiques -Tome 1 Hiérarchisation des couples danger/aliment et état des lieux des mesures d'information[END_REF].

After the above exclusions, the selected pathogens associated with red meat consumption were Campylobacter spp., C. perfringens, S. enterica, S. aureus, STEC, T. gondii, hepatitis E virus and norovirus.

Estimation of the foodborne disease burden in France

In France, the number of foodborne diseases due to red meat consumption was estimated to have a mean of 670 [95% CI = 380-1100] illness cases per 100,000 inhabitants.

Campylobacter spp. was responsible for 32% of foodborne incidents due to red meat consumption, with a mean of 210 [95% CI = 50-520] cases per 100,000 population (Figure 1). C. perfringens was the second pathogen responsible of the highest number of cases with a mean of 150 [95% CI = 40-420] cases per 100,000 population, followed by non-typhoidal S.

enterica with a mean of 110 [95% CI = 30-280] per 100,000 population. The least frequent foodborne pathogen was T. gondii, which contributed to 12 [95% CI = 4-25] cases (estimated mean values) per 100,000 population. The pathogen that induced the highest mortality was non-typhoidal S. enterica, with a mean of 0.04 [95% CI = 0.01-0.10] death per 100,000 population (Table 2), followed by hepatitis E, T. gondii and Campylobacter spp., with means of 0.02 death per 100,000 population (Figure 2). The total number of deaths was estimated to a mean value of 0.12 [95% CI = 0.07-0.19] per 100,000 population.

Our study estimated a mean of 39 [95% CI = 8-71] DALYs per 100,000 population due to foodborne diseases in France. The major contributor to the loss of years in good health from red meat consumption in France was hepatitis E (mean: 33 [95% CI = 1-64] DALYs per 100,000 population), specifically due to pork consumption, even though it was ranked fourth in terms of the overall incidence of foodborne illnesses from red meat consumption (Table 2, Figure 1 and Figure 3). The main bacteria associated with burden of disease in terms of DALY from pork consumption were non-typhoidal S. enterica, which was three times higher than C. perfringens or Campylobacter spp. For beef, the main bacteria contributor of foodborne burden was Campylobacter spp., C. perfringens, STEC and non-typhoidal S. enterica (Table 2).

Discussion

The first objective of the present study was to aggregate data available in the literature to identify and characterise the main microbiological hazards when consuming red meat in France. These sources included muscle and offal from beef, pork and other small ruminants, but not dairy products. Subsequently, a risk assessment model was built to estimate the associated number of foodborne illnesses and deaths. Finally, the goal was to estimate the consequent burden of diseases, considering the severity of the illness, and perform further comparisons with other health effects and compare consumption scenarios.

From the literature search, 17 foodborne pathogens were identified as involved in foodborne diseases attributable to red meat consumption. This number was less than the main zoonotic agents identified by Haddad et al. [START_REF] Haddad | Les zoonoses infectieuses. In Polycopié des Unités de maladies contagieuses des Ecoles vétérinaires française[END_REF], who identified more than 31 agents from red meat, but those authors included additional transmission pathways of infection (e.g. occupational transmission, animal bites, etc.). A team from the Centre d'Information des Viandes (Meat Information Center) identified four bacterial diseases associated with meat product consumption (foodborne outbreaks, listeriosis, botulism and haemolytic uraemic syndrome [HUS]), three parasitic diseases (taeniasis, toxoplasmosis and trichinellosis) and one viral disease (hepatitis E) [START_REF] Bailly | Micro-organismes et parasites des viandes : les connaître pour les maîtriser, de l'éleveur au consommateur[END_REF]. However, for L. monocytogenes and C. botulinum identified in that study, the main meat products were processed and consumed without precooking [START_REF] Bailly | Micro-organismes et parasites des viandes : les connaître pour les maîtriser, de l'éleveur au consommateur[END_REF]. In 2014, ANSES classified the main hazard-food pathogen couples. Meat was associated with STEC, T. gondii, non-typhoidal Salmonella spp., Y. enterocolitica and T.

saginata. Campylobacter was mostly from poultry meat and hepatitis E with raw pork liver [START_REF] Anses | Information des consommateurs en matière de prévention des dangers biologiques -Tome 1 Hiérarchisation des couples danger/aliment et état des lieux des mesures d'information[END_REF].

The incidence, attribution source and data availability were considered when selecting the pathogens to quantify the disease burden due to red meat consumption. Eight pathogens were selected for this study: Campylobacter spp., C. perfringens, non-typhoidal S. enterica, STEC, S. aureus, T. gondii, hepatitis E and norovirus. In the Netherlands, 12 pathogens were identified for red meat-including beef, lamb and pork-with the same criteria. In addition to the pathogens chosen in our study, L. monocytogenes, rotavirus, C. parvum and Giardia lamblia were considered in that study [START_REF] Havelaar | Disease burden of food-related pathogens in the Netherlands[END_REF].

To estimate the attribution of foodborne diseases to red meat consumption, our estimations were mostly based on WHO data, which aggregated the judgments from 73 international experts [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF]. Hereby, per 100,000 inhabitants, our study's estimated number of enterica, STEC and T. gondii in red meat accounted for 15% of the total foodborne illnesses estimated. These pathogens infection associated with red meat also accounted for 16% of the total deaths and 15 % of the total DALYs due to foodborne pathogens From our estimations, the major contributor of foodborne illness cases attributable to red meat consumption was Campylobacter spp. This pathogen has been the most commonly reported hazard that induced gastrointestinal issues in the European Union since 2005 [START_REF] Efsa/Ecdc | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF].

cases
Indeed, infection with this pathogen may cause diarrhoea, abdominal pain, bloody stools, fever, headaches, vomiting and acute enteritis. Moreover, campylobacteriosis was responsible for 30.1% of the total cases of Guillain-Barré syndrome according to a WHO study [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne diseases burden epidemiology reference group[END_REF]. Even though the main reservoir of Campylobacter jejuni is birds-including poultry-beef and pork can also serve as a Campylobacter reservoir (essentially Campylobacter coli) [START_REF] Anses | Fiche de description de danger biologique transmissible par les aliments : Campylobacter jejuni, Campylobacter coli[END_REF]. In 2017, the EFSA/ECDC reported that 51% of the strong-evidence foodborne outbreaks caused by Campylobacter were due to milk consumption, versus 3% for meat and meat products (excluding strong-evidence waterborne outbreaks) [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF]. However, this pathogen was reported to be present in fresh pork and beef meat (8.3% of positive units) [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF]. In addition, in our study, it was estimated that 30% of foodborne illnesses from red meat were due to Campylobacter spp., from which 55% were attributable to beef meat. In terms of incidence, it was also determined that the second pathogen inducing the highest number of cases was C. perfringens (22%), followed by non-typhoidal S. enterica (17%) and hepatitis E (11%). S.

aureus accounted for 6% of the cases related to red meat consumption.

The proportion of foodborne illnesses associated with the distinct pathogens in our study was different from Dutch studies. Indeed, in the same years in the Netherlands, the National Institute for Public Health and the Environment (RIVM) estimated that C.

perfringens was the major contributor of foodborne illness from red meat consumption, with 56% of foodborne illness cases [START_REF] Havelaar | Disease burden of food-related pathogens in the Netherlands[END_REF]. Moreover, the proportion of Campylobacter spp., S.

aureus and S. enterica cases were approximately two-times higher in our study compared to the Dutch studies [START_REF] Havelaar | Attribution of Foodborne Pathogens Using Structured Expert Elicitation[END_REF][START_REF] Havelaar | Disease burden of foodborne pathogens in the Netherlands[END_REF]. The strategy used to estimate incidence of foodborne illnesses in Van Cauteren et al. [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF] was not the same as the Dutch studies. The former used an underestimation factor to calculate the number of illness from the reported cases [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF], while the Dutch study based the incidence estimates for gastro-enteritis on population-based cohort studies [START_REF] Havelaar | Disease burden of foodborne pathogens in the Netherlands[END_REF]. Moreover, the disease surveillance system coverage is not the same in France as in the Netherlands, a factor that makes comparison difficult. For example, the campylobacteriosis and salmonellosis surveillance system coverage in 2016 was estimated to be 20% and 48%, respectively, in France, versus 52% and 64%, respectively, in the Netherlands [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF]. In addition, the list of mandatory notifiable infectious diseases is not the same for all countries. For instance, STEC infection is required to be reported in the Netherlands but not in France [START_REF] Ecdc/Efsa | The European Union summary report on trends and sources of zoonoses, zoonotic agents and food-borne outbreaks in[END_REF].

Among microbiological hazards relevant to beef consumption, STEC is the most studied [START_REF] Tesson | A Systematic Review of Beef Meat Quantitative Microbial Risk Assessment Models[END_REF]. In 2010, 122 cases of HUS, which is characterised by acute kidney and renal failure in young children [START_REF] Fao | Enterohaemorrhagic Escherichia coli in raw beef and beef products: approaches for the provision of scientific advice[END_REF], were reported in France [START_REF] Anses | Information des consommateurs en matière de prévention des dangers biologiques -Tome 1 Hiérarchisation des couples danger/aliment et état des lieux des mesures d'information[END_REF] following STEC ingestion from ground beef [START_REF] Anses | Information des consommateurs en matière de prévention des dangers biologiques -Tome 1 Hiérarchisation des couples danger/aliment et état des lieux des mesures d'information[END_REF][START_REF] Anses | Avis des consommateurs en matière de prévention des risques biologiques liés aux aliments: Tome 2 -Évaluation de l'efficacité des stratégies de communication[END_REF]. Ground beef is considered the most common source of STEC foodborne illnesses, along with raw milk [START_REF] Anses | Information des consommateurs en matière de prévention des dangers biologiques -Tome 1 Hiérarchisation des couples danger/aliment et état des lieux des mesures d'information[END_REF]. In a previous report, ANSES estimated a probability of HUS between 0.02 and 0.05 of illness after STEC infections [START_REF] Afssa | Appréciation quantitative des risques liés à Escherichia coli O157:H7 dans les steaks hachés surgelés consommés en restauration familiale en France par les enfants de moins de 16 ans[END_REF]. In our estimations, 19 cases per 100,000 population were due to STEC infections attributable to red meat consumption, from which the incidence due to beef consumption was estimated at 14 would be around 170 cases, which is close to the lower bound of our estimations.

The major contributor of deaths due to red meat consumption was non-typhoidal S.

enterica associated with pork, followed by hepatitis E, T. gondii and Campylobacter spp. In terms of DALYs, hepatitis E was responsible for the highest loss of years in good health resulting from consumption of red meat. In France, this loss was exclusively due to pork meat, specifically pork liver. After hepatitis E, T. gondii and non-typhoidal S. enterica were hepatitis B and maternal anti D-fetal allo-for which screening is mandatory. This protocol has been a part of prenatal screening programmes in France since the late 1970s [START_REF] Autorité De Santé | Surveillance sérologique et prévention de la toxoplasmose et de la rubéole au cours de la grossesse et dépistage prénatal de l'hépatite B -Pertinence des modalités de réalisation[END_REF]. Almost all of the congenital forms of T. gondii infection are identified in France, in contrast to other European countries where the screening is not performed or is not mandatory [START_REF] Ecdc | Congenital toxoplasmosis[END_REF]. When fetal infection occurs, the treatment against toxoplasmosis infection in utero was demonstrated to allow children to have a similar quality of life to those not infected [START_REF] Montoya | Systematic screening and treatment of toxoplasmosis during pregnancy: is the glass half full or half empty?[END_REF]. The proportion of congenital toxoplasmosis sequela in France might be lower than estimated by WHO [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne disease burden epidemiology reference group[END_REF][START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne diseases burden epidemiology reference group[END_REF].

Therefore, the burden estimated in our study is likely to be overestimated.

In this study, red meat consumption was responsible for a mean of 0.37 [95% CI: 0.10-0.77] DALY per 100,000 population from STEC infection. This value corresponded to a mean of 232 [95% CI: 62-489] DALYs annually for the population in France, which is onehalf the DALYs estimated by the ANSES (465 years in good health lost) [START_REF] Anses | Avis des consommateurs en matière de prévention des risques biologiques liés aux aliments: Tome 2 -Évaluation de l'efficacité des stratégies de communication[END_REF]. This discrepancy might be due to the higher proportion of deaths considered by the BCoDE toolkit, which was used for the ANSES estimations, compared to the proportion of deaths considered for the 2015 WHO estimations. However, we could not use the BCoDE toolkit for comparison with our estimations due to the lack of foodborne illness incidence data per age class and gender, which is required for BCoDE estimations. The estimations from Havelaar et al. [START_REF] Havelaar | Disease burden in The Netherlands due to infections with Shiga toxin-producing Escherichia coli O157[END_REF] were also higher than ours, even though the considered disability weight was lower than the one used by the WHO (0.123 versus 0.210, respectively). This finding might be explained by the duration of the sequelae, which was considered to be longer in the Dutch's study, i.e. 1 year against 28 days in the Hoffmann study [START_REF] Who | WHO estimates of the global burden of foodborne diseases: foodborne diseases burden epidemiology reference group[END_REF][START_REF] Havelaar | Disease burden in The Netherlands due to infections with Shiga toxin-producing Escherichia coli O157[END_REF].

Using existing studies in the literature allowed us to estimate the number of cases and deaths and the foodborne disease burden in France attributable to red meat consumption, without generating new data with additional monitoring costs. The estimations might be improved by considering the effect of age on outcomes of foodborne diseases, such as sequela and mortality. Indeed, if deaths or permanent sequela occur during childhood, the number of years lost will be higher than if death occurs at an advanced age. However, this estimation was not possible in this study because all the information was given for a global population.

The study by Hoffmann et al. [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF] was chosen to determine the attribution fraction of a pathogen to a red meat type because it is the most recent and reliable study conducted by the WHO with expert elicitation. Although it did not specifically refer to France, data from the "EUR A" region included France. Nevertheless, we are aware that the estimations provided by this study are somewhat different from other published estimates [START_REF] Hoffmann | Attribution of global foodborne disease to specific foods: Findings from a World Health Organization structured expert elicitation[END_REF]. This discrepancy introduced unquantifiable uncertainty into our results. Moreover, to increase the reliability of this work, the existing French attribution study might be updated. Additionally, considering other red meat types, including a larger number of pathogens selected and separate attribution of unprocessed and processed red meat types, might improve the reliability.

Our study estimates the number of foodborne illnesses and DALYs dedicated to red meat in France, with French incidence data. In terms of foodborne bacteria, for beef and pork meat, Campylobacter spp., non-typhoidal Salmonella enterica, C. perfringens and STEC represented a mean of 2.2 [95% CI = 1.0-4.0] DALYs per 100,000 individuals per year.

Overall, the estimations provided in this study might help authorities to focus on these hazards and ultimately reduce their impact on the health of the French population.

With the use of the DALY metric, we were able to compare our estimates to include the effects of other foods components on health. The burden estimated in this study was lower than the burden caused by diet high in sugar-sweetened beverages (46 DALYs [95% CI = 15-83] per 100,000 population) and the use of alcohol (1,818 [95% CI = 1,359-2,368] DALYs per 100,000 population) [START_REF]GBD compare/ Viz Hub[END_REF]. In future studies, the microbiological burden will be balanced by nutritional risks and benefits brought by red meat consumption in a broader risk-benefit assessment as done by other studies [START_REF] Hoekstra | Integrated risk-benefit analyses: Method development with folic acid as example[END_REF][START_REF] Hoekstra | contaminants and human health: quantifying and weighing benefits and risks[END_REF][START_REF] Hoekstra | Benefit-risk assessment of plant sterols in margarine: A QALIBRA case study[END_REF]. It was recently estimated that a mean of 19 [95% 22 CI = 8-33] DALYs per 100,000 people per year were due to colorectal cancer, and a mean of 21 [95% CI = 12-32] DALYs per 100,000 people per year due to cardiovascular disease, were associated with the consumption of red meat [START_REF] Oliveira Mota | Estimation of the burden of disease attributable to red meat consumption in France: Influence on colorectal cancer and cardiovascular diseases[END_REF]. Red meat consumption does have some benefits with regard to the nutrients it provides, especially iron, which may help decrease the major nutritional deficiency in the world [START_REF] Kassebaum | on behalf of GBD 2013 Anemia Collaborators. The global burden of anemia[END_REF]. This condition accounts for a mean of 16 [95% CI = 11-20] DALYs per 100,000 individuals per year [START_REF] Oliveira Mota | Estimation of the burden of iron deficiency anemia in France from iron intake: Methodological approach[END_REF].

C l o s t r i d i u m p e r f r i n g e n s

N o n -t y p h o i d a l S a l m o n e l l a e n t e r i c a

C l o s t r i d i u m p e r f r i n g e n s

N o n -t y p h o i d a l S a l m o n e l l a e n t e r i c a H e p a t i t i s E N o r o v i r u s

S t a p h y l o c o c c

C l o s t r i d i u m p e r f r i n g e n s

N o n -t y p h o i d a l S a l m o n e l l a e n t e r i c a H e p a t i t i s E N o r o v i r u s

S t a p h y l o c o c c

Figure captions:Fig. 1 .

 1 Figure captions:

Fig. 2 .

 2 Fig. 2. Mean number of deaths per 100,000 French population per year and per pathogen attributable to red meat estimated in this study. The full lines represent the 95% uncertainty around the mean value.

Fig. 3 .

 3 Fig. 3. Mean number of disease-adjusted life years (DALYs) per 100,000 French population per year and per pathogen attributable to red meat estimated in this study. The full lines represent the 95% uncertainty around the mean value.

  12 bacteria: Bacillus cereus, Brucella spp., Campylobacter spp., Clostridium botulinum, C. perfringens, Shiga-toxin producing Escherichia coli (STEC), Listeria monocytogenes, Salmonella spp. (mostly Salmonella enterica), Shigella spp., S.

aureus, Vibrio spp. and Yersinia spp.;

-Two viruses: hepatitis E and norovirus;

  The severity of each pathogen was estimated by dividing the number of DALY by the number of cases. As an example, the severity of T. gondii per case was estimated by dividing

	the number of DALY per 100,000 population (3.86 DALY) by the number of cases per
	100,000 population (12 cases). The most severe pathogen per case was hepatitis E, with 0.46
	DALY per case, followed by T. gondii (0.32 DALY per case), STEC (0.02 DALY per case)
	and non-typhoidal S. enterica (0.01 DALYs per case). C. perfringens, Campylobacter spp.
	and S. aureus had similar impacts in terms of severity, with 0.003 DALY per case. The least
	severe pathogen was norovirus, with 0.002 DALY per case.

This research was funded by the Microbiologie et chaîne alimentaire department from Institut national de recherche pour l'agriculture, l'alimentation et l'environnement and Région Pays de la Loire (grant number 34000653).

responsible for the greatest loss of years in good health. This reversal of ranking can be explained by an overestimation of the hepatitis E severity. Indeed, the majority of the DALYs estimated for hepatitis E by the Dutch team were from deaths [START_REF] Havelaar | Disease burden of foodborne pathogens in the Netherlands[END_REF]. However, the proportion of deaths due to this virus in the Netherlands (1.4% [START_REF] Havelaar | Disease burden of foodborne pathogens in the Netherlands[END_REF]), which was the reference study, was higher than that observed in France (0.03% [START_REF] Van Cauteren | Estimated Annual Numbers of Foodborne Pathogen-Associated Illnesses, Hospitalizations, and Deaths, France, 2008-2013[END_REF]). Havelaar et al. [START_REF] Havelaar | Disease burden of foodborne pathogens in the Netherlands[END_REF] assumed that mortality from hepatitis E resulted in 33.4 years of life lost. Therefore, if we considered mortality in France (0.02 deaths [95% CI: 0-0.04] per 100,000 population) and the number of years lost from hepatitis E estimated by the Dutch study, the most probable DALY from hepatitis E in France would be 0.7 per 100,000 population.

Without considering hepatitis E, the mean number of DALYs due to consumption of red meat muscle was 6.6 [95% CI: 3.4-11.1] per 100,000 population, from which 2.8 [95% CI: 1.2-5.2] per 100,000 population were associated with beef meat. Pork meat accounted for 1.5 [95% CI: 0.4-3.8] DALYs per 100,000 population per year. These values were of the same order of magnitude as the estimations from the Netherlands based upon the following calculations: 934 DALY for beef & lamb and 1280 DALY for pork in 2012 for the all Netherlands population [START_REF] Havelaar | Disease burden of food-related pathogens in the Netherlands[END_REF] (16.73 million of inhabitants considered according Eurostat), corresponding to 5.6 DALYs per 100,000 population and 7.7 DALYs per 100,000 population, respectively T. gondii infection was ranked second in terms of DALYs. The burden of this parasite might affect the general population (but mostly in a benign form). The most severe forms in France, including deaths, concern immunosuppressed populations (acquired form) [START_REF] Anses | Fiche de description de danger biologique transmissible par les aliments : Toxoplasma gondii[END_REF][START_REF] Bultel | Bulletin epidémiologique: Nouvelles données sur le risque alimentairelié à Toxoplasma gondii[END_REF] [38]; congenital forms have a lower effect on burden. In fact, in the French population, pregnant women are very aware of the toxoplasmosis risk, and blood samples are taken from the beginning of pregnancy for the detection of immunisation following possible contamination. Indeed, it is one of the four infectious diseases-with rubella, syphilis and (1), ( 2) and ( 3) 1 Following R parametrisation: μ = mean; P = standard deviation; \ = shape 1 of the beta distribution, ] = shape 1 of the beta distribution 28