Tchadine Djaogol

Hélène Fontaine

Maël Baudoin

Camelia Protopopescu

Fabienne Marcellin
email: fabienne.marcellin@inserm.fr

Céline Dorival

Mélanie Simony

Ventzislava Petrov-Sanchez

Marc Bourlière

Elisabeth Delarocque-Astagneau

Petrov-Sanchez

Dr Stanislas Pol

Fabrice Carrat

Patrizia Carrieri

Myers Squibb

Janssen

Gilead

Roche

Effectiveness of direct-acting antivirals for chronic hepatitis C treatment in migrant and non-migrant populations in France

Keywords: Hepatitis C, vulnerable population, migrant, direct-acting antivirals, sustained virological response, central Asia

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.

ABSTRACT

Background & aims

Although the efficacy of direct-acting antivirals (DAA) treatment against hepatitis C virus (HCV) infection has been widely proven, data on their effectiveness in the most socially vulnerable groups are lacking. Despite universal health coverage in France, migrants face specific socioeconomic barriers that increase the likelihood of a suboptimal cascade of care for chronic HCV infection and impaired treatment effectiveness in this sub-population. Using data from the prospective multicenter ANRS CO22 HEPATHER cohort, we tested whether treatment failure rates differed between HCV-infected migrants and non-migrants receiving DAA in France.

Methods

We selected data collected from 2012 to 2018 in the ANRS CO22 HEPATHER prospective cohort study for chronic HCV participants with available data on treatment failure (defined as the presence of a detectable HCV-RNA load 12 weeks after their first DAA treatment ended). We performed multivariable Poisson regression models to assess whether treatment failure rates significantly differed between migrants and non-migrants (cross-sectional analysis), while taking into account the former's world region of birth and other potential social vulnerability factors (drug use, unhealthy alcohol use, living in poverty, and for men, having has sex with men).

Results

Among the study population's 7,879 patients, 5,829 (74%) were non-migrants, and 2,050 (26 %) migrants. Median [interquartile range] age was 57 [START_REF] Mp | Patient-reported outcomes with direct-acting antivirals for the treatment of chronic hepatitis C: current knowledge and outstanding issues [Internet]. Expert review of gastroenterology & hepatology[END_REF][52][53][54][55][56][57][58][59][60][61][62][63][64][65] years, 4433 (56%) were men, and 369 (5%) of the entire study population had treatment failure. After multivariable adjustment, migrants from Central Asia were the only migrant subgroup at higher risk of treatment failure than non-migrants (aIRR=2.83; 95% CI [1.72, 4.65]).

Conclusions

Results from this large-scale study performed in France suggest a higher risk of DAA treatment failure in migrants from Central Asia than in non-migrants. They also provide real-world evidence confirming the overall low treatment failure rate in chronic HCV patients treated with DAA (whether migrants or not) in France. Simplified models of care taking into account language and cultural barriers are needed to improve DAA effectiveness in migrants from Central Asia. These findings can help stakeholders advocate for improved screening and access to treatment for HCV-infected migrants, especially those most vulnerable.

KEYWORDS

Hepatitis C; vulnerable population; migrant; direct-acting antivirals; sustained virological response;

Central Asia

LAY SUMMARY

In this study, we tested whether the effectiveness of direct-acting antivirals differed between migrants -a socially vulnerable population -and non-migrants in France. Our results showed a higher risk of treatment failure in migrants from Central Asia than in non-migrants. This suggests the need for tailormade treatment and care strategies for this population.

INTRODUCTION

According to data from the French National Institute for Statistical and Economic Studies (INSEE), 6.7 million migrants were living in France in 2019 (i.e., 9.9% of the country's total population). Of these, 2.5 million had acquired French nationality [START_REF] Sur | les immigrés et les étrangers[END_REF]. A further 700,000 residents were born in France but had another nationality. With regard to migrants, 33.3% were European, 46.5% African, 14.7% Asian, and 5.4% American or Oceanian [START_REF]Étrangers -Immigrés -Tableaux de l'économie française[END_REF]. Chronic hepatitis C (CHC) prevalence in migrants was estimated at 1.8% to 3.1% in the PRECAVIR and Comede surveys (data collected between 2007 and 2016 by French care centers for migrants and hospital-based medico-social care units for comprehensive access to healthcare and social support (called PASS in France) ) [START_REF] Management | SETTINGS IN FRANCE: THE PRECAVIR[END_REF]4). This contrasts with the 2016 Barotest survey's estimated 0.3% in the French general population (5). CHC prevalence in migrants already infected with hepatitis C virus (HCV) before their arrival in France largely depends on how endemic hepatitis C is in their country of birth [START_REF] Falla | Estimating the scale of chronic hepatitis C virus infection in the EU/EEA: a focus on migrants from anti-HCV endemic countries[END_REF]. Available epidemiological data in countries from Central Asia and Eastern Europe underline the heavy burden of HCV infection in these regions [START_REF]Hepatitis C in Eastern Europe and Central Asia: a survey of epidemiology, treatment access and civil society activity in eleven countries [Internet[END_REF]. Moreover, data from the social rights association COMEDE (French committee for the health of exiles) show that among individuals provided with a medical consultation in their premises between 2007 and 2016, people from Central Asia were more likely to have HCV (8).

Since 2016, irrespective of liver disease stage, direct-acting antiviral (DAA) treatments have been prescribed free of charge to all CHC patients in France. These include people from the most vulnerable groups, who are often isolated from the healthcare system and for whom the HCV cascade of care is not yet optimized [START_REF] Dicom_Anne | Accès universel aux traitements innovants contre l'hépatite C : Après avoir permis l'accès de tous les malades aux traitements, Marisol Touraine obtient une baisse de prix importante[END_REF](10)(11)[START_REF] Sous La Direction Dr | Prise en charge thérapeutique et suivi del'ensemble des personnes infectées par le virus de l' Hépatite C[END_REF] as follows: regular and irregular migrants infected with HCV, people who use drugs (PWUD), prisoners, HCV-HIV (human immunodeficiency virus) co-infected patients, and men who have sex with men (MSM) [START_REF] Bressy | Prise en charge du VHC -Recommandations 2016[END_REF]. All these groups are priority targets for screening, risk reduction and antiviral treatment. Migrants in particular face delayed HCV screening and entry into HCV care in France [START_REF] Berchet | État de santé et recours aux soins des immigrés en France : une revue de la littérature[END_REF][START_REF] Duracinsky | Good acceptability of HIV, HBV, and HCV screening during immigration medical check-up amongst migrants in France in the STRADA study[END_REF][START_REF] Pauti | Limiter les opportunités manquées de dépistage des hépatites B et C chez les migrants en situation de précarité : le programme de Médecins du Monde en France[END_REF][START_REF] Rigal | Factors associated with the lack of proposition for HIV-AIDS and hepatitis B and C screening to underprivileged immigrants[END_REF][START_REF] Greenaway | The Effectiveness and Cost-Effectiveness of Hepatitis C Screening for Migrants in the EU/EEA: A Systematic Review[END_REF]. Moreover, having migrant status -especially for individuals coming from low-resource countries -is associated with multiple socioeconomic difficulties, including problems finding accommodation, employment and care [START_REF] Rigal | Factors associated with the lack of proposition for HIV-AIDS and hepatitis B and C screening to underprivileged immigrants[END_REF](19)[START_REF]La santé des migrants[END_REF][START_REF] Comede | Rapport d'observation et d'activité Comede[END_REF].

The 2016 French guidelines for managing HCV infection represent a major step toward the country's goal of HCV elimination by 2025 and are aligned with the World Health Organization's (WHO) target for worldwide elimination of the virus by 2030 [START_REF]Combating hepatitis B and C to reach elimination by 2030[END_REF].

Although the effectiveness of DAA in HCV-infected individuals has been demonstrated in several clinical trials [START_REF] Chopp | Simeprevir and sofosbuvir for treatment of hepatitis C infection[END_REF][START_REF] Kwo | Simeprevir plus sofosbuvir (12 and 8 weeks) in hepatitis C virus genotype 1-infected patients without cirrhosis: OPTIMIST-1, a phase 3, randomized study[END_REF][START_REF] Bunchorntavakul | Review article: the efficacy and safety of daclatasvir in the treatment of chronic hepatitis C virus infection[END_REF][START_REF] Cheng | Paritaprevir/ritonavir/ombitasvir and dasabuvir for the treatment of chronic hepatitis C virus infection[END_REF][START_REF] Carrion | Glecaprevir + pibrentasvir for treatment of hepatitis C[END_REF][START_REF] Aspinall | Real-world treatment of hepatitis C with second-generation direct-acting antivirals: initial results from a multicentre Canadian retrospective cohort of diverse patients[END_REF], 'real-world' data, especially for the most vulnerable groups described above, are lacking. Migrants face multiple difficulties, including a precarious administrative status (29) and discrimination, both of which may preclude their access to the healthcare system and impact the care they receive [START_REF]Parcours-Parcours de vie et santé chez les migrants d'origine d'Afrique subsaharienne vivant en Île-de-France-DESGRÉES du LOÛ Annabel[END_REF][START_REF] Rivenbark | Discrimination in healthcare as a barrier to care: experiences of socially disadvantaged populations in France from a nationally representative survey[END_REF].

Given the results mentioned above regarding Asian migrants in France, we used data for HCV-infected individuals participating in the prospective multicenter ANRS CO22 HEPATHER cohort (full title: 'French National Agency for HIV and viral hepatitis research-Therapeutic option for hepatitis B and C: a French cohort') to test whether treatment failure rates differed between migrants from central Asia, migrants from other world regions, and non-migrants receiving DAA, while taking into account the presence of additional socio-behavioral vulnerabilities, and other potential predictors of sustained virological response (SVR).

METHODS

Study design

ANRS CO22 HEPATHER (ClinicalTrials.gov number NCT01953458) is an ongoing French nationwide multicenter observational prospective cohort study, characterized by the longitudinal collection of both clinical/biological and socio-behavioral data. Its primary aim is to assess the benefits and risks associated with existing treatment modalities for patients diagnosed with HCV and/or HBV infection (chronic, acute or cured), and to identify the virological, environmental, and social factors predicting the clinical evolution of patients with CHC infection after receiving DAA [START_REF] Carrat | Clinical outcomes in patients with chronic hepatitis C after direct-acting antiviral treatment: a prospective cohort study[END_REF].

Patients were enrolled from August 2012 to September 2014 in 34 hepatology expert centers throughout France. They are being followed for 10 years.

Exclusion criteria in the cohort were HIV co-infection, ongoing HCV treatment, having discontinued HCV treatment for less than three months, life expectancy of less than one year, being aged under 18, current incarceration, and for women, being pregnant. CHC was defined as testing positive for anti-HCV antibodies for at least six months and a positive HCV-RNA test. The design of ANRS CO22 HEPATHER is detailed in full elsewhere [START_REF] Pol | The negative impact of HBV/HCV coinfection on cirrhosis and its consequences[END_REF][START_REF] Feldman | Signal detection on a patient cohort: A disproportionality analysis of the ANRS CO22 HEPATHER cohort to identify associations between direct acting antivirals and adverse events in patients with hepatitis C virus chronic infection[END_REF]. Sociodemographic, behavioral, clinical, and biological data were collected at cohort enrolment using a dedicated electronic case-report form and biological samples. Historical patient data were imported from existing medical files in each center. Data were updated both during clinical follow-up visits scheduled once a year, and through spontaneous reports on dedicated forms for particular events (such as clinical events or therapy initiation).

In the present study, we used data collected in ANRS CO22 HEPATHER until 2018.

Our study population included cohort participants with CHC, whether HCV treatment-naive or not at enrolment, who received DAA treatment during follow-up and who had available data on treatment failure, defined as the presence of detectable HCV-RNA 12 weeks after ending their first DAA treatment.

Ethical considerations

Written informed consent was obtained from each patient before enrolment. The protocol was developed in accordance with the Declaration of Helsinki and French law for biomedical research and was approved by the 'CPP Ile de France 3' ethics committee (Paris, France) and the French Regulatory Authority (ANSM) in 2012.

Variables

Study outcome

The study outcome was treatment failure, defined as the lack of SVR -measured by Polymerase Chain Reaction (PCR) -12 weeks after the end of patients' first DAA treatment.

Variables for migrant status and additional social vulnerabilities

Migrants were defined as individuals not born in France who reported having at least one parent of non-French origin. We created different variables for migrant status to take into account two components. First, patients' world country and region of birth (distinguishing between endemic regions e.g., Sub-Saharan Africa, North Africa, and Asian countries). Countries of birth were defined using the World Bank definition, with a distinction made between certain regions according to HCV prevalence (for instance, Europe was not grouped with Central Asia). The following countries of birth were categorized into the Central Asia region: Armenia; Azerbaijan; Georgia; Kazakhstan; Kirghiziztan; Mongolia; and Uzbekistan. Second, the presence of the following additional social vulnerabilities, as defined by the French guidelines for the management of HCV infection [START_REF] Sous La Direction Dr | Prise en charge thérapeutique et suivi del'ensemble des personnes infectées par le virus de l' Hépatite C[END_REF]: drug use, unhealthy alcohol use, living in poverty, and being an MSM. Data on social vulnerabilities were collected at enrolment.

With regard to drug use, people who use drugs (PWUD) included individuals who reported that they had been infected with HCV through drug injection, crack cocaine users, and individuals who reported having injected or snorted drugs at least once in their lives and/or who were receiving opioid agonist therapy (OAT), including methadone, buprenorphine, morphine sulfate or any other opioid prescribed as an OAT. When the mode of drug administration was not reported, only heroin or cocaine users were considered as PWUD.

Unhealthy alcohol use was defined as reporting alcohol consumption > 2(3) alcohol units (AU)/day for women (men).

Living in poverty was defined as reporting a monthly household income below 1,015 euros per adult equivalent, which corresponds to the relative poverty line for France in 2015, as defined by the French National Institute for Statistical and Economic Studies (INSEE) [START_REF]Définition -Pauvreté monétaire / Seuil de pauvreté / Seuil de pauvreté[END_REF].

MSM were identified by asking men whether they had had a sexual relationship with another man at least once in their lifetime.

Other variables considered

The following variables were also tested as potential correlates of treatment failure: i.

Sociodemographic characteristics: age at treatment initiation, sex, living with a main partner, educational level, employment status, having primary health insurance (through France's universal healthcare system).

ii.

Environmental factors: family history of liver disease (HCV, HBV, decompensated cirrhosis, hepatocellular carcinoma (HCC)).

iii. Clinical data: time between diagnosis and treatment initiation, HCV genotype, HBV-HCV coinfection at inclusion, METAVIR score at enrolment (measured by invasive and non-invasive tests), Child-Pugh score at inclusion, decompensated cirrhosis at inclusion, hepatocellular carcinoma at treatment initiation.

iv. Calendar year at the end of treatment: this variable provided information about the different 'generations' of patients in terms of both levels of disease severity (decreasing over time) and generation of DAA, with more recent antivirals presumed to be more effective than older ones.

Age was considered as a fixed variable, measured at treatment initiation date. All other variables in 'i.' and 'ii.' were measured at cohort enrolment.

Statistical analysis

First, we performed a descriptive analysis of the sociodemographic, behavioral and clinical characteristics of the study population.

Poisson regression models then helped us assess the relationship between 'migrant status' and treatment failure. Categorical variables with a p-value <0.20 for at least one category in the univariable analysis were considered eligible to enter the multivariable model. The variable 'migrant status' was systematically included in the multivariable model, independently of its p-value. We performed a backward selection of all the other variables to maintain only significant variables (p-value <0.05 for at least one category of each variable) and confounders (variables modifying the association between migrant status and treatment failure) in the multivariable model.

The stability of the results obtained was then checked in a sensitivity analysis which was restricted to patients who were HCV treatment-naive at enrolment in ANRS CO22 HEPATHER (n=3401).

All analyses were performed with STATA/SE 14.2 software for Windows (StataCorp, Lakeway Drive, College Station, USA).

RESULTS

Sociodemographic and clinical characteristics of the study population

For the 9,212 patients who received DAA treatment during their follow-up in the ANRS CO22

HEPATHER cohort, we selected SVR data collected for the first DAA treatment received and excluded patients that did not meet the present study's criteria (i.e., HCV-treated with DAA before cohort inclusion or having no data on SVR or having missing data on geographical world region of origin or having missing data on migrant status) (Figure 1). Accordingly, 7,879 individuals were included (i.e., study population), 5,829 (74%) being classified as non-migrants, and 2,050 (26 %) as migrants. Median

[interquartile range (IQR)] age was 57 [START_REF] Mp | Patient-reported outcomes with direct-acting antivirals for the treatment of chronic hepatitis C: current knowledge and outstanding issues [Internet]. Expert review of gastroenterology & hepatology[END_REF][52][53][54][55][56][57][58][59][60][61][62][63][64][65] years, 4433 (56 %) were male, 4503 (57%) were living with a main partner, 3474 (45%) had an educational level higher than high-school diploma, 3276 (42%)

were employed, and all 7,879 (100%) had primary health insurance (through France's universal healthcare system) (Table 1).

Some sociodemographic characteristics differed significantly between migrants and non-migrants.

Migrants were more likely than non-migrants to be living with a main partner and to have an educational level higher than high-school diploma (N=1260 (62 %) versus N=3243(56%), p<10 -3 and N=952 (47 %) versus N=2522 (44%) p= 0.013), respectively. However, they were less likely to be employed (N=728 (36%) than non-migrants (N=2548 (44%), p<10 -3 ) (Table 1). 1).

No significant difference was observed between both groups regarding treatment failure. Neither was the type of treatment prescribed significantly different between migrants and non-migrants. However, migrants were more likely to have shorter delays between diagnosis and treatment than non-migrants.

They were also more likely to be HBV coinfected and to have a family history of liver disease (Table 1).

Analysis of factors associated with treatment failure

In the univariable analyses, being a migrant from Central Asia, not having primary health insurance, being an MSM, shorter time between diagnosis and treatment, and calendar year of the end of treatment, were all significantly associated with treatment failure (p< 0.05) (Table 2). The other variables eligible for the multivariable analysis (p< 0.20) were employment, living in poverty, accumulation of social vulnerabilities, and being HCV treatment naive (Table 2).

In the multivariable model, which was adjusted for calendar year of treatment (the only other significant variable in the final multivariable model), migrants from Central Asia were the only migrant subgroup at higher risk of experiencing treatment failure than non-migrants (aIRR=2.83, 95% CI [1.72, 4.65]) (Figure 2). Furthermore, the treatment failure rate decreased between 2014 and 2017-2018 (with a 59%, 64% and 78% reduction in 2015, 2016 and 2017-2018, respectively, in comparison with 2014) (p<10 -3 ).

These results were confirmed in a sensitivity analysis (n=3401), with an aIRR [95% CI] =3.15 [1.80 -5.50] for migrants from Central Asia (compared with non-migrants) after adjustment for calendar year of treatment, which, just as in the main analysis, was the only adjustment variable significantly associated with treatment failure in the multivariable model.

Among the 105 migrants from Central Asia, 25 (24%) were born in Armenia, 16 (15%) Azerbaijan, 45 (43%) Georgia, 6 (6%) Kazakhstan, 5 (5%) Kirghiziztan, 7 (7%) Mongolia, and 1 (1%) Uzbekistan.

Migrants from Central Asia (94%) were more likely to face an accumulation of social vulnerabilities than other migrants (63%) and non-migrants (18%). They were also more affected by poverty (90%) than other migrants (52%) and non-migrants (26%). However, non-migrants were more likely to be PWUD (41%) and MSM (2%) than were migrants from Central Asia (37% and 0%) and other migrants (19% and 1%). Unhealthy alcohol use rates were similar for non-migrants (5%), migrants from Central Asia (5%) and other migrants (2%) (Figure 3).

Migrants from Central Asia were more likely to be infected only by HCV genotypes 1, 2 and 3 while non-migrants and other migrants were more likely to have HCV genotypes 1 to 5. Time between HCV diagnosis and treatment was shorter (5 years in median, [interquartile range]: [2-10]) in Central Asia migrants than in non-migrants (16[9-21] years) and other migrants (12[6-18] years). However, treatment failure was higher in the former group (13% versus 5% in both non-migrants and other migrants). Calendar year, METAVIR score, Child-Pugh score, decompensated cirrhosis and HCC were not significantly different between the three groups (Table 3 in supplementary materials).

DISCUSSION

This is the first study in France to compare DAA treatment failure rates between migrants and nonmigrants in a real-world setting, in a large sample of chronically HCV-infected patients treated with DAA. Using data on the first DAA treatment received, overall, we found a very low treatment failure rate over the study period (2012)(2013)(2014)(2015)(2016)(2017)(2018). This result reflects findings from the only other recent study on DAA effectiveness in migrant populations in France -the PRECAVIR study -which showed the effectiveness of a coordinated HCV care network organized for a migrant population [START_REF] Rosa-Hezode | Cascade of care for migrants tested Hepatitis C antibodies positive in France through a systematic screening programme: The PRECAVIR study[END_REF].

However, despite being low globally, the treatment failure rate in our study was significantly higher in migrants from Central Asia than in non-migrants. Available data on the HCV cascade of care in the Central Asia region show great disparities between countries [START_REF]Hepatitis C in Eastern Europe and Central Asia: a survey of epidemiology, treatment access and civil society activity in eleven countries [Internet[END_REF]. For instance, Georgia, which is the country of birth most represented among Central Asian migrants in our study, has significantly scaled up HCV treatment since the establishment of its national HCV program in 2015 [START_REF] On | OVERCOMING BARRIERS IN LOW-AND MIDDLE[END_REF]. Indeed, the country is now well on the way to eliminating the disease [START_REF]Three Years of Progress Toward Achieving Hepatitis C Elimination in the Country of Georgia, April 2015[END_REF]. By contrast, there is still a lack of epidemiological data for Azerbaijan, another of the Central Asia countries strongly represented in our study [START_REF] Somi | Estimating the incidence rate of hepatitis B and C in East Azerbaijan, Islamic Republic of Iran[END_REF].

Unlike our study, several studies on migrant populations in Europe have found good rates of HCV treatment effectiveness, with no association between treatment effectiveness and geographic world region of origin [START_REF] Rosa-Hezode | Cascade of care for migrants tested Hepatitis C antibodies positive in France through a systematic screening programme: The PRECAVIR study[END_REF][START_REF] Brezzi | Impact of geographic origin on access to therapy and therapy outcomes in the Swiss Hepatitis C Cohort Study[END_REF].

The higher risk of treatment failure observed among migrants from Central Asia in our study could have been related to differences with other migrants and non-migrants concerning type of DAA received, HCV genotype, calendar year of treatment ("generational" effect), and liver disease stage.

However, post-hoc comparisons of characteristics between migrants from Central Asia, other migrants and non-migrants (Table 3 in supplementary material) showed no significant differences in the type of DAA treatment received between these three groups.

In addition, sofosbuvir-based treatments -which were the most frequent DAA in our cohort -have been proven to be over 90% effective in CHC patients with HCV genotypes 1 to 3 [START_REF] Lanini | Impact of new DAA therapy on real clinical practice: a multicenter region-wide cohort study[END_REF][START_REF] Werner | Second-generation direct-acting-antiviral hepatitis C virus treatment: Efficacy, safety, and predictors of SVR12[END_REF][START_REF] Huang | Equal treatment efficacy of direct-acting antivirals in patients with chronic hepatitis C and hepatocellular carcinoma? A prospective cohort study[END_REF][START_REF] Fa | Identification of the Best Direct-Acting Antiviral Regimen for Patients With Hepatitis C Virus Genotype 3 Infection: A Systematic Review and Network Meta-analysis[END_REF][START_REF]A model-based meta-analysis of sofosbuvir-based treatments in chronic hepatitis C patients [Internet[END_REF][START_REF] V P, R B | New Direct-Acting Antivirals for the Treatment of Patients With Hepatitis C Virus Infection: A Systematic Review of Randomized Controlled Trials [Internet[END_REF]. Considering that migrants from Central Asia in our study were only infected by these same genotypes, and that the association between this sub-population and treatment failure persisted even after adjustment for genotype, we therefore also presume that this association is not attributable to genotype.

Moreover, we found no significant difference in the calendar year of the end of treatment between migrants from Central Asia, non-migrants and other migrants and liver disease status (measured at cohort enrolment) of migrants from Central Asia was not significantly different from that of the other subgroups of patients (Table 3 in supplementary materials).

We found that migrants from Central Asia reported drug use and very poor social conditions more frequently than the other patient subgroups (Figure 3). However, in the univariable analyses, drug use and living in poverty were not significantly associated with SVR.

Given all the points above, the question therefore arises as to what were the probable reasons for the higher risk of treatment failure we observed in migrants from Central Asia. We hypothesize that other possible social vulnerabilities, not measured in our study (e.g., literacy, language barriers, discrimination), may partially explain this finding.

Nevertheless, the treatment failure rate was relatively low among migrants from Central Asia (13%) and could probably be reduced further with adequate interventions focused on improving adherence and retention in care. To this end, there is a need to implement care strategies which take into account language and cultural barriers specific to migrants from Central Asia. Feedback from field-based experience, including feedback from the non-governmental organization Médecins du Monde's centers of care and orientation (CASO) [START_REF] Les | centres d'accès aux soins et d'orientation[END_REF], can be of great help in designing such strategies. Proposing HCV screening during immigration medical check-up [START_REF] Duracinsky | Good acceptability of HIV, HBV, and HCV screening during immigration medical check-up amongst migrants in France in the STRADA study[END_REF] and implementing test-and-treat strategies could also potentially improve the HCV cascade of care for migrant populations.

SVR rates increased significantly according to the calendar year of the end of treatment in our study.

This may be the result of increased effectiveness of newer generations of DAA which foster better adherence and fewer treatment interruptions [START_REF] Rosa-Hezode | Cascade of care for migrants tested Hepatitis C antibodies positive in France through a systematic screening programme: The PRECAVIR study[END_REF][START_REF] Brezzi | Impact of geographic origin on access to therapy and therapy outcomes in the Swiss Hepatitis C Cohort Study[END_REF][START_REF] Huang | Direct-acting antivirals in East Asian hepatitis C patients: real-world experience from the REAL-C Consortium[END_REF] However, we did not have data to determine whether individuals with detectable HCV-RNA load had not been fully adherent to treatment, whether they were non-responders to treatment or whether they were re-infected (although this was unlikely to occur in patients in HEPATHER as they were not exposed to classic reinfection risk factors (injecting drug use, chemsex, etc.)). Although there is a dearth of studies on DAA treatment adherence in migrant populations, studies on the general population in various countries have shown good adherence [START_REF] Tm | Assessing Patient Preferences for Treatment Decisions for New Direct Acting Antiviral (DAA) Therapies for Chronic Hepatitis C Virus Infections [Internet[END_REF][START_REF] Mp | Patient-reported outcomes with direct-acting antivirals for the treatment of chronic hepatitis C: current knowledge and outstanding issues [Internet]. Expert review of gastroenterology & hepatology[END_REF]. Another hypothesis for the increase in SVR rates according to the calendar year of the end of treatment, was that patients treated with DAA in the first years of the advent of these new treatments had the most complex liver conditions. However, this hypothesis was rejected, as the proportion of those with advanced liver disease did not change according to the calendar year of the end of treatment.

Our study found that migrants from Central Asia and other migrants had shorter delays between diagnosis and treatment initiation than non-migrants, which may suggest delayed diagnosis for the former two groups, although this cannot be verified, as data on fibrosis at diagnosis were not available.

Another reason for shorter delays could be a family history of liver disease -a classic social vulnerability factor -, which tended to be higher in migrants than non-migrants-, and which, in clinical practice, is positively associated with treatment acceptability and demand.

Our finding that migrants from Central Asia had significantly higher treatment failure rates than nonmigrants and other migrants suggests the need for specific care and treatment strategies for this subpopulation. Previous studies in France highlighted that, in general, migrants are under-screened and under-treated [START_REF] Management | SETTINGS IN FRANCE: THE PRECAVIR[END_REF]. Other studies on vulnerable populations, including migrants, have shown that the latter are less likely to access DAA treatment, and more likely to have delayed treatment than nonvulnerable populations (19, 20).

Strengths and limitations:

The main strength of our study is its statistical power, which is crucial to minimize beta error. However, this can also be considered a limitation, as negligible differences in size can become significant due to the statistical power. Accordingly, results need to be interpreted with caution. Some self-reported items (e.g., alcohol use) may have been underestimated in our study. This may have reduced estimates of incidence rate ratios to more conservative values. Furthermore, exposure to non-DAA treatments for some individuals in the study sample may have influenced treatment failure rates. However, we found a very low rate of treatment failure. Furthermore, the results of the sensitivity analysis on a population of naive patients at enrolment and receiving a single DAA treatment showed similar results.

CONCLUSIONS

This is the first large real-world study in France to explore differences in SVR rates following DAA treatment between HCV-infected migrants and non-migrants. Despite an overall low treatment failure rate, migrants from Central Asia presented a higher risk of treatment failure than non-migrants.

Simplified models of care taking into account language and cultural barriers are needed to improve effectiveness of DAA for this sub-population. Findings from this study can help stakeholders advocate for improved screening and access to treatment for HCV-infected migrants, especially those who are most vulnerable, not only in France but worldwide.

Migrants from Southeast Asia

Migrants from East/South/Pacific Asia Migrants from other world regions 1 The following countries of birth were categorized as belonging to Central Asia: Armenia; Azerbaijan; Georgia; Kazakhstan; Kirghiziztan; Mongolia; and Uzbekistan

Missing data in variables:

Unhealthy alcohol use = 61(01%); Living in poverty=259(3%); Accumulation of vulnerability factors=292(4%)

Definition of variables:

Treatment failure = the lack of sustained virological response (SVR), measured by Polymerase Chain Reaction (PCR), 12 weeks after the end of first DAA treatment. Migrants = individuals not born in France who reported having at least one parent of non-French origin.

People who use drugs (PWUD) = individuals who reported that they had been infected with HCV through drug injection, crack cocaine users, and individuals who reported having injected or snorted drugs at least once in their lives and/or who were receiving opioid agonist therapy (OAT), including methadone, buprenorphine, morphine sulfate or any other opioid prescribed as an OAT. When the mode of drug consumption was not reported, only heroin or cocaine users were considered PWUD.

Unhealthy alcohol use = alcohol consumption > 2(3) alcohol units (AU)/day for women (men).

Living in poverty = a monthly household income below 1,015 euros per adult equivalent, which corresponds to the relative poverty line for France in 2015, as defined by the French National Institute for Statistical and Economic Studies (INSEE).

Men who have sex with men (MSM) = men who reported having sexual relationships with male partners at least once in their life.

  Figure 2: Distribution of DAA treatment failure and vulnerability factors according to migrant status and world region of birth in patients with chronic HCV infection (ANRS CO22 HEPATHER cohort, n=7,879) Men who have Sex with Men; PWUD: People Who Use Drugs Migrants from Central Asia 1

			Non-migrants
			Migrants from Central Asia
			Migrants from Southeast Asia
	0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% birth MSM: particpants acoording to geographical region of	5% 13% 8% 4% 5% Treatment failure n=36	41% 37% 14% 4% 19% PWUD n=2792 distribution of treatment failure and vulnerability factors 5% 26% 2% 5% 90% 0% 0% 52% 1% 0% 48% 0% 3% 52% 1% Unhealthy alcohol use Poverty MSM Migrants from East/South/Pacific Asia 18% 94% 61% 52% 63% 2-4 vulnerabillity factors Migrants from other world regions n=335 n=2514 n=118 n=2276 P<0.05 for all variables (Chi-square tests )

Acknowledgments

We thank the study participants and participating clinicians at each study site. We also thank the INSERM-ANRS for sponsoring, funding and supervising the ANRS CO22 Hepather cohort in collaboration with the French Association for the Study of the Liver (Association Française pour l'Etude du Foie: AFEF). Finally, our thanks to Jude Sweeney for the English revision and editing of the manuscript.

Tables and figures

The total for some variables may differ from the number of individuals in the study population because of missing data. Missing data in variables: Age at treatment initiation=10(0%); Living with a main partner=41(1%); Educational level=123(2 %); Employment=62(1 %); Having primary health insurance=83(0 %); Time between diagnosis and treatment=229(3%); HCV treatment-naive=47(1%); Family history of liver disease=105(1%); METAVIR score=768(10%); Child-Pugh score=612(8%); Decompensated cirrhosis=85(1); Hepatocellular carcinoma=2(0%); HCV genotype=185(2%); Type of HCV treatment=429(5%); Chronic active HBV coinfection=1753(22%) Abbreviations: IQR= interquartile range; HCV=hepatitis C; HCC= hepatocellular carcinoma Statistical tests used: Chi-square test and Wilcoxon-Mann-Whitney test for categorical and continuous variables, respectively.


Geoffrey Decrouez

Pierre-Olivier Amblard

Jean-Marc Brossier

A Wavelet Analysis of Random Iterated Function Systems

Random fractal signals obtained as fixed points of Iterated Function Systems (IFS) are good examples of signals which possess discrete scale invariance. In the deterministic case, the problem of approximating a target signal as a fixed point of an IFS with appropriate parameters has been widely studied and is known as the inverse problem [FOR]. So far, the random case has not received much attention and estimating the unknown statictics of the IFS is the focus of our work. To this end, we consider an orthonormal decomposition of the random target signal and extend the results in [MEN] to the random case. Then, we derive the wavelet decompostion of the signal and emphasize the redundancy in the information carried by the wavelet coefficients. This will be used in the last part where we derive an empirical estimator of the variance of the unknown random maps of the IFS in a restrictive case.

Definitons

Fractal sets obtained as fixed points of IFS has been widely studied by Barnsley and Hutchinson in [BAR,HUT]. The idea is to apply a contractive operator T (deterministic or random) on an element of a complete metric space. By iterating this procedure, the process converges to a limit point, usually fractal. The existence and uniqueness of the fixed point (also denoted as the attractor of the IFS) is due to the Banach fixed point theorem. We are mainly concerned with random operators T acting on the space L 2 (X) of compactly supported square integrable functions. A more rigorous definition of this space is given in the next section. Generally, one defines the operator T in the following way:

(T f )(x) = M i=1 φ i [f i (ω -1 i (x)), ω -1 i (x))]1 ωi(X) (x) (1.1)
where X is a compact interval of the real line, ω i : X → X partition the interval X into disjoint subintervals and φ i : R × X → R are random operators Lipschitz in their first variable. Lastly, f i are independent and identically distributed copies of f . Loosely speaking, this operator realises dilatations, compressions and distorsions of i.i.d. copies of the random function f ∈ L 2 (X). The limit function obtained is self-similar up to probability distribution.

Expansion of Random Functions

Let X denote a compact support. Without loss of generality, we will consider X = [0, 1].

In the remainder, we will only consider compactly supported signals with finite energy. The space of deterministic square integrable functions is denoted by L 2 (X). We endow L 2 (X) with its usual metric

l 2 (f, g) = ( X |f (t) -g(t)| 2 dt) 1 2
where f and g are two elements of L 2 (X). To deal with random attractors of IFS and their decomposition over an orthonormal basis, we will need to define new spaces. Let Ω be a sample space. Let us first start with random square integrable signals:

L 2 (X) = {f (ω, t), ω ∈ Ω | E ω X |f (ω, t)| 2 dt < +∞} (2.1)
The associated metric is

l * 2 (f, g) = E 1 2
ω l 2 2 (f, g) . Next we define the space D 2 (N) of coefficients of deterministic square integrable functions decomposed on an orthonormal basis. In the remainder of this section, we denote by {ϕ n } an orthonormal basis of L 2 (X).:

D 2 (N) = {f = (f 0 , ..., f j , ...) | f (x) = k≥0 f k ϕ k (x), f ∈ L 2 (X)} (2.2)
This space is equipped with the usual metric

d 2 (f , g) = ( k≥0 |f k -g k | 2 ) 1 2
. Likewise, we define the space D 2 (N) which contains the decomposition coefficients of random square integrable functions decomposed on an orthonormal basis. The distance between 2 elements of this space is

d * 2 (f , g) = E 1 2 ω [d 2 2 (f ω , g ω )]. Then for any f ∈ L 2 (X), f (x) = k≥0 f k ϕ k (x) (2.3) where f k =< f, ϕ k >= X f (x)ϕ k (x)
dx are random variables, {ϕ n } remain deterministic. Clearly, the random process f induces a distribution on its coefficients f k . The purpose of this part is to generalise the work of [FOR] in the random setting. The major result is to show that we can associate with T a contractive operator ϑ acting on the decomposition coefficients of a random function, converging to a fixed point, which is the vector of expansion of the fixed point of T . To this end, let f and g be two elements of L 2 (X) such that g = T f . Consider their decomposition over {ϕ n }. (g(x) = k≥0 g k ϕ k (x)). Clearly:

g k =< g, ϕ k >=< T f, ϕ k >=< M i=1 φ i (f (i) (ω -1 i ), ω -1 i )1 ωi(X) , ϕ k >
To go further, we need to set a particular expression for φ i . One could think of any possible expression and one of the simplest ones is given by:

φ i (u, v) = s i u + ζ i (v) s i < 1 (2.4)
where ζ i is a non-linear function, leading to a nonlinear transformation of the coefficients f k . We denote by ϑ the mapping which transforms the coefficients of f into the coefficients of g after applying T . We have the following result:

Theorem 1. Let • {ϕ n } be an orthonormal basis of L 2 (X).

• T be the contractive operator of a random IFS and f * its fixed point. Then ϑ is contractive in the complete metric space (D 2 (N), d *

2 ) and for any initial condition f 0 (random or non random), ϑ •k f 0 → f * a.s. as k → +∞ where ϑ •k is the k th iterate of ϑ. Moreover, f * is unique in distribution and is the vector of expansion of f * in the {ϕ n } basis.

The proof is not given here. This theorem shows the correspondance between the 2 spaces L 2 (X) and D 2 (N) as illustrated below. What can we deduce from all of this? Since the operator acting on the decomposition coefficients converges in distribution to the vector of expansion of the fixed point of the IFS, one can use the statistics of the coefficients to estimate the statistics of the random IFS. This will be achieved in the last part. The choice of the orthonormal basis is therefore crucial and is explained in the following section.

L 2 (X) T ≡ / / D 2 (N) ϑ L 2 (X) ≡ / / D 2 (N)

Discrete wavelet decomposition

Though not strictly self similar, the wavelet basis is obtained by translations and dilatations of a single mother wavelet, like fixed point of IFS. The two constructions have therefore strong similarities and it is natural to consider wavelet expansion of fractal functions. The discrete wavelet transform represents a signal in terms of a low-pass scaling function φ 00 and a band-pass wavelet function ψ 00 which can be derived from φ 00 . By considering contractions and dilations of a compactly supported mother wavelet function, ψ ij (t) = 2 i 2 ψ 00 (2 i t -j), the family (ψ ij ) i,j is an L 2 (X) orthonormal basis. Any signal with compact support X = [0, 1] can be represented in the following way:

f (t) = b 00 φ 00 (t) + i 0 2 i -1 j=0 f ij ψ ij (t) (3.1)
Without loss of generality, we have considered a decomposition of the signal up to scale 0, reducing the number of scaling coefficients to 1. We now derive the wavelet expansion for an IFS with two maps but the result can be easily extended to IFS with M maps using an M -band wavelet transform. We denote by W f (n, m) the wavelet coefficient of f at scale n and position m:

W f (n, m) = [0,1] ψ nm (t)f (t)dt = 2 i=1 ωi([0,1]) 2 n 2 ψ(2 n t -m)φ i [f i (ω -1 i (t)), ω -1 i (t)]dt
Choosing uniform partition maps ω i (t) = t 2 + i-1 2 for i = 1, 2, we get:

W f (n, m) = 1 √ 2 2 i=1 W φi n -1, m -2 n-1 (i -1) where n 1 (3.2)
where W φi (n, m) = [0,1] ψ nm (t)φ i (f (t), t)dt and whenever 2 n-1 (i -1) m i2 n-1 -1, i = 1, 2. This clearly emphasizes the redundancy in the wavelet decomposition of fractal attractors of IFS: one can recursively compute the wavelet coefficients in terms of the IFS parameters from coarse to fine scale. When decomposing the signal on a Haar basis, recursive formulae can be computed in the same way for the coarsest coefficient f 00 and the scaling coefficient b 00 .

Parameter estimation

The inverse problem in the random case is the following. Suppose we know the deterministic parameters of the IFS (contraction ratio, partition maps...) , the goal is then to estimate the statistics (for example the moments) of the randomness introduced in the maps from one or more snapshots of the fixed point. This seems to be impossible in general cases since we cannot infer anything about a random variable just from one realisation, but the scenario is quite different here: by exploiting the fractal property of the fixed point, one has access not to one realisation but to several realisations of the fixed point. This is what we will be using here, in the wavelet domain. In order to derive an estimator, we need to set a particular form for φ i :

φ i (u, v) = s i u + Xζ i (v)
where X is a zero mean Gaussian random variable with variance σ 2 . The only parameter to estimate here is the variance of the random variable X. Using (3.2), it is straightforward to derive recursive expression for the variances of each wavelet coefficient:

Varf i,j = s 2 1 2 Varf i-1,j + σ 2 2 (ζ 1 i-1,j ) 2 (4.1) Varf i,j = s 2 2 2 Varf i-1,j-2 i-1 + σ 2 2 (ζ 2 i-1,j-2 i-1 ) 2 (4.2)
where ζ n ij is the wavelet coefficient of ζ n at scale i and position j. The first equality is valid if j ∈ [0, 2 i-1 -1] and the second one for j ∈ [2 i-1 , 2 i -1]. The knowledge of marginal probability density functions of the wavelet coefficients is not enough to derive an estimator of the variance as the coefficients are correlated. One can proceed in the same way as for the variance and using various independencies one can express correlation of any two wavelet coefficients in terms of the IFS parameters. An important fact is that the covariance matrix Γ of the wavelet decomposition can be expressed by σ 2 Υ where σ 2 is the random parameter to be estimated. One can use the following empirical estimator (here equal as the Maximum Likelihood estimator since we are in the Gaussian case) to estimate the variance of X:

σ2 M L = 1 N f T Υ -1 f (4.3)
where N is the total number of coefficients.

Conclusion

We have shown that the wavelet decompostion of the attractor of the IFS acting over the space of functions possesses redundancy from one scale to another, which is little surprise considering the similarities between the wavelet and IFS constructions. This redundancy can be exploited for example to estimate the statistics of random fixed points. It would be interesting to obtain more general estimators in a more general setting, and to adapt the results to 2-D images.