A mon jury de thèse : Je remercie le Pr Jean-Yves LE RESTE de m'avoir fait l'honneur d'être le président de cette thèse, mais aussi pour la transmission de son savoir lors de mon stage au pôle médical de Lanmeur. Soyez assuré de toute ma reconnaissance.

Merci à mon directeur de thèse, le Dr Patrice NABBE, pour la confiance qu'il a eu en moi afin d'aboutir dans ce projet, mais aussi pour son expertise et sa disponibilité durant ce travail de recherche.

Merci au Pr Bernard LE FLOC'H pour m'avoir fait l'honneur de juger cette thèse et de m'avoir accordé cette dérogation qui me permet encore aujourd'hui de parfaire ma pratique en médecine libérale.

Merci au Dr Gilles GRENIER, médecin généraliste à Kerlouan, d'avoir accepté de faire partie de mon jury de thèse. J'en suis très touchée. Merci avant tout d'avoir été ce père qui m'a inculqué sa passion de la médecine dès mon plus jeune âge, et de ce fait, de m'avoir permis d'exercer ce beau métier.

A mes proches : Merci à ma mère, pour m'avoir soutenue durant ces longues années d'études, et m'avoir rassurée dans les moments les plus difficiles. Merci pour toutes les valeurs que tu m'as enseignées. Je t'en suis éternellement reconnaissante. J'espère t'avoir rendue fière.

Merci à mon amour Thomas, pour son soutien inconditionnel et sa patience, ses mots réconfortants dans les nombreux moments de doute. Rien de tout cela n'aurait été possible sans toi. Merci de faire de chaque jour passé à tes côtés un bonheur.

Merci à ma belle-famille, pour les nombreux encouragements et l'écoute dont vous avez su faire preuve à mon égard. Je ne l'oublierai jamais.

Merci à mes amis, de médecine ou d'autres horizons, pour avoir toujours été là malgré les longs moments d'absence et d'avoir fait en sorte que nos relations perdurent. J'ai de la chance de vous avoir dans ma vie.

En ce jour charnière, j'ai également une pensée émue pour deux femmes qui ont joué un rôle important dans ma vie et qui nous ont malheureusement quitté : ma tante et ma grand-mère, deux personnalités fortes et battantes, qui je l'espère auraient été fières aujourd'hui.

Enfin :

Un remerciement tout particulier au Dr Véronique Lenoir, chef de service de Médecine Post Urgences au Centre Hospitalier de Quimperlé, pour le partage de son savoir, sa grande bonté, son humanité et son accompagnement toujours bienveillant. Les mois passés dans ton service ont été pour moi les plus enrichissants de mon internat et m'ont redonné foi en ma pratique de la médecine.

Merci infiniment à toute l'équipe de

Annex A: HSCL-25 original version Annex B: Polish results

Annex C: Bulgarian results

Annex D: Croatian results

Annex E: Italian results

Annex F: French results

Annex G: Castilian results

Annex H: Catalan results

Annex I: Galician results

Annex J: Consent form

Résumé

Introduction : La dépression est la deuxième maladie chronique rencontrée en soins primaires. L'étude Family Practice Depression Multimorbidity (FPDM) avait désigné la Hopkins Symptom Check List-25 (HSCL-25) comme son meilleur outil diagnostique. Afin de disposer d'un même outil en Europe, la HSCL-25 a été traduite dans chaque pays européen participant à l'étude. Pour garantir sa fiabilité, un contrôle culturel était nécessaire pour s'assurer que les échelles traduites en Castillan, Catalan, Galicien, Bulgare, Polonais, Croate, Français, Grec et Italien, conservaient le sens de l'échelle anglaise d'origine. Une synthèse des contrôles culturels effectués dans ces langues a été réalisée, pour définir quelles modifications culturelles étaient induites par les spécificités linguistiques des langues d'arrivée dans leur traduction finale.

Méthodes : Les chercheurs des pays participants à l'étude se sont réunis en 2014 à Barcelone et Héraklion : un contrôle culturel a été mené par un groupe composé de leaders internationaux et traducteurs officiels, à partir des traductions aller-retour obtenues par méthode Delphi.

Résultats : Les traductions retour étaient comparées à la version originale. Des différences étaient notées, liées à des aspects culturels propres aux langues d'arrivée. Certains items ont été reformulés. Les échelles Grecque, Italienne, Castillane, Galicienne et Catalane ont été adaptées en terme de genre. L'échelle Française a été traduite au présent, l'échelle Croate au passé composé. Les items ayant posé problème l'était sur le plan conceptuel. Tous les items ont été validés après consensus.

Discussion : Le contrôle culturel était nécessaire pour s'assurer de la conservation du sens après traduction. L'échelle Grecque est restée la plus stable, suivie par la Bulgarie. La conservation du sens de l'item «Feeling blue» a été la plus difficile à obtenir, suivi des items «Faintness» et «Heart racing».

Conclusion

1-Introduction

Depression is the second most common chronic disorder in primary care. GPs are the first port of call in most European countries (1) [START_REF] Torzsa | Diagnosis and therapy of depression in family practice[END_REF].

Depression is a syndrome disease comprising contextual distress, anxiety and somatoform disorders. Patients themselves experience difficulties to express their suffering and display their own form of illness expression [START_REF] Jorm | Mental health literacy: Public knowledge and beliefs about mental disorders[END_REF].

The difficulties to diagnose and assess the severity of depression are based in this inter-individual variability. Clinicians may overestimate or underestimate the distress level of their patients [START_REF] Ani | Depression symptomatology and diagnosis: discordance between patients and physicians in primary care settings[END_REF]. Those difficulties may lead to inappropriate care and cause public health issues. Diagnostic and Statistical Manual of Mental Disorders (DSM) is widely used but rarely in General Practice (4). GPs seem to be uncomfortable with depression definition and available diagnostic tools (5) [START_REF] Demyttenaere | Prevalence, severity, and unmet need for treatment of mental disorders in the World Health Organization World Mental Health Surveys[END_REF]. Incidence and prevalence rates of depression differ in General Practice across Europe, due to complex contextual variations with differences in health care systems, concepts, objectives and practices as well as cultural variations in the expression of the disease.

Collaborative primary care mental health models can improve care and outcomes for patients. With this aim, the EGPRN developed collaborative research in Primary Care Medicine throughout Europe. This network requires a reliable, efficient and ergonomic tool which will take into account cultural and linguistic differences across Europe [START_REF] Lehti | Recognition of depression in people of different cultures : a qualitative study[END_REF] [START_REF] Kirmayer | Psychotherapy and the cultural concept of the person[END_REF]. International experts from different cultures, speaking different languages and with different health systems have to undertake a consensus, to identify such tools [START_REF] Steinert | The Prospective Long-Term Course of Adult Depression in General Practice and the Community. A Systematic Literature Review[END_REF]. These tools have to be acceptable and informative for both GPs and for secondary care (Psychiatrist, Psychologist) and to improve their collaboration [START_REF] Zhang | A cognitive taxonomy of medical errors[END_REF]. 'Screening for depression can bring added value to the identification of the condition if it can be undertaken in a routine manner in the doctor's surgery' but only if followed by goodquality treatment, either in primary care or in specialized psychiatric care [START_REF] Mitchell | Clinical utility of screening for clinical depression and bipolar disorder[END_REF].

The Family Practice Multimorbidity Depression (FDPM) study started in 2011. The aim was to select a single tool that could be consensually used by GPs to diagnose adult patients depression. In order to be satisfactory, it had to be validated, reliable and easy to use by GPs. This tool must be applicable in the European countries taking part in the study.

Four steps were necessary: -The Hopkins Symptom Checklist-25 items (HSCL-25) was selected as the consensual tool at the end of the first and second steps. It is a reliable diagnostic tool validated against the DSM, easy to use in practice [START_REF] Fröjdh | The Hopkins Symptom Checklist-25 is a sensitive case-finder of clinically important depressive states in elderly people in primary care[END_REF] [START_REF] Nettelbladt | Test characteristics of the Hopkins Symptom Check List-25 (HSCL-25) in Sweden, using the Present State Examination (PSE-9) as a caseness criterion[END_REF].

-This tool was translated into the language of each country taking part in the study during the third step [START_REF] Oruc | Screening for PTSD and depression in Bosnia and Herzegovina: validating the Harvard Trauma Questionnaire and the Hopkins Symptom Checklist[END_REF] [START_REF] Mouanoutoua | Hopkins Symptom Checklist-25, Hmong version: a screening instrument for psychological distress[END_REF] [START_REF] Halepota A A | Hopkins Symptoms Checklist 25(HSCL-25) Urdu translation: An instrument for detecting Anxiety and Depression in Torture and Trauma Victims[END_REF]. Using a Forward-Backward Delphi procedure translation, HSCL-25 was translated in Castilian, Catalan, Galician, Bulgarian, Polish, Croatian, French, Greek, and Italian. The translation analysis was performed by official translators and a panel of GPs' experts. To keep the original meaning, a linguistic translation was insufficient [START_REF] Guillemin | Cross-cultural adaptation of health-related quality of life measures: literature review and proposed guidelines[END_REF] [START_REF] Perneger | Cross-cultural adaptation of a psychometric instrument: two methods compared[END_REF] [START_REF] Elsass | Questioning western assessment of trauma among Tibetan torture survivors. A quantitative assessment study with comments from Buddhist Lamas[END_REF]. Cultural and ethnic backgrounds had to be taken into account.

A German version of HSCL-25 already existed, a backward translation was performed by GPs' experts to ensure reliability to the English original version.

The aim of the current study was to make a synthesis of all previous control cultural check that has been made in the past years for the following group of languages: Hellenic (i.e Greek), Slavic (i.e Bulgarian, Polish and Croatian), and Romance (i.e Italian, French, Greek, Catalan, Castilian and Galician):

-the primary objective was to compare the results between those 9 countries. The aim was to determine what modifications have been induced by languages' cultural specificities (semantic, conceptual, grammatical…) in the HSCL-25 translated versions.

-the secondary objective was to define what items were the most challenging to translate.

2-Materials and methods

Definition of HSCL-25

HSCL-25 (Annex A) contains 25 self-reported questions about the presence and intensity of anxiety and depression symptoms over the last week [START_REF] Derogatis | The Hopkins Symptom Checklist (HSCL): a selfreport symptom inventory[END_REF]. There are 10 items about anxiety and 15 about depression. Each item is rated on a 4 degree Lickert scale. Ratings are summarized and the total score is divided by 25. A result between 1 to 4 is obtained [START_REF] Sandanger | The meaning and significance of caseness : the Hopkins Symptom schecklist-25 and the Composite International Diagnostic Interview II[END_REF]. A score of >= 1,75 defines "a case in need of treatment". A score of >= 1,55, defines a "probable psychiatric case" (12) [START_REF] Nettelbladt | Test characteristics of the Hopkins Symptom Check List-25 (HSCL-25) in Sweden, using the Present State Examination (PSE-9) as a caseness criterion[END_REF]. The principal use of HSCL-25 has been in primary care, family planning services, among refugees and migrants [START_REF] Fröjdh | The Hopkins Symptom Checklist-25 is a sensitive case-finder of clinically important depressive states in elderly people in primary care[END_REF] [START_REF] Mouanoutoua | Hopkins Symptom Checklist-25, Hmong version: a screening instrument for psychological distress[END_REF] [START_REF] Elsass | Questioning western assessment of trauma among Tibetan torture survivors. A quantitative assessment study with comments from Buddhist Lamas[END_REF] [START_REF] Jamil | Mental health symptoms in Iraqi refugees: posttraumatic stress disorder, anxiety, and depression[END_REF].

Consents

The french EGPRN was in charge to supervise the translation and check the voluntary, the absence of potential risks or profits related to participants. They were asked to sign a consent form (Annex J). As the study involved no patient, it did not require an ethic committee's decision.

Data collection and analysis

A forward linguistic translation was performed by GPs' experts from original HSCL-25, using a Delphi procedure, for each country participating in the study.

At the end of this process, a backward translation was performed with two goals: to ensure no linguistic translation problems.

to collect translation problems independent from the linguistic translation.

A linguistic translation was insufficient to ensure the reliability of the translations. Translations' bias were related to cultural aspects of each country. The analysis was conducted as follows, step by step, starting from the backward translation (Figure 1):

-First, a GP researcher and a PhD linguist analyzed all backward translations and compared them with the original version of HSCL-25. Their first objective was to establish if there was a real difference between those two versions in terms of meaning. Their report was submitted to a consensus group whose task was to precise and discuss the nature of the anomaly between 3 problems: Backward Translation Problem (BTP), Forward Translation Problem (FTP) or Cultural Effect (CE). A BTP was eliminated if the difference was explained by an incorrect way to translate once again the forward version to English; a FTP was defined by an anomaly of transcribing the original English version in one of the 9 languages (whether if it was due to the use of an incorrect term, an addition…). Finally, a CE was validated if there was no linguistic problem with the translation but when the item needed an adaptation (in terms of tense, gender, or on a conceptual level) to be understood by the patients in their own language. In the light of these elements, a definitive translation was then proposed.

-If there were any disagreements, the National Leader (NL) was asked to interfere and give his correction.

His proposal was once again discussed among the group, until it reached consensus. Then only the translation was validated.

Participants

The sample was composed of international academic researchers and GPs. A workshop standed in 2014, in Barcelona and Heraklion in attendance of all representatives of each country taking part of FPDM, in order to share and discuss the results.

The consensus group was formed by: Jean Yves Le Reste, Patrice Nabbe, Bernard Le Floch, Claire Lietard, Jeremy Derriennic, Etienne Melot (France), Djurdjica Lazic, Stanislava Stojanovic-Spehar (Croatia), Slawomir Czachowski, Agnieszka Sowinska (Poland), Radost Assenova (Bulgaria), Heindrun Lingner, Christa Doerr (Germany), Ana Claveria, Maria Isabel San Martin Fernandez, Miguel Angel Munos Perez (Spain), Charilaos Lygidakis (Italy), Melida Hasanagic (Bosnia), Harm Van Marwijk (Nederland), Paul Van Royen (Belgium). Some participants were missing : Harris Lygidakis, Stella Argyradiou (Greece).

3-Results

Participants

12 National Leaders took part of cultural analysis (Table 1): 72,7% were women and 27,3% were men. 10 of them worked in an area of more than 5000 inhabitants. Among them, 8 were teachers and researchers, and 3 were teachers. The average of international publications per leader was 13,8, for a total of 152 publications. The average of years of practice was 21,3 years, and 12.4 in terms of years of research. Considering their international background, they were all fluent English speaker.

Global analysis

All group of languages included, the analysis showed that, for a total of 26 items (comprising, the beginning instruction: item A) 22 have been problematic. On the contrary, the items 15 « Feeling lonely », 18 « Thinking of ending one's life », 19 « Feeling trapped » and 25 « Sleep disturbance » remained perfectly stable after backward translation. Concerning the 10 scale's instructions, the backward translation was different from the original version for 9 items except the explanation concerning the administration time of the tool (Annex J). Lots of translation problems were related to cultural effects specific to the languages.

For Slavic languages, there was a real difference for 16 items in total (i.e 61,5%), and for 5 of 10 instructions (i.e 50%). The difference was related to a cultural effect for 16 items and 2 instructions.

For Romance languages, the translation was modified for 14 items in total (i.e 53,8%), and 8 of 10 instructions (i.e 80%). A cultural effect was implicated for 7 items and 4 instructions.

For Hellenic language, only represented by Greece, there were no modifications for any of the items, including the scale's instructions.

Item 17 « Feeling Blue » was a typical English expression that induced a cultural effect for 6 of 9 languages. A word by word rendition was then impossible.

Interesting thing to note: not only there were translation similarities (often with stronger or medical connotations) between languages belonging to the same linguistic group, but also similarities between different groups: the best example concerns Slavic and Hispanic languages about item 3 « Faintness », which was translated by « Weakness » in Catalan, Castilian, Galician, but also in Croatian.

4."Extremely" CE

The HSCL-25 score is based on pencil-and-paper…

Hellenic language results

The HSCL-25 translation in Greek was mainly based on an adaptation according to the gender. In the light of that finding, the experts concluded on a general cultural effect affecting all parts of the scale. However, there were no real differences in meaning between original version and backward translation, and the Greek scale remained pretty stable in comparison to the original.

Slavic languages results

For Poland (Annex B), 13 items on 26 (i.e 50%) were different. -6 of them (i.e 46,2%) were related to cultural effects: items 5, 6, 8, 10, 17 and 22.

-7 (i.e 53,8%) backward translation problems have been eliminated: items 2, 3, 7, 9, 13, 14 and 20.

As for the scale's instructions, 3 of 10 were different, due to 2 CE and 1 BTP.

For Bulgaria (Annex C), 3 items on 26 (i.e 11,5 %) were different. -only 1 of them (i.e 33,3%) was related to a cultural effect: item 11.

-2 (i.e 66,7%) backward translation problems have been eliminated: items 10 and 12.

As for the scale's instructions, 1 of 10 was different, but analysis didn't detect any CE.

For Croatia (Annex D), 8 items on 26 (i.e 30,8%) were different. -6 of them (i.e 75%) were related to cultural effects: items 2, 3, 7, 9, 10 and 17.

-1 (i.e 12,5%) backward translation problems has been eliminated: item 14.

As for the scale's instructions, 2 of 10 were different, but once again analysis didn't detect any CE.

Most items were an issue on a conceptual level: therefore « Heart racing » became « Palpitations », « Trembling » « Tremors », and « an effort » « a burden » in Polish, moreover « Feeling low of energy » became « A sense of low energy » in Bulgarian, and « Feeling restless » was traduced by « Anxiety » in all three languages, for there were no equivalent words to express these ideas. A word by word translation was in that case impossible. « Headache » turned into plural form « Headaches » in Polish for grammatical reasons.

For Croatia, the main cultural aspect induced by the language was the use of present perfect, which is a tense of state and not of action, commonly expressed in all day life: in items 2, 7, 9, 10, « feeling » was logically replaced by « you have been ». Only one item appeared to be stronger, « Faintness », where the term was replaced by « weak », but the word weak in Croatian was in fact equivalent.

Finally, Bulgaria was the most stable of those three languages.

Romance languages results

For Italy (Annex E), [START_REF] Lehti | Recognition of depression in people of different cultures : a qualitative study[END_REF] As for the scale's instructions, only 1 of 10 was different, but no CE was involved.

Many CE were collected for Romance languages:

for the French scale, it was mainly the tense used in common language, the present, which led to several modifications on the final translation, compared to the forward version that used the past tense: e.g. « Tout était un effort pour vous », was modified by « Tout est un effort pour vous » in the final definition. Also, there were a few cultural effects concerning the scale's instructions, where some terms were replaced by typical French expressions commonly employed in questionnaires: e.g « pencil-and-paper » was translated by « autoquestionnaire » and « Not at all » by « Pas du tout d'accord ».

for the Hispanic languages (i.e Castilian, Catalan and Galician) and Italian, the translation had to be adapted on the gender, and more precisely on the male plural form for the Italian scale, which was the usual way of speaking in that country.

also, from a conceptual point of view: item « Faintness » has been translated into « Weakness » for all three Hispanic languages (i.e respectively « Debilad », « Debilidat » and « Debilidade » in Castilian, Catalan and Galician). Same observation for the item « Heart racing », translated into « Palpitations » (i.e « Palpitaciones » and « Palpitacions » in both Castilian and Galician versions). From a Galician and Catalan point of view, « Blame oneself » turned into « Blame yourself » in backward translation, as the term « oneself » wasn't commonly employed. To finish, « Feeling no interest » was translated by « No siente interes por nada » in Castilian to be understood by the patient, and « Worthless feeling » became « Feeling useless » which was not exactly the same. But in Castilian, « inutil » meant « worthless » as well. As far as the Galician scale is concerned, item 14 « Losing sexual interest », has been translated into « Loss of sexual interest » which expressed a state, not an action like in original English version: it was a normal way of speaking in that language.

German results

Unfortunately, it was not possible to ensure the linguistic stability of the German version of the HSCL-25 in general practice, as a German translation already existed. This version was planned to be published as the study began. All backward translations were performed based on that previous version, despite the NIs disagreement. Moreover, the number of experts at the end of the first Delphi round was insufficient. However, the cultural analysis couldn't be initiated for the German scale.

At the end of cultural analysis, the consensus group finally concluded that there were no changes of meaning, and the translation was finalized in all 9 languages (Table 3).

Discussion

Main results

Control cultural check was necessary to ensure the meaning reliability of the translated scales. By this process we obtained 9 consensual translations, with no loss of meaning. Lots of translation problems were related to cultural effects. All items were validated by the consensus group. Some items and instructions were rephrased.

Greek translation remained the most stable, followed by Bulgaria. Item 17, « Feeling blue » was the most challenging to translate, followed by item 3 « Faintness » and item 5 « Heart racing ». Some scales needed an ultimate adaptation in terms of tense (French, Croatian) and other in terms of gender (Greek, Italian, and for Hispanic languages).

The translation process was composed of two major phases:

the linguistic translation based on blind Forward-Backward translation procedure.

finally the cultural analysis.

The combination of those two methods guaranteed multiple supervisions, to reinforce the final results. These methods were specifically employed in order to meticulously track any translation's inconsistencies, which could lead to misinterpretations when used in native populations. This methodical and transcultural validation ensured the transfer of the same content from one language to another and its reliability. Moreover, forward and backward translation (inspired from the Brislin's model) is a consensual procedure internationally used in cross-cultural studies (23) [START_REF] Jones | An adaptation of Brislin's translation model for cross cultural research[END_REF].

Without these important precautions, it would have been impossible to affirm either the capacity of the instrument to analyze the same psychological characteristics or parameters as the original one; nor its content reliability through the translation process. Scales would become inusable and inadequate for the target populations. Comparability would also be inaccurate between two languages. More importantly, it has been previously proved in many studies that administrating an inadequate tool to a population of patients could cause misdiagnosis and unjustified treatments [START_REF] Daugherty | Diagnostic mistakes of culturally diverse individuals when using North American neuropsychological tests[END_REF].

The statistical power of the study relied on many aspects:

-The involvement of GPs in linguistic translation was a key-point to pursue this study. Indeed, as described by many translators when discussing scientific translation's work: it is essential in that case that a specialist in the field (i.e the medical field) takes a last look at the translation, because he is the main holder of the quality of the final translation [START_REF] Balliu | L'enseignement de la traduction médicale : pour une nouvelle pragmatique[END_REF]. Thus, a specific attention was paid to choose GP researchers and certified bilingual translators with sufficient health care terminology knowledge.

-Control cultural check was a rigorous method. It implicated a step by step analysis, in order to prevent bias and linguistic problems. The intervention of a consensus group allowed several and gradual evaluations of each item, strengthening the accuracy of the validated translations.

-Ethically speaking, all participants had to fill out a consent form, before each phases. Regularly, a report was sent to the National Leaders, to keep them informed of the current progress of the study.

-This work is the result of a multicultural collaborative research between European countries, thanks to the EGPRN.

What is the HSCL-25 ? It's a screening instrument (13): a self-questionnaire in 25 items, designed to identify common psychiatric symptoms, and designated as the consensual tool to diagnose depression by the FPDM study. It's a validated tool against DSM IV, with a Sensibility (Se) of 0.94, and a Specificity (Sp) of 0.94 (versus DSM-IV). It's an effective instrument, as evidenced by its Youden Index of 0.88. It's also a reliable tool with a Cronbach Alpha of 0.9 [START_REF] Nabbe | FPDM Study: Project for multimorbidity and depression after 50. FPDM (Family Practice Depression and Multimorbidity Study)[END_REF].

Strengths and limits

The translating process from one language to another has proved to be a difficult exercise in many domains, such as science and literature [START_REF] Dingwaney | Between Languages and Cultures : Translation and Cross-Cultural Texts[END_REF]. Translation remains the most crucial step in the adoption of a well-developed instrument to another language. Errors in translations may distort the original intent of this instrument and compromise the validity and reliability of the resulting instrument (Chang, Chau and Holroyd;1999; Sireci 1997) [START_REF] Yu | Issues and challenges of instrument translation[END_REF]. There are what may be called semantic issues affecting comparability in international studies, since the same original word (in English original) is interpreted differently across countries and cultures [START_REF] Schnohr | Semantic bias in cross-national comparative analyses : is it good or bad to have 'fair' health ? Health and quality of life outcomes[END_REF]. Moreover, certain terms and concepts may not exist in other languages, or have additionnal connotations that back translations do not always reveal. Challenges arise because of not only the content of word for word, literal translation, but the linguistic form of the language, such as tone, syntax...

Confusion bias

At the beginning of the study, forward and backward translations were achieved by two official translators who worked independently and blindly. They had no contact with each other, and the team in charge of the backward translation had no prior knowledge of original HSCL-25. During the Delphi procedure, all proposals were anonymized for each experts. Therefore, this method guaranteed no confusion bias.

Nonetheless, one confusion bias can be discussed as far as the German scale is concerned: indeed, the existence of a previous German version before the study even began, complicated the process. The meaning reliability of the existent scale was in fact impossible to confirm, and the backward translations were based on a version that never proved its stability compared to the English version. Germany left the study prematurely.

Sample and selection bias

All participants were academic researchers and GPs with international background. They were all native from different countries, and thus had different cultures. Together, they formed a multicultural consensus group. The cultural heterogeneity of the sample was a prerequisite for this study: a global vision of all 9 languages (not only from a linguistic or semantic point of view but also from a cultural one) was essential to obtain translations as close as possible to the original version. All experts were chosen wisely according to quality and quantity standards, all sufficient to conduct the study. Therefore, the results were not affected by any sample or selection bias.

Information bias

There was no information bias either: all experts had access to the same datas, contents and instructions. There was no loss of information as the translations were performed by official translators. A PhD. linguist analyzed all the results. Even though all teams worked independently from one another, all results were discussed regularly among the consensus group during annual meetings and by mail, in representative of all National Leaders. Finally, all National Leaders appropriated the scale, and knew perfectly its functioning.

Further and future applications

Having now a common validated instrument that can be used in several countries of Europe, in order to help diagnose depression, will have great impacts in the future, especially in terms of research: datas could be compared between countries, allowing statistics reviews on the epidemiology and symptoms of depression throughout Europe. 'The use of the same instrument can unify the conceptualization of the studied phenomenon across different studies, and the finding can then be compared' (Brislin 1986) [START_REF] Yu | Issues and challenges of instrument translation[END_REF].

The stability and reproducibility of the scale makes it simple to use from one GP to another, with little disparity, and could tend to be widely used on education field.

In terms of clinical impact, HSCL-25 is also a highly precise scale in diagnosing depression, reproducible and easy to implement: thus an efficient instrument to use in general practice [START_REF] Nabbe | FPDM Study: Project for multimorbidity and depression after 50. FPDM (Family Practice Depression and Multimorbidity Study)[END_REF].

The result of this work finally points out the importance of knowing and studying the tools that we daily use in general medicine: are they adapted to our practice? Are there better ways to diagnose such diseases? For example, a few studies showed that using tests from one culture to assess individuals from other cultures produces false positives. The DSM has also recognized the importance of culture in the diagnostic criteria [START_REF] Daugherty | Diagnostic mistakes of culturally diverse individuals when using North American neuropsychological tests[END_REF]. The awareness of those facts and caution when using such tools could lead to a better medical care.

Conclusion

The translation of the HSCL-25 is now available for 9 countries of Europe (Castille, Galicia, Catalonia, France, Greece, Italy, Poland, Bulgaria, and Croatia) (Table 3) and is now ready to be tried out in actual and representative primary care populations, in order to validate its parameters' efficiency. This might, in the future, help GPs to overwhelm the actual difficulties to diagnose and have better knowledge of this complex condition. Eventually, it could lead to better treatments and follow up.

Annex A: HSCL-25 original version

Choose the best answer for how you felt over the past week: Items 1: "Not at all" 2:"A little" 3:Quite a bit": 4: "Extremely" The HSCL-25 score is calculated by dividing the total score (sum score of items) by the number of items answered (ranging between 1,00 and 4,00). It is often used as the measure of distress. The patient is considered as a "probable psychiatric case" if the mean rating on the HSCL-25 is ³ 1,55. A cut-off value of ³ 1,75 is generally used for diagnosis of major depression defined as "a case, in need of treatment". This cut-off point is recommended as a valid predictor of mental disorder as assessed independently by clinical interview, somewhat depending on diagnosis and gender.The administration time of HSCL 25 is 5 to10 minutes. The HSCL-25 score is calculated by dividing the total score (sum score of items) by the number of items answered (ranging between 1,00 and 4,00). It is often used as the measure of distress.

Annex B: Polish results

La puntuación del HSCL-25 se calcula dividiendo la puntuación total (sumando la puntuación de todos las preguntas) entre el número de respuestas (varía entre 1,00 y 4,00). Se usa habitualmente para medir el malestar psicológico (angustia).

The HSCL-25 score is calculated dividing the total score (the sum of the scores of all the questions) by the number of items answered (from 1 to 4). It is usually used to measure the level of anxiety.

Y BTP Y

La puntuación del HSCL-25 se calcula dividiendo la puntuación total (sumando la puntuación de todos las preguntas) entre el número de respuestas (varía entre 1,00 y 4,00). Se usa habitualmente para medir el malestar psicológico.

Page 39

Annex H: Catalan results The HSCL-25 score is calculated by dividing the total score (sum score of items) by the number of items answered (ranging between 1,00 and 4,00). It is often used as the measure of distress.

A puntuación do HSCL-25 calcúlase dividindo a puntuación total (a suma de todas as preguntas) entre o número de respostas (cuxa puntuación oscila entre 1,00 e 4,00). Úsase de forma habitual para medir o nivel de angustia.

HSCL-25 scores are calculated by dividing the total score (sum of all the questions) by the number of answers (scores ranging from 1.00 to 4.00). The questionnaire is frequently used to measure anxiety levels.

Y BTP Y

A puntuación do HSCL-25 calcúlase dividindo a puntuación total (a suma de todas as preguntas) entre o número de respostas (cuxa puntuación oscila entre 1,00 e 4,00). Úsase de forma habitual para medir o nivel del malestar psicológico.

« 2 -

 2 Menez chaque journée à son terme, un point c'est tout. Vous avez fait de votre mieux, non sans quelques gaffes, quelques absurdités : oubliez-les dès que possible. Demain est un nouveau jour et vous l'entamerez sereinement, avec l'élan nécessaire pour ne pas vous encombrer des bévues d'hier. » Liste des abréviations EGPRN: European General Practice Research Network FPDM: Family Practice Depression Multimorbidity HSCL-25: Hopkins Symptom Checklist -25 items GP: General Practician DSM: Diagnostic and Statistical Manual of Mental disorders FTP: Forward translation problem BTP: Backward translation problem CE: Cultural effect NL: National Leader Summary Résumé ............................................................................................................................... Abstract ............................................................................................................................... 1-Introduction ................................................................................................................... Materials and methods .................................................................................................. 2.1. Definition of HSCL-25 ....................................................................................................... 2.2. Consents ........................................................................................................................... 2.3. Data collection and analysis .............................................................................................

Figure 1 :

 1 Figure 1: Final translation agreement process 2.4. Participants ....................................................................................................................... 3-Results ............................................................................................................................ 3.1. Participants .......................................................................................................................

3. 2 .

 2 Global analysis ..................................................................................................................

3. 3 .

 3 Hellenic language results .................................................................................................. 3.4. Slavic languages results ................................................................................................... 3.5. Romance languages results .............................................................................................. 3.6. German results ..................................................................................................................

4 .

 4 Discussion ..................................................................................................................... 4.1. Main results ....................................................................................................................... 4.2. Strengths and limits ..........................................................................................................

4. 2 . 1 .

 21 Confusion bias 4.2.2. Sample and selection bias 4.2.3. Information bias 4.3. Further and future applications ......................................................................................... 5. Conclusion ..................................................................................................................... 6. Bibliography ................................................................................................................... 7. Annex ..............................................................................................................................

  : Une traduction fidèle à l'échelle d'origine est disponible dans 9 pays d'Europe et en attente d'être testée en conditions réelles.

Figure 1 :

 1 Figure 1: Final translation agreement process

  Médecine Générale 22, avenue Camille Desmoulins CS 93837 -29238 -Brest CEDEX 3 Tél : 02 98 01 65 52 -fax : 02 98 01 64 74

Table 1 :

 1 National leaders panel characteristics

Table 2 :

 2 Cultural effects synthesis (items and scale's instructions)

Table 3 :

 3 final translation after cultural analysis in 9 european languages

Table 1 :

 1 National leaders panel characteristics

	Experts	Gender	Country	University statement	Number of inhabitants	Office type	International publication number *	Years of practice	Years of research
	1	F	Spain	Teacher/ Researcher	>5000	GPs group office	15	20	14
	2	F	Spain	Teacher/ Researcher	>5000	GPs group office	13	22	25
	3	F	Greece	Teacher/ Researcher	>5000	GPs and para-medic group office	14	30	18
	4	M	Italy	Researcher	>5000	GPs group office	23	7	6
	6	M	Poland	Teacher/ Researcher	>5000	GPs group office	20	30	12
	7	F	Croatia	Teacher/ Researcher	>5000	Alone	6	20	12
	8	F	Croatia	Teacher/ Researcher	>5000	GPs group office	18	30	20
	9	F	Bulgaria	Teacher/ Researcher	>5000	GPs group office	9	14	12
	10	M	France	Teacher/ Researcher	>5000	GPs group office	11	20	5
	11	F	Germany	Researcher	2000 to 5000	Practice stopped since 2 years	19	23	5
	12	F	Germany	Researcher	> 5000	GPs group office	4	18	7
	Men : 27,3 %					Average : 13,8	Average : 21,3	Average : 12,4
	Women : 72,7%					Total : 152	Total : 254	Total : 138
	* PubMed Database

Table 2 :

 2 Cultural effects synthesis (items and scale's instructions)

		ITEMS	POLISH	BULGARIAN	CROATIAN	CASTILIAN	CATALAN	GALICIAN	ITALIAN	FRENCH	GREEK
				SLAVIC LANGUAGES				ROMANCE LANGUAGES	HELLENIC LANGUAGE
	2	Feeling fearful			CE
	3	Faintness			CE	CE	CE		CE
	5	Heart racing	CE			CE			CE
	6	Trembling	CE
	7	Feeling tense			CE
	8	Headache	CE
	9	Feeling panic			CE
	10	Feeling restless	CE		CE
	11	Feeling low in energy		CE
	12	Blaming oneself					CE		CE
	14	Losing sexual interest							CE
	17	Feeling blue	CE		CE	CE	CE				CE	CE
	21	Feeling no interest				CE
	22	Feeling that
		everything is an effort	CE
	23	Worthless feeling				CE
			POLISH	BULGARIAN	CROATIAN	CASTILIAN	CATALAN	GALICIAN	ITALIAN	FRENCH	GREEK
		SCALE'S
	INSTRUCTIONS
	ORIGINAL VERSION
				SLAVIC LANGUAGES				ROMANCE LANGUAGES	HELLENIC LANGUAGE
	1."Not at all"	CE								CE
	2."A little"									CE
	3."Quite a bit"	CE								CE

  items on 26 (i.e 26,9%) were different.

	-	1 of them (i.e 20%) was related to a cultural effect: item 17.
	-	4 (i.e 80%) forward or backward translation problems have been eliminated, concerning items 12, 21, 22
		and 23.
		As for the scale's instructions, 7 of 10 were different, due to 5 CE and 2 FTP.
		For Castille (Annex G), 6 on 26 items (i.e 23%) were different.
	-	5 of them (i.e 83,3%) were related to cultural effects: items 3, 7, 9, 10 and 17.

-1 of them (i.e 14,3%) was related to a cultural effect: item

[START_REF] Guillemin | Cross-cultural adaptation of health-related quality of life measures: literature review and proposed guidelines[END_REF]

. -6 (i.e 85,7%) forward or backward translation problems have been eliminated, concerning items 1, 5, 9, 11, 23 and 24. As for the scale's instructions, 3 of 10 were different, but no CE was involved. For France (Annex F), 5 on 26 items (i.e 19,2%) were different. -1 (i.e 16,7%) backward translation problem has been eliminated: item 2 As for the scale's instructions, only 1 of 10 was different, but no CE was involved. For Catalonia (Annex H), 7 on 26 items (i.e 26,9%) were different. -3 of them (i.e 42,9%) were related to cultural effects: items 3, 12 and 17. As for the scale's instructions, 2 of 10 were different, but no CE was involved. For Galicia (Annex I), 5 on 26 items (i.e 19,2%) were different. -4 of them (i.e 80%) were related to cultural effects: items 3, 5, 12 and 14. -1 (i.e 20%) backward translation problem has been eliminated: item 1.

Table 3 :

 3 final translation after cultural analysis in 9 European languages (scale's instructions)

	SCALE
	INSTRUCTIONS ORIGINAL	GREECE	POLAND	BULGARIA	CROATIA	SPAIN (CASTILLE)	SPAIN (CATALONIA)	SPAIN (GALICIA)	ITALY	FRANCE
	VERSION
	The HSCL-25 score is based on pencil-and-paper self-report of 25 questions about the presence and intensity of anxiety and depression symptoms over the last week.	Η βαθμολογία του HSCL-25 βασίζεται σε γραπτό ερωτηματολόγιο αυτοαξιολόγησης 25 ερωτήσεων σχετικά με την παρουσία και την ένταση των συμπτωμάτων άγχους και κατάθλιψης κατά την τελευταία εβδομάδα. Οι	Ocena testu HSCL-25 oparta jest na kwetionariuszu 25 pytań, w którym zakreśla się na papierze obecność i nasilenie objawów lęku i depresji w ciągu ostatnie-go tygodnia.	Резултатът от HSCL-25 се основава на самостоятелно попълнен инструмент на хартиен носител, включващ 25 въпроса за наличието и интензивността на симптоми на тревожност и депресия през последната седмица.	HSCL-25 skor sastoji se od 25 pitanja koja se rješavaju jednostavno olovkom i papirom, a temelji se na samoprocjeni prisutnosti i intenzitetu ansksioznih i depresivnih simptoma tijekom tjedna. prošlog	La puntuación HSCL-25 se basa en un cuestionario autocumplimentado con lápiz y papel, de 25 preguntas sobre la presencia y la intensidad de ansiedad y sínto-mas depresivos en la última semana.	L'escala HSCL-25 es basa en un qüestionari auto administrat de 25 pre-guntes, sobre la presència i la intensitat de símptomes d'ansietat i depressió en la darrera setma-na.	A puntuación HSCL-25 baséase nun cuestionario cumprimentado con lapis e papel, de 25 preguntas sobre a pre-senza e a intensidade de ansiedade e síntomas depresivos na última semana.	Il punteggio settimana. dell'HSCL-25 si basa sulla compilazione di un questionario di autovaluta-zione in cartaceo ("carta/penna") di 25 domande sulla presenza e intensità di sintomi di ansia e depressione nel corso dell'ultima	La HSCL-25 est un auto-questionnaire en 25 ques-tions relatives à la présence et à l'intensité des symp-tômes d'anxiété et de dépression durant toute la semaine dernière.
		συμμετέχοντες
		απαντούν σε μία
		από τις τέσσερις
		κατηγορίες για
	Participants answer to one of four categories for each item on a four-point scale ranging from 1 to 4	κάθε ερώτημα σε μια κλίμακα εύρους τεσσάρων βαθμών με τιμές από 1 μέχρι 4. ???	Badani odpowiadają na jedno z czterech możliwych kategorii na skali mierzącej wartości od 1 do 4.	Участниците избират една от категориите за всяка позиция по скала от четири точки от 1.00 до 4.00.	Ispitanici odgovaraju jednom od četiri kategori-ja za svako pitanje na skali od 1-4.	Los/ las partici-pantes responden una de cuatro categorías para cada ítem, en una escala de cuatro puntos que van desde 1 a 4.	Els/les partici-pants responen a una de les quatre catego-ries per a cada ítem en una escala de quatre punts que va de l'1 al 4.	Os partici-pantes respon-den unha de catro ca-tegorías para cada ítem, nunha escala de catro puntos que van desde 1 a 4.	I partecipanti rispondono ad una delle quattro catego-rie per ciascun sintomo su una scala di pun-teggio che va da 1 a 4.	Les partici-pants cotent chaque proposition, sur une échelle en quatre points, cotée de 1 à 4.
	1."Not at all"	Καθόλου	Wcale	Съвсем не	Nimalo	En absoluto	Gens	En absoluto	Per niente	Pas du tout d'accord
	2."A little"	Λίγο	Trochę	Незначително	Malo	Un poco	Una mica	Un pouco	Poco	Un peu d'accord
	3."Quite a bit"	Αρκετά	Znacznie	Съвсем малко	Dosta	Bastante	Bastant	Bastante	Abbastanza	Plutôt d'accord
	4."Extremely"	Πάρα πολύ	Bardzo mocno	Извънредно	Jako	Mucho	Molt	Moito	Moltissimo	Complètement d'accord

(i.e

57,1%) forward or backward translation problems have been eliminated: items16, 21, 23 and 24.

Remerciements

Yes / N = No ** BTP = Backward Translation Problem / CE = Cultural Effect / FTP = Forward Translation Problem * Y= Yes / N = No ** BTP = Backward Translation Problem / CE = Cultural Effect / FTP = Forward Translation Problem * Y = Yes / N = No **BTP = Backward Translation Problem / CE = Cultural Effect * Y = Yes / N = No ** BTP = Backward Translation Problem / CE = Cultural Effect / FTP = Forward Translation Problem * Y = Yes / N = No ** BTP = Backward Translation Problem / CE = Cultural Effect

University:

Asked me to participate in a Forward-Backward translation.

I had time to reflect on my involvement in this study. I am aware that my participation is completely voluntary and that the study will entail no additional cost to my charge. I can, at any time, decide to leave the study without giving reasons for my decision and that it does without consequences. I understood that the data collected during the research would be protected in accordance to confidentiality. They can only be accessed by persons subject to professional secrecy belonging to the team-investigating physician, mandated by the promoter. I accept the computerized processing of personal data in accordance with the data protection act. I have been informed of my right to access and rectify data concerning me.

My consent does not absolve the responsibilities of the organizers of this research. I retain all my rights guaranteed by Law. Done in two originals at……………, the dd/mm/yyyy Name, first name of national leader:

Name, first name of the interviewee:

Signature:

Page 42 Introduction: Depression's the second most common chronic disorder in primary care. FPDM study designated the HSCL-25 as the consensual tool to diagnose depression. In order to have the same tool in Europe, the scale was translated in each participating European country. A cultural check was necessary to ensure the meaning reliability to the English version in Castilian, Catalan, Galician, Bulgarian, Polish, Croatian, French, Greek, and Italian. The aim was to make a synthesis of all cultural check made in these languages. What cultural modifications have been induced by languages' specificities in the translated versions? Methods: A workshop standed in 2014 in attendance of researchers of each country: a cultural check based on backward and forward translations obtained via Delphi consensus procedure was conducted by a consensus group.

Results: All backward translations were compared to the original scale. Differences have been collected, related to cultural effects specific to each languages. Some items were rephrased. Greek, Italian, Castilian, Galician and Catalan scales have been adapted on the gender. French scale have been written in present, Croatian scale in present perfect. Keeping the same meaning was difficult for some items, related to conceptual aspects. All items were validated. Discussion: The cultural check was necessary to ensure the meaning reliability. Greek translation remained the most reliable, followed by Bulgaria. Item «Feeling blue» was the most challenging to translate, followed by items «Faintness» and «Heart racing».

Conclusion:

A faithful translation's available for 9 countries of Europe. It's now ready to be tried out in representative primary care populations.

MOTS CLES


François Mirabel

Mathias Reymond
email: mathias.reymond@univ-evry.fr

The urban toll revenue recycling : what is the optimal share distributed towards mass transit system?

Keywords: Congestion pricing, Public Transport, Revenue. JEL classi…cations: R41, R48

. A very interesting result is shown in our model : in a pricing regime with a …ne toll and a mass transit fare based on the average cost, the optimal redistribution towards mass transit users allows to obtain an equilibrium similar to the benchmark optimal situation with marginal cost fare.

Introduction

In order to regulate auto tra¢ c, public authorities can use various methods inspired by the Pigovian tax [START_REF] Pigou | Wealth and Welfare[END_REF]. Thus, congestion pricing would allow the reduction of negative externalities caused by tra¢ c congestion. A wide empirical and theoretical literature exists on the e¢ ciency of urban road toll. In recent papers, this literature focuses on the technical constraints supported for the implementation of optimal road toll (De Palma and Lindsey 2011) that force the public authorities to implement second-best or third-best toll in order to reduce ine¢ ciencies.

The recent debates on urban road tolls focus on the question concerning acceptability and equity. More precisely, the question concerning acceptability deals with the related measures that would make the toll more widely accepted. In this framework, it is very relevant to evaluate the role of revenue use in the acceptability of transport pricing policies [START_REF] Schuitema | The role of revenue use in the acceptability of transport pricing policies[END_REF].

In examining multiple toll case studies, [START_REF] King | The political calculus of congestion pricing[END_REF] explain that toll revenues must be allocated towards city budgets to ensure the feasibility of this policy. In our paper, in the same way of [START_REF] Goodwin | The 'Rule of Three' : a possible solution to the political problem of competing objectives for road pricing[END_REF] 1 , we propose channeling a part of toll revenues towards mass transit and public budget so as to allow a better acceptability, to encourage modal transfer in order to reduce externalities due to automobile use (pollution, congestion, noise...). Along this line of thought, [START_REF] Kidokoro | London-type congestion tax with revenue-recycling[END_REF] developed a model that explicitly uses revenue recycling to deal with cordon area congestion tax, as seen in London, and analyses its e¤ects. In other models with two routes for commuting, some papers [START_REF] Adler | A direct redistribution model of congestion pricing[END_REF]Cetin 2001, Kidokoro 2010) analyze the toll revenue collection from one route and the revenue recycling used in particular to subsidize commuting in the other route.

Here we examine the question of the redistribution of toll revenue as seen in a bottleneck congestion model (see [START_REF] Arnott | Economics of a bottleneck[END_REF][START_REF] Arnott | A structural model of peak-period congestion: a tra¢ c bottleneck with elastic demand[END_REF][START_REF] Vickrey | Pricing in urban and suburban transport[END_REF][START_REF] Vickrey | Congestion theory and transport investment[END_REF]. It is the …rst time that redistribution of tolls revenue is introducted in the framework of Arnott De Palma Lindsey bottleneck models. Our objective is to analyse the impact of this redistribution model on total cost and on modal split between railroad and road. Following Tabuchi's model (1993) and, by extension, that of [START_REF] Danielis | Bottleneck road congestion pricing with a competing railroad service[END_REF], [START_REF] Mirabel | Bottleneck congestion pricing and modal split: Redistribution of toll revenue[END_REF] discussed the situation where the toll revenue is totally used to subsidize mass transit. In this framework, we extend this analysis assuming that toll revenue is allocated between mass transit (share towards mass transit) and public budget (share ( 1) distributed for public budget). In this context, we study the impact of a redistribution of toll revenues along a …ne toll regime (time-varying road pricing) that would allow the elimination of waiting lanes thus streamlining tra¢ c.

In Section 2, we present our model based on Tabuchi's which consists of a …ne toll with public transport marginal cost pricing; into this model we integrate a redistribution of toll revenue between mass transit and collectivity. This scenario shows a very interesting result : the higher is the part of toll revenue distributed towards mass transit, the lower is the number of motorists and the lower is the level of toll revenue. In Section 3, we enlarge this analysis integrating an other pricing regime with public transport average cost pricing. In this scenario, we evaluate the optimal allocation of revenue accrued from congestion pricing, between the public transportation and public budget. In this pricing regime, the optimal redistribution towards mass transit users allows to obtain an equilibrium similar to the benchmark optimal situation with marginal cost fare. Section 4 concludes the paper and emphasizes ways for further analyses.

The model 2.1 Bottleneck congestion and modal split

First we present Tabuchi's model (1993) as the starting point of our analysis.

Tabuchi has developed a two-mode model, comprising a road with a bottleneck and a railroad between a residential area and a central business district. In his analysis, N commuters 2 split into N a and N b (motorists and public transport users, respectively). In this case the average travel cost of a motorist is rewritten as : C a = Na s (where = + , with the unit cost of an early arrival at the workplace and the unit cost of a late arrival, and where s is the road capacity), and city authorities set the railroad fare at marginal cost (p = c). The travel cost of public transport is expressed by:

C b = c
At equilibrium, commuters are indi¤erent to the mode of transport that they use, because time costs of driving and taking public transport are the same (Wardrop's equilibrium, 1952) 3 .

Equilibrium can thus be de…ned as follows:

C a = C b =) N a s = c =) (N N b ) cs = 0 (1)
In this case, N b > 0 if N > N y for N y = cs / . However if N N y , N a = N and N b = 0. N y may thus be considered as the threshold below which there is no transit users4 . In this case, below N y , it is not bene…cial to construct public transport networks as N b = 0. Under this condition, Tabuchi obtains the modal split at equilibrium associated with price reference system5 :

(N m a ; N m b ) = cs ; N cs for N > N y (2) = (N; 0) for N N y
Total travel cost is expressed by:

T C m = C a N m a + C b N m b + F = cN + F for N > N y (3) = C a N = N 2 s for N N y
Where F represents …xed public transportation costs.

Here the temporal division of commuters at equilibrium causes a signi…cant loss of time. Public authorities can intervene to eliminate waiting lines during rush hour periods by encouraging commuters to stagger the time they leave home.

Implementation of a …ne toll

The implementation of tolls permits the elimination of the queue and thus allows the reduction of social cost incurred by all individuals. When city authorities set the railroad fare at marginal cost (p = c), this pricing regime represents our benchmark that induces the lowest total cost. With the implementation of the …ne toll ( f ) 6 , the true travel cost incurred by each driver would be C a = N a =s. This is the same cost as the cost borne by individuals at equilibrium without a toll (1), but the internal "structure"of this cost is not the same. The travel time cost disappears. The true travel cost incurred by each driver is on average equal to the total of the schedule delay cost ( N a =2s ) and the …nancial cost of the toll ( N a =2s).

Tabuchi …nds the modal split obtained in the base case i.e. 7 :

N f a ; N f b = cs ; N cs for N > N y (4) = (N; 0) for N N y
The main di¤erence from the previous situation is that currently, the implementation of a tari¤ setting on urban roads generates revenue that reduces the total cost incurred by the population. From the average toll, we can deduce the revenue:

R f = N f a 2 2s = c 2 s 2 2s 2 = c 2 s 2 for N > N y (5)
As noted by Arnott et al. (1994, p. 144): "The toll replaces queuing time as the rationing device for desired arrival time slots, leaving drivers'private costs inclusive of the toll unchanged, but overall welfare higher by the amount of toll revenue." It is then possible to calculate the total net cost: 6 The …ne toll is determined by the railroad fare minus the schedule delay costs:

f (t) = c (t t 0 ) for t 2 t 0 ; t = c (t 1 t) for t 2 t; t 1
As noted by Tabuchi (1993, p.426), "the role of the …ne toll is therefore to replace any queue time by the toll (...) and to allocate the number of users in each sector."

7 Where f represents the scenario at marginal cost with …ne toll.

T C f = cN + F c 2 s 2 for N > N y (6) = N 2 2s for N N y

Redistribution of toll revenue in the benchmark case with public transport marginal cost pricing

Our objective is to evaluate the e¤ects of toll revenue redistribution. More precisely, we analyze how this redistribution modi…es modal split and the total cost incurred by drivers and railroad users. We assume that the government has the possibility to allocate the toll revenue between mass transit (share towards mass transit) and public budget (share (1 ) distributed for public budget). This last part ( 1) is allocated towards other economic sectors non included in our partial equilibrium model.

In this context, the cost supported by public transport users is reduced because a share of toll revenue is used to subsidize mass transit sector:

e C f b = c recettes e N f b = c e N f a 2 2s(N e N f a )
With 0 < < 1:

The average travel cost of a motorist is the same and is written as : e

C f a = e N f a s . In this case, the modal split is such that : e C f a = e C f b () e N f a s = c ( e N f a ) 2 2s(N e N f a ) () 2 e N f a 2 2(sc + N ) e N f a e N f a 2 + 2scN = 0
In that case, we obtain the following solution for modal split at equilibrium :

e N f a ; e N f b = 0 @ cs + N q (cs N ) 2 + 2cs N (2 ) ; N cs + N q (cs N ) 2 + 2cs N (2 ) 1 A for N > 0 (7)
Proposition 1 The number of motorists and the toll revenue are decreasing with the share : the higher is the part ( ) of toll revenue distributed towards mass transit, the lower are the number of motorists e N f a and the toll revenue e R f (see Proof on appendix A).

In this context, we can highlight a very interesting result : in our model, the objective of toll revenue increase could be incompatible with the objectives of tra¢ c reduction. This result is a good illustration of the con ‡ict between revenue collection and tra¢ c reduction. For example in Singapore, the implementation of a …ne toll during the rush hours has induced a very high decrease of the road tra¢ c but has entailed a strong reduction of toll revenue collected.

Using relation (7), we can now evaluate average cost supported by the motorist or the mass transit user :

e C f a = e C f b = e N f a s = cs + N q (cs N ) 2 + 2cs N (2 )s for N > 0 (8)
In this scenario, the total cost at equilibrium is therefore equal to:

g T C f = N cs + N q (cs N ) 2 + 2cs N (2 )s cs + N q (cs N ) 2 + 2cs N 2 2 s( 2) + F (9)
At equilibrium, we can note that the redistribution of toll revenue naturally accumulates to the total cost due to the distorsion from pricemarginal cost : g T C f > T C f : In that case, the use of the toll revenue as subsidy for public transport is welfare decreasing, when the price of public transport is initially set based on its marginal cost. Moreover, the level of individual cost supported by a motorist or a mass transit user is lower after redistribution of toll revenue : e

C f a = e C f b < C f a = C f b
We can easy show that the total cost g T C

f increases with the level of ( ): @ g T C f @ > 0. In this case, the total cost is minimized with = 0 that corresponds to the initial case without redistribution.

When the toll revenue is totally distributed towards mass transit sector ( = 1), distorsions are higher that induce a strong increase of the total cost (see [START_REF] Mirabel | Bottleneck congestion pricing and modal split: Redistribution of toll revenue[END_REF]. On the contrary,when the toll revenue is completly integrated into the public budget ( = 0), there is no e¤ect on the commuters behavior and the total cost does not change. It is thus important to underline that higher is the a¤ectation of revenue towards mass transit and higher is the total cost because of the e¤ects of distortion. However, according to the new objectives for public authorities, the policy of toll revenue redistribution towards mass transit allows to decrease the number of motorists in the city inducing reduction of environmental damages.

Redistribution of toll revenue and self-…nancing of the mass transit system

In this pricing regime, we suppose that mass transit fare is set equal to the average cost, p = c + F N b . This pricing regime allows taking into account increasing return to scale in mass transit sector. In the same way as the previous scenario, we integrate a redistribution of toll revenue between mass transit and public budget. We can write the new individual cost supported by a motorist and a mass transit user and after the redistribution of toll revenue towards mass transit sector (share of the revenue)8 :

e C F a = e N F a s e C F b = c + F e N F b R F b e N F b = c + F e N F b e N F a 2s e N F b (10)
Logically, the level of mass transit fare is decreasing with the number of mass transit users. In this case, the modal split is such that e C F a = e C F b . Using this condition and expression (10), the modal split and the level of toll revenue can be derived at equilibrium:

e N F a ; e N F b = 0 @ cs+ N p (cs N ) 2 +2cs N 4 F s+2 F s (2 )
;

N (1 ) cs+ p (cs N ) 2 +2cs N 4 F s+2 F s (2 ) 1 A if N > e N F s e N F a ; e N F b = (N; 0) if N e N F s (11) e R F = e N F a 2s = cs + N p (cs N ) 2 + 2cs N 4 F s + 2 F s 2 2 s(2 ) 2
Using expression (11), we can write the following proposition :

Proposition 2 In the pricing regime with …ne toll and mass transit fare based on the average cost, the higher is the part ( ) of toll revenue distributed towards mass transit, the lower are the number of motorists e N F a and the toll revenue e R F .

According to the previous scenario, this result is a good illustration of the con ‡ict between revenue collection and tra¢ c reduction. As seen in the previous scenario, we evaluate the level of individual cost using expressions ( 10) and ( 11):

e C F a = e C F b = cs + N p (cs N ) 2 + 2cs N 4 F s + 2 F s (2 )s (12)
Using this expression, we obtain …nally the total cost supported by all users integrating the redistribution of toll revenue towards the public budget (share ( 1) distributed):

g T C F = N e C F a (1 ) e R F g T C F = N cs + N p (cs N ) 2 + 2cs N 4 F s + 2 F s (2 )s (13)
(1 )

cs + N p (cs N ) 2 + 2cs N 4 F s + 2 F s 2 2 s(2 ) 2
With this expression of total cost, we can highlight a very interesting result : when we compare the level of total cost T C F before redistribution (see annex B) and the level of this cost g T C

F after redistribution, we obtain the following result : if the …xed cost of mass transit is higher than the threshold b F F 9 , the redistribution of toll revenue induces a decrease of total cost so that : g T C F < T C F . This result can be easily explained : the redistribution of toll revenue towards urban mass transit users induces a decrease of the fare; it entails therefore an increase of mass transit users, allowing a better amortization of the …xed cost that is pro…table for a high level of …xed cost.

Using the expression (13), we can evaluate the optimal share of toll revenue that is distributed towards mass transit users. We can show that the total cost is minimized for the value of equal to = 2 F c 2 s 10 . In that case, the optimum level of redistribution is such that = min 2 F c 2 s ; 1 > 0. We obtain then the characterization of equilibrium in this pricing regime after

9 F > b F F = 5 N cs 2 N 2 +(6 N 2cs) p ( N ) 2 N cs N 10 If < b , the function g T C
F is convex that allows to attain the minimum level for the total cost.

b = (2Nc +4 F 2c 2 s) p c 4 s 2 +7 2 N 2 c 2 8c 3 sN +22cF N 2 10 F sc 2 +16 2 F 2 9c 2 s (cN +F ) + (19c N F +c 2 N 2 +N c 3 s+16 F 2 +5c 2 sF ) c 4 s 2 9c 2 s (cN +F )
redistribution :

e N F a ; e N F b = cs ; N cs if N > e N F s e N F a ; e N F b = (N; 0) if N e N F s e N F a = e N F b = c e R F = c 2 s 2 g T C F = cN + F c 2 s 2 (14)
Logically, we obtain the lowest level of total cost similar to the scenario with public transport marginal cost pricing without redistribution. This result can be intuitively explained :

is such that the toll revenue redistributed towards mass transit sector allows covering …xed cost F so that :

e R F = F () = F e R F = 2 F c 2 s . An interior solution < 1 is obtained if and only if 2 F c 2 s < 1 () F < c 2 s 2 .
If the …xed cost is superior to this value, the toll revenue is not su¢ cient to cover the …xed cost. In that case, even if the toll revenue is entirely distributed towards mass transit users ( = 1), the level of the fare remains superior to the level of marginal cost pricing ; the total cost is higher due to lack of toll revenue in order to cover the …xed cost.

Proposition 3 In a pricing regime with a …ne toll and a mass transit fare based on the average cost, the optimal redistribution towards mass transit users is such that :

The total cost is minimized and corresponds to the level of total cost supported in the benchmark situation with marginal cost fare The optimal share distributed towards mass transit users is increasing with the level of the …xed cost (F ) and is decreasing with the level of road capacity (s).

In this context, it is important to make three relevant remarks: -First, the minimization of total cost can be obtained with a mass transit fare based on the average cost according to a …ne tuning redistribution of toll revenue. We enlarge and moderate therefore the results of Tabuchi who wrote in his article (Tabuchi 1993 p420): "Under these circumstances (average cost fare), it is well known that the average cost pricing never attains an optimum because the total social cost is not minimized when both modes are in use".

-Second, in this scenario with redistribution, the mass transit sector is self-…nanced. Moreover, the redistribution of toll revenue allows subsidizing the mass transit fare that entails better acceptability of urban toll.

-Third, the modal split is corresponding to the benchmark situation with the highest level of mass transit users. This scenario is socially pro…table since it induces a decrease of the pollution level in urban areas due to the reduction of tra¢ c.

From a transport policy perspective, this analysis could be a relevant framework to set the level of urban toll and the redistribution of toll revenue towards mass transit and public budget. The model put on light the relevance of a …ne-tuning policy in order to choose the best pricing regime and revenue redistribution scenario. In that context, public authorities could then determine the level of the …ne toll and the optimal share of toll revenue distributed toward mass transit. With a self-…nancing mass transit sector (the fare is equal to the average cost), public authorities could then determine the level of toll revenue redistribution which allows to subsidize the mass transit fare until the marginal cost that entails to lessen the social cost. Moreover, public authorities could use the road capacity (s) as an additional instrument for transport policy. For example, since the optimal share distributed towards mass transit is equal to = 2 F c 2 s , the reduction of road capacity11 justify an increase of the toll revenue share distributed towards mass transit users.

Conclusion

In this article, we assume in an innovative way that the toll revenue is allocated towards public transport and public budget as an instrument of public policy. The revenue redistribution towards public transport results in a distortion of travel demand (there is a strong tendency to commute with public transport rather than driving) inducing an increase in the total cost. However, this total cost does not take into account external e¤ects related to the environment, and a reduction of automobile use would allow e reduction of city tra¢ c jams.

Section 2 focuses on the case where the railroad fare is set equal to marginal cost. The subsidies corresponding to …xed costs are integrated into the total cost ex post. The total cost is always higher after redistribution towards mass transit sector and public budget. And the higher is the part of toll revenue distributed towards mass transit, the lower is the number of motorists.

Section 3 enlarges the analysis integrating a new pricing regime with the mass transit fare based on the average cost. In this pricing regime, the distribution of toll revenue towards mass transit and public budget allows to minimize the total cost and therefore to obtain the benchmark optimal situation with marginal cost fare.

From a transport policy perspective, the redistribution of toll revenues that was integrated in our model would induce bene…ts for the collectivity. Firstly, the number of user transit is higher when revenue is redistributed. The decline in the number of drivers allows the reduction of environmental externalities related to city automobile use. Secondly, redistribution of revenue allows a better acceptability: when citizens are aware that revenue is assigned towards public transport, toll acceptability is greater than when it is not redistributed. This point has already been highlighted on various occasions (See Reymond 2004, Schade and[START_REF] Schade | Reactance or acceptance? Reactions towards the introduction of road pricing[END_REF]. In order to extend our new analysis, other pricing regimes will be integrated for further researches. It will be so relevant to compare the impact of theses pricing regimes on the total cost and modal split. Finally, it will allow to evaluate the best splitting of toll revenue between mass transit and public budget in order to make some recommandations for a …ne-tuning redistribution of the toll revenue.

[START_REF] Goodwin | The 'Rule of Three' : a possible solution to the political problem of competing objectives for road pricing[END_REF] proposes that a third of the toll revenue be used to improve the e¤ectiveness of public transport, that a third be used for new road infrastructure and maintenance, and that a third be used for general city funds.

Here we assume N to be inelastic, which means that we assume total travel demand to be constant.

In other words, when individuals seek to optimise their route, they are confronted with a situation at equilibrium which prevents any single user from improving their travel time by unilaterally altering their route.

This threshold (the "city size" in the Tabuchi's analysis) is calculated by solving the former equation.

Where m represents the scenario at marginal cost, with no-toll.

Where F represents the scenario at average cost with …ne toll.

For example, a transfert of road capacity for other uses : walking, cycling, railroad,...

Appendix A Sign of @ e N f a @ . Evaluate the value of this derivate

In order to sign this derivate, we sign the numerator of the expression using the assumption about the value of N : N > cs ) N = r cs with r > 1. In that case, the denominator is positive and the numerator writes (after simpli…cations):

Evaluate the value of this expression for = 0 and = 1:

If r > 1, the expression N um of the numerator is de…ned and continuous on the interval 2 [0; 1]. Moreover, we can show that N um = 0 for = 2: In that context, whatever the value of 2 [0; 1] ; N um < 0

In that case, the sign of @ e R f @ is similar to the sign of @ e N f a @ < 0 since toll revenue writes f