Anna Zaytseva

Pierre Verger

Bruno Ventelou

Better together? A mediation analysis of general practitioners' performance in multi-professional group practice

Keywords: general practitioners, medically underserved area, integrated care, France I11, I18

Ob jectives: To analyse how general practitioners (GPs) respond to insucient GP supply in their practice area in terms of quantity and quality of care, and how this response can be mediated by enrolment in integrated primary care teams (multi-professional group practices (MGP)). Methods: We used three representative cross-sectional surveys (2019-2020) of 1,209 French GPs. Using structural equations, we assumed that low GP density inuences GPs' work-related stress (mediator 1) as well as their use of e-health tools (mediator 2) and ultimately quantity and quality of care. Quantity (respectively quality) of care were approximated by demand absorption capacities (respectively frequencies of vaccine recommendations). We estimated an additional specication where enrolment in an MGP was a mediator between GP density and the two mediators dened above.

Results: GP density was signicantly and positively associated with work-related stress, which was consecutively associated with deteriorated demand absorption capacity. Higher use of e-health tools was associated with greater involvement in vaccine recommendations. Lastly, GPs in MGP tend to use more e-health tools than those practicing outside MGP, with a favourable eect on quality of care.

Discussion: This study demonstrates that a lower level of work-related stress is the key mediator in handling patients' requests. Correcting for the self-selection into MGP, we amend some unstable results contained in the literature: there is no signicant mediation eect of enrolment in integrated primary care teams on the quantity of care, but rather an eect on the quality of care. Although probably disappointing for the quantity of care provided, our results pinpoint a novel added value of enrolment in an integrated practice as a response to decreasing GP density.

Introduction

Primary care remains an important concern for the policymakers, as emphasized by the 2018 Astana declaration following the Global Conference on Primary Health Care, which celebrated the fortieth anniversary of the Declaration of Alma-Ata (WHO, 2018). Resulting from this meeting, the 2019 Global Monitoring Report on progress on universal health coverage (WHO, 2019) indicates that reorganization of care provision, and especially the improvement of primary care coordination is one of the key strategies to tackle the inequalities in access to primary care and achieve universal health coverage.

As other developed countries, France is currently facing a shortage of primary care workforce, due to mass retirement of self-employed general practitioners (GPs) that are ensuring more than 90% of primary care associated with population growth and population aging as well as lack of anticipation of this demographic evolution [START_REF] Anguis | Quelle démographie récente et à venir pour les professions médicales et pharmaceutique ? Constat et projections démographiques [What is the recent and future demography of the medical and pharmaceutical professions? Findings and demographic projections[END_REF]. According to the French Ministry of Health, the number of GPs is supposed to decline at least up to 2026. Once adjusted for healthcare demand, the 2021 GP density level should be attained once again by 2036.

In the meantime, a clear trend towards integration of primary care providers is observed: in a 2010 survey, 54% of GPs indicated practicing in a group practice; there were already 61% in 2019 [START_REF] Chaput | Plus de 80 % des médecins généralistes libéraux de moins de 50 ans exercent en groupe [More than 80% of private GPs[END_REF]. However, most of these group practices only share premises, and/or back-oce functions.

Up to now, the most advanced form of integrated healthcare teams in France is the so-called multiprofessional primary care group practice (MGP) [in French: maison de santé pluridisciplinaire]. The MGPs are created on a voluntary basis and are required to have at least two full-time equivalent GPs and one paramedic. This policy was launched in 2007 and has proven to be extremely popular among physicians: in 2020, more than 1,300 MGPs were actively operating compared to less than 20 in 2008 [START_REF] Chevillard | Medically underserved areas: are primary care teams ecient at attracting and retaining general practitioners?[END_REF].

Current literature mostly demonstrates improvements in the quantity of care provided in integrated healthcare teams, e.g., longer patient lists and more home and oce visits [START_REF] Cassou | General practitioners' income and activity: the impact of multi-professional group practice in France[END_REF][START_REF] Kerrissey | Medical Group Structural Integration May Not Ensure That Care Is Integrated, From The Patient's Perspective[END_REF][START_REF] Lalani | Understanding integrated care at the frontline using organisational learning theory: A participatory evaluation of multi-professional teams in East London[END_REF][START_REF] Mousquès | Multiprofessional Group Practices Generate Gains in Terms of Productivity and Expenditures. Results of the Evaluation of Multidisciplinary Group Practices (MGP), Health Care Networks (HCN) and Health Care Centers (HCC) Participating in Experiments with New Modes of Remuneration (ENMR)[END_REF][START_REF] Singer | Care integration within and outside health system boundaries[END_REF]. However, evidence is mixed and scarce regarding the gains related to integrated practices in terms of quality of care.

This paper contributes to this literature exploring the impact of existing variability in GPs' accessibility both on quantity and quality of care using data from a representative panel of 1,209 French private practice GPs. In addition, we sought to provide evidence on the eciency of the MGP policy by estimating the mediation eect of MGP enrolment on quantity and quality of primary care provided. To our knowledge, their continuous and valuable support throughout the data collection process. We warmly thank Alain Paraponaris, Anne-Laure Samson, Anthony Scott, Paul Frappé, Julien Mousquès, as well as the participants of the 21 st Journées Louis-André Gérard-Varet (LAGV) conference for their helpful comments.

The project leading to this publication has received funding from the French government under the "France 2030" investment plan managed by the French National Research Agency (reference: ANR-17-EURE-0020) and from Excellence Initiative of Aix-Marseille University -A*MIDEX as well as from French Institute for Public Health Research grant (reference IReSP-LIAAP18-HSR-008).

A.Z. has benetted a PhD grant from the (non-prot) Sud Provence-Alpes-Côte d'Azur regional council during the research for this article.

this is the rst study to analyse the eects of GP density on quantity and quality of primary care using mediation analysis, which allows to disentangle indirect and direct eects of GP density and the real eect of the MGP policy. To preface our results, we provide limited evidence on the eciency of the MGP policy at least the way it has been implemented in France.

Conceptual framework

We start by arguing that low GP density might hinder both the quality and the quantity of care provided.

This section presents the conceptual framework (based on relevant literature) that sheds light on the potential mechanisms, both direct and indirect, that might explain this relationship.

Extensive literature documents higher workload for GPs practicing in rural or remote areas [START_REF] Groenewegen | The primary care workforce in Europe: a cross-sectional international comparison of rural and urban areas and changes between 1993 and 2011[END_REF][START_REF] Van Hassel | Assessing the variation in workload among general practitioners in urban and rural areas: An analysis based on SMS time sampling data[END_REF][START_REF] Lurquin | Comparison of rural and urban French GPs' activity: a cross-sectional study[END_REF][START_REF] Steinhaeuser | A comparison of the workload of rural and urban primary care physicians in Germany: analysis of a questionnaire survey[END_REF]. In addition, higher workload might result in shorter consultation length [START_REF] Deveugele | Consultation length in general practice: cross sectional study in six European countries[END_REF][START_REF] Irving | International variations in primary care physician consultation time: a systematic review of 67 countries[END_REF]. Growing literature points out work-related stress as one of the important mediators of the GP productivity [START_REF] Soler | Burnout in European family doctors: the EGPRN study, Family Practice[END_REF][START_REF] Wallace | Physician wellness: a missing quality indicator[END_REF]. According to a recent French study in the Upper Normandy region, GP density below 7.75 per 10,000 inhabitants is positively correlated with all of three dimensions (emotional exhaustion, depersonalization, and personal accomplishment) of Maslach Burnout Inventory [START_REF] Picquendar | Inuence of medical shortage on GP burnout: a cross-sectional study[END_REF][START_REF] Maslach | Maslach Burnout Inventory: Third edition, in Evaluating stress: A book of resources[END_REF]. [START_REF] Wallace | Physician wellness: a missing quality indicator[END_REF] also argue that lack of GPs is one of the reasons for their professional burnout. Overall, GPs have been found to have relatively high levels of burnout: two recent literature reviews indicate that the burnout incidence is around a third among the GPs [START_REF] Karuna | Prevalence of burnout among GPs: a systematic review and meta-analysis[END_REF][START_REF] Shen | The global prevalence of burnout among general practitioners: a systematic review and meta-analysis[END_REF]. Higher levels of burnout are in turn associated with suboptimal productivity [START_REF] Shen | The global prevalence of burnout among general practitioners: a systematic review and meta-analysis[END_REF][START_REF] Wallace | Physician wellness: a missing quality indicator[END_REF]. Recent studies that took place during the Covid-19 pandemic indicate that work-related stress among healtcare professionals was entirely due to subjective factors, i.e., the perceptions of their working conditions [START_REF] Spányik | Subjective COVID-19-related work factors predict stress, burnout, and depression among healthcare workers during the COVID-19 pandemic but not objective factors[END_REF].

Empirically, practice in underserved areas is frequently associated with worse patients' health outcomes obtained from the use of primary care services, especially regarding time-consuming activities such as prevention [START_REF] Lane | Primary care physician volume and quality of care for older adults with dementia: a retrospective cohort study[END_REF][START_REF] Silhol | General Practitioners' medical practices in territories that have become subject to high-priority intervention ( Zones d'intervention prioritaire (ZIP)), Insee Analyses[END_REF][START_REF] Zyzanski | Trade-os in high-volume primary care practice[END_REF]. This is precisely the case for vaccination activity, in which GPs may play a key role in many countries.

In France, vaccination coverage remains suboptimal, especially against seasonal inuenza [START_REF] Robert | Flu vaccine coverage for recommended populations in France, Médecine et Maladies Infectieuses[END_REF] and human papillomavirus [START_REF] Eliès | Impact of catch-up human papillomavirus vaccination on cervical conization rate in a real-life population in France[END_REF], while almost half of the population is vaccinehesitant [START_REF] Larson | The State of Vaccine Condence 2016: Global Insights Through a 67-Country Survey[END_REF][START_REF] Rey | on behalf of the Baromètre santé 2016 Group, Vaccine hesitancy in the French population in 2016, and its association with vaccine uptake and perceived vaccine riskbenet balance[END_REF]. Moreover, a quarter of GPs declare that some of the recommended vaccines are not useful [START_REF] Verger | Vaccine Hesitancy Among General Practitioners and Its Determinants During Controversies: A National Cross-sectional Survey in France[END_REF].

While the evidence is mixed, expanding literature suggests that e-health solutions, e.g., use of electronic health records combined with automated reminders, might be a convenient tool to improve the vaccination rates from 5 up to 20 percentage points [START_REF] Derrough | Immunisation Information Systems useful tools for monitoring vaccination programmes in EU/EEA countries[END_REF][START_REF] Dumit | Carolina Danovaro-Holliday, The use of eHealth with immunizations: An overview of systematic reviews[END_REF][START_REF] Groom | Immunization Information Systems to Increase Vaccination Rates: A Community Guide Systematic Review[END_REF][START_REF] Vann | Patient reminder and recall interventions to improve immunization rates, The Cochrane Database of Systematic Reviews[END_REF]. For example, an US study indicates that introduction of automated reminders within the electronic health record signicantly improves the pertussis postpartum immunization rate [START_REF] Morgan | Association of a Best-Practice Alert and Prenatal Administration With Tetanus Toxoid, Reduced Diphtheria Toxoid, and Acellular Pertussis Vaccination Rates[END_REF]. Two recent literature reviews reveal greater levels of HPV vaccine initiation and completion using communication technologies, including electronic health records [START_REF] Francis | Communication technologies to improve HPV vaccination initiation and completion: A systematic review[END_REF][START_REF] Niccolai | Practice-and Community-Based Interventions to Increase Human Papillomavirus Vaccine Coverage: A Systematic Review[END_REF]. Another review [START_REF] Okoli | Interventions on health care providers to improve seasonal inuenza vaccination rates among patients: a systematic review and meta-analysis of the evidence since 2000[END_REF] pinpoints an important increase (19%) in seasonal inuenza in adult patients and a smaller, but still signicant, increase in paediatric patients associated with the use of e-health tools.

Greater use of e-health tools is also promoted to bridge inequalities in access to primary care [START_REF] Petrie | What a Pandemic Has Taught Us About the Potential for Innovation in Rural Health: Commencing an Ethnography in Canada, the United States, Sweden, and Australia[END_REF][START_REF] Wakerman | Sustainable primary health care services in rural and remote areas: Innovation and evidence[END_REF]. The implementation of e-health technologies, and especially, telemedicine has been even more encouraged since the beginning of Covid-19 pandemic, both by the patients and the health authorities [START_REF] Davin-Casalena | The impact of the COVID-19 epidemic on primary care in South-eastern France: implementation of a real-time monitoring system based on regional health insurance system data[END_REF][START_REF] Woodall | Telemedicine Services During COVID-19: Considerations for Medically Underserved Populations[END_REF]. In addition, use of e-health tools appears cost-saving due to better administrative eciency [START_REF] Patel | Economic Review of Immunization Information Systems to Increase Vaccination Rates: A Community Guide Systematic Review[END_REF].

Finally, interprofessional collaboration is supposed to deal with both the quantity and the quality of care provided. On the one hand, it is benecial to the GPs wellbeing and is supposed to reduce their workload due to better practice organization [START_REF] Kerrissey | Medical Group Structural Integration May Not Ensure That Care Is Integrated, From The Patient's Perspective[END_REF][START_REF] Singer | Care integration within and outside health system boundaries[END_REF]. On the other hand, better coordination and proximity with specialists and other health professionals allows to improve the quality of care, especially for the patients with complex needs [START_REF] Colla | Organizational integration, practice capabilities, and outcomes in clinically complex medicare beneciaries[END_REF][START_REF] Sutter | Interprofessional collaboration reduces the burden of caring for patients with mental illnesses in primary healthcare. A realist evaluation study[END_REF][START_REF] Singer | Care integration within and outside health system boundaries[END_REF][START_REF] Smith | Interventions for improving outcomes in patients with multimorbidity in primary care and community settings[END_REF]. These points suggest that the practice in an integrated care setting is an 'upstream' (opening) determinant of both the quantity and quality of care. Nonetheless, GPs might have diverse attitudes towards cooperation and prescriptions management with specialists and other health professionals [START_REF] Carrier | General practitioners' attitude towards cooperation with other health professionals in managing patients with multimorbidity and polypharmacy: A cross-sectional study[END_REF].

Following this theoretical framework, we were inclined to test the following chain of pathways (Figure 1): low density leads to (1) increase in work-related stress that inuences GPs' productivity; and (2) higher use of e-health tools that in turn aect the quality of care provided. We then add (3) enrollment in MGP as an 'opening' mediator that inuences both the other two mediators and the outcome variables. This is the theoretical framework which will be tested by using an appropriate statistical analysis (see next section). The eect of low GP density on each potential mediator is represented by paths δ 1 , γ 1 and η 1 . The eect of potential mediators on quantity and quality of care is representedby paths α 2 , β 2 , α 3 , and β 3 . The direct eect, i.e., the eect not explained by the use of mediators, of low GP density on quantity and quality of care is represented by paths α 1 and β 1 .

3 Materials and Methods

Study population

We used data from the fourth round (2018-2022) of a national panel survey of French private practice (non salaried) GPs, designed to collect information about GPs' medical behaviors, working conditions and opinions on public health policies. Participating GPs were randomly selected from a French National Registry of Health Care Workers as of January 1 st , 2018.

Sampling was stratied for gender, age (<50, 50-59, 60+), workload (annual number of oce and home visits in 2017; in terciles) and GP density of practice area (low, moderate, high). The survey is representative of GPs practicing in France (except Mayotte). GPs planning to retire or to move before the end of data collection, those exclusively practicing alternative medicine or those having less than 200 patients as a gatekeeper were excluded. Of the 12,022 eligible GPs contacted, 3,304 (27%) completed the inclusion questionnaire and undertook to answer six future cross-sectional surveys (one every nine months). The sample benets from the French public statistics label of the National Authority for Statistical Information (Conseil National de l'Information Statistique) that conrms the quality of the processes used to produce the data and their compliance with the best practices, e.g., the burden that the survey implies for the subjects and the degree of consultation with users. Second questionnaire addressed GPs' self-reported vaccine recommendation frequency (1 = never to 4 = always) in six specic vaccine situations, chosen because their current vaccination coverage rates in France do not meet ocial public health objectives: (1) measles, mumps, and rubella for non-immune adolescents (catch-up), (2) pertussis in the immediate postpartum period for new mothers who did not receive a dose prior to their pregnancy, (3) meningococcal C for 12-month-old infants, (4) human papillomavirus for children aged 1114, (5) hepatitis B for adolescents (catch-up), and (6) seasonal inuenza for adults under 65 with chronic condition.

We use a dummy variable indicating GPs reporting enrollment in MGP. GPs were also asked about their (part-time) practice of alternative medicine, e.g., homeopathy and acupuncture.

We also enriched the survey data by the French Deprivation index (FDEP) calculated at the municipality level in 2015 [START_REF] Rey | Ecological association between a deprivation index and mortality in France over the period 1997 -2001: variations with spatial scale, degree of urbanicity, age, gender and cause of death[END_REF]. 4) the median income per consumption unit. The FDEP index varies between -4 and 4: the higher the score, the greater the deprivation. We used a dummy variable to isolate the most deprived municipalities (with positive FDEP index).

Statistical analysis

For the descriptive analyses, data were weighted to match the nationwide GP population in terms of stratication variables to correct for possible systematic non-response bias.

We used conrmatory factor analysis (CFA) to construct four latent variables of interest: (1) diculties when dealing with patients' requests (demand absorption capacity, a proxy of quantity of care, DV1), (2) self-reported vaccine recommendation frequency (a proxy for quality of care, DV2), (3) work-related stress (mediator 1, M1), and (4) use of e-health tools (mediator 2, M2). Full list of variables used to construct the latent variables is presented in Tables 1 and2.

We draw on the conceptual framework described above to motivate our mediation analysis. We assumed that low GP density inuences GPs' work-related stress (M1) as well as their use of e-health tools (M2)

and ultimately the quantity of care (DV1) and the quality of care (DV2) (Model 1). We therefore estimate the following reduced-form base model (Model 1) for quantity of care (DV1) and the quality of care (DV2):

Quantity i = α 0 + α 1 Density i + α 2 Stress i + α 3 X i + ϵ i (1)
Quality i = β 0 + β 1 Density i + β 2 Ehealth i + β 3 X i + ζ i (2)
with Quantity i as the quantity of care provided by the GP i, explained by the GPs density Density i , her work-related stress Stress i and a vector of covariates X i (age, gender, deprivation index and occasional practice of complementary medicine). The specication is similar for the quality of care Quality i . We assume that the error terms ϵ i and ζ i are uncorrelated.

To estimate the indirect eects, we modify equations ( 1) and (2) as follows:

Quantity i = α 0 + α 1 Density i + α 2 Stress i (Density i ) + α 3 X i + ϵ i (3) Quality i = β 0 + β 1 Density i + β 2 Ehealth i (Density i ) + β 3 X i + ζ i (4)
We assume that the indirect eect of GP density on quantity of care (DV1) is mediated through GPs' work-related stress (M1), while the indirect eect on the quality of care (DV2) is mediated through the use of e-health tools (M2). We disentangle the direct eect from the indirect eect by total dierentiation with respect to Density i :

dQuantity i dDensity i = α 1 + ∂Quantity i ∂Stress i × ∂Stress i ∂Density i
(5)

dQuality i dDensity i = β 1 + ∂Quality i ∂Ehealth i × ∂Ehealth i ∂Density i (6)
While the left-hand side displays the total eect of equation ( 5), the right-hand side decomposes the total eect into (1) the direct eect α 1 of GP density on quantity of care, and (2) the indirect eect (in parentheses) as cross-derivatives. Equation ( 6) is the equivalent of ( 5) for the of GP density on quality of care.

The mediating factors are estimated in two additional equations below:

Stress i = δ 0 + δ 1 Density i + δ 2 X i + µ i (7) Ehealth i = γ 0 + γ 1 Density i + γ 2 X i + ν i (8)
Moreover, we estimate a second model where we consider enrollment in MGP as an opening mediator (M3) between GP density and the two mediators dened above (Model 2). Consequently, the reduced-form model is adjusted as follows:

Quantity i = α 0 + α 1 Density i + α 2 Stress i + α 3 M GP i + α 4 X i + ϵ i (9) Quality i = β 0 + β 1 Density i + β 2 Ehealth i + β 3 M GP i + β 4 X i + ζ i (10)
with M GP i acting as a mediator for the two dependendent variables. In addition, M GP i aects both the work-related stress and the use of e-health tools, so that (3) and (4) become

Quantity i = α 0 + α 1 Density i + α 2 Stress i (M GP i (Density i ), Density i ) + α 3 M GP i (Density i ) + α 4 X i + ϵ i (11) Quality i = β 0 + β 1 Density i + β 2 Ehealth i (M GP i (Density i ), Density i ) + β 3 M GP i (Density i ) + β 4 X i + ζ i (12)
so that the decomposition of the total eect is

dQuantity i dDensity i = α 1 + ∂Quantity i ∂Stress i ∂Stress i ∂M GP i × ∂M GP i ∂Density i + ∂Stress i ∂Density i + ∂Quantity i ∂M GP i × ∂M GP i ∂Density i (13) dQuality i dDensity i = β 1 + ∂Quality i ∂Ehealth i ∂Ehealth i ∂M GP i × ∂M GP i ∂Density i + ∂Ehealth i ∂Density i + ∂Quality i ∂M GP i × ∂M GP i ∂Density i (14)
Equations ( 13) and ( 14) could be also written as

dQuantity i dDensity i = α 1 + α 2 [λ × η 1 + δ 1 ] + (α 3 × η 1 ) (15)
dQuality i dDensity i = β 1 + β 2 [θ × η 1 + γ 1 ] + (β 3 × η 1 ) (16)
The mediating factors are estimated in three additional equations below:

Stress i = δ 0 + δ 1 Density i + δ 2 X i + λM GP i + µ i (17)
Ehealth i = γ 0 + γ 1 Density i + γ 2 X i + θM GP i + ν i (18) M GP i = η 0 + η 1 Density i + η 2 X i + ω i (19)
The issue of the potential endogeneity of variables (MGP in particular) due to omitted variables is addressed through the inclusion of adequate controls in the multiple-stage least squares analysis (since instrumental variables method is not recommended to deal with omitted variables, as it would require a specic instrument for each link assessed in the SEM). The risk of reverse causality is handled by the outline of the structural equation modelling [START_REF] Collier | Applied Structural Equation Modeling Using AMOS: Basic to Advanced Techniques[END_REF][START_REF] Pearl | Causality: Models, Reasoning, and Inference[END_REF][START_REF] Vanderweele | A new criterion for confounder selection[END_REF].

For example, note that in our case (Model 2) the endogeneity of practice in MGP to GP density is included in the structural modelling, with the reverse causality excluded (that practice in MGP causes GP density to decline, which is not a plausible assumption). However, we do provide the results that include covariance between practice in MGP and GP density (the causality ows both ways) as a robustness check. We also test a model that includes the eects of work-related stress on quality of care and that of use of e-health tools on quantity of care.

Model t was assessed by the root mean square error of approximation (RMSEA), the comparative t index (CFI), the Tucker-Lewis index (TLI), and the standardized root mean square residual (SRMR).

Models with CFI>0.90, TLI>0.90, RMSEA<0.08, and SRMR<0.08 were considered to t reasonably or well [START_REF] Hooper | Structural Equation Modelling: Guidelines for Determining Model Fit[END_REF].

All analyses were based on two-sided P values and conducted with Stata 14 (StataCorp, College Station, Texas).

Results

Summary statistics

Of 1,209 French GPs still enrolled in 2020, 40% of GPs were female, about a third were younger than 50 years old (Table 1). Twelve percent were enrolled in an MGP and 15% occasionally practiced complementary medicine. Twenty-one percent reported that they practiced in an area with very insucient GP density compared to 10% that were objectively practicing in an underserved area, i.e., an area where a patient could have had access to less than 2.8 consultations per year (Ministère des solidarités et de la santé, 2021). Among the 10% of GPs that were objectively practicing in an area with very insucient GP supply, only 38% had the matching perception. The proportion of those reporting to practice in an area with very insucient GP density was signicantly higher (29%) for those practicing in an MGP. More than a half (56%) were practicing in deprived areas; this proportion was signicantly higher (70%) for those enrolled in MGP.

More than four GPs out of ten reported that their working hours did not adapt well to their personal commitments or that they had to cut on training time. Seventy percent reported that they had to work longer than desired.

The vast majority of GPs declared using diverse e-health tools: 92% used electronic patient record and secure email services, and 85% used e-prescribing software. These proportions were signicantly higher for GPs enrolled in MGP (99%, 99% and 94% respectively).

Around half of GPs were able to accept new patients: 44% for consultations with enrolled patients and 57% for casual consultations (Table 2). Forty-six percent managed to maintain their waiting times compared to 32% of GPs in MGP.

Almost all GPs (92%) claimed to always or often recommend meningococcal C vaccine for 12-monthold infants (97% in MGP) and seasonal inuenza for adults with chronic conditions. More than 80% recommended measles, mumps, and rubella catch-up for adolescents, pertussis for new mothers and human papillomavirus vaccines for children aged 11-14. Two-third of GPs declared recommending hepatitis B catch-up for adolescents. Some vaccines, e.g., hepatitis B catch-up, human papillomavirus, a seasonal inuenza, were less systematically recommended by the GPs. † Pertussis in the immediate postpartum period for new mothers who did not receive a dose prior to their pregnancy.

Mediation analysis results

The results of the mediation analysis are presented in Table 3. Total standardized eects are displayed in order to compare across models.

Overall, the quantity of care delivered was negatively aected by perceived GP density as well as work-related stress. The quality of care was not signicantly aected by the GP density, while higher levels of quality were linked to greater use of e-health tools. Female GPs were likely to have lower demand absoption capacity and to recommend vaccines more often. Older GPs were more likely to absorb demand more eciently. Practice of complementary medicine was associated with lower frequency of vaccine recommendations, while greater workload had a positive impact on quality. Adding MGP as a mediator (Model 2) had no signicant impact on the outcome variables.

As for the mediating factors, low perceived GP density was associated with higher levels of work-related stress and more enrollment in MGP. Older GPs were less likely to use e-health tools and enroll in MGP.

Finally, there was a positive association between practice in a deprived area and enrollment in a MGP.

When disentangling between direct and indirect eects, in the absence of potential mediators, our results suggest that the relation between GP density and quantity of care delivered was negative and signicant (α 1 = -0.220); there was no signicant eect found on the quality of care (Figure 2). In the presence of mediators (work-related stress (M1) and use of e-health tools (M2)), GP density was signicantly and positively associated with work-related stress (δ 1 = 0.122), which was consecutively associated with a degraded demand absorption capacity (α 2 = -0.191). This sequence of correlations shows that the initial correlation between GP density and demand absorption capacity is mediated by work-related stress and this mediating eect can be quantied by the product of these coecients (δ 1 × α 2 = -0.023). Moreover, higher use of e-health tools (M2) was associated with greater vaccine recommendations frequency (β 2 = 0.317). Lastly, after the introduction of enrollment in MGP as a mediator of mediators (Figure 3), we found that GPs in MGP tended to use more e-health tools, with a favorable eect on our measure of quality of care, vaccine recommendations. However, we failed to nd any signicant improvements of practice in MGP on work-related stress. These results hold when accounting for covariance between GP density and practice in MGP as well as when we include the eects of work-related stress on quality of care and that of use of e-health tools on quantity of care.

* To the best of our knowledge, this is the rst study to analyse the underlying mediation eects behind the relationship between GP density and quantity and quality of primary care that also analyses integrated primary care teams' option as a possible response to the decreasing density.

We found that lower density is associated with lower demand absorption capacity as a proxy for quantity of care. We conrmed, at the country level, the existence of a negative relationship between GP density and work-related stress, in line with [START_REF] Picquendar | Inuence of medical shortage on GP burnout: a cross-sectional study[END_REF]. We show that lower level of work-related stress is a key mediator in handling patients' requests [START_REF] Shen | The global prevalence of burnout among general practitioners: a systematic review and meta-analysis[END_REF][START_REF] Wallace | Physician wellness: a missing quality indicator[END_REF].

As the statistical framework (using structural equations) allows correcting for the self-selection into MGP, we also amend some unstable results contained in the related literature: contrary to Cassou et al.

( Security that represent about half of French MGPs, that are subject to stricter requirements from the health authorities to receive an add-on payment. For instance, the accredited MGPs are supposed to have extended hours to ensure the continuity of care, which might explain the increase in the number of patients seen by the GP that they observe.

Even outside the French context, the nding that there is no signicant eect of an enrolment in integrated practices on absorption capacity is unusual (but not without precedent, see [START_REF] Nolte | Integration and chronic care: a review[END_REF])) The heterogeneity in conguration of the integrated practices that we have in our study might be an explanation: while MGPs require two full-time equivalent GPs and one paramedic to be recognized as such by health authorities, the size and list of professionals available at the practice might vary across the country. Therefore, the size of the integrated practices might be insucient to fully absorb the demand and/or its composition (e.g., in paramedics) might not be adapted to the characteristics of the practice area, e.g., does not consider the part of the aging population that generates more care demand. Another plausible explanation might be that once enrolled in an MGP, GPs adjust their working hours to achieve better work-life balance. Finally, it is possible that the eciency gains generated by enrolment in an MGP are not reected in quantity, but rather in quality [START_REF] Singer | Care integration within and outside health system boundaries[END_REF][START_REF] Zaytseva | United, can we be stronger? Did French general practitioners in multi-professional groups provide more chronic care follow-up during lockdown?[END_REF].

GP density indirectly aects the quality of care. As expected, more MGPs are located in underserved areas (Chevillard et al., 2019). While we do not nd a direct eect of practicing in MGP on the quality of care, we found that practicing in MGP is indirectly able to generate better quality of care. Enrolment in MGP was associated with higher use of e-health tools and, consecutively, with higher frequency of vaccine recommendations: e-health tools can be used to systematically identify unvaccinated patients in a practice and send an automated reminder to the GP when the patient visits that a vaccination is due [START_REF] Derrough | Immunisation Information Systems useful tools for monitoring vaccination programmes in EU/EEA countries[END_REF][START_REF] Dumit | Carolina Danovaro-Holliday, The use of eHealth with immunizations: An overview of systematic reviews[END_REF][START_REF] Groom | Immunization Information Systems to Increase Vaccination Rates: A Community Guide Systematic Review[END_REF][START_REF] Vann | Patient reminder and recall interventions to improve immunization rates, The Cochrane Database of Systematic Reviews[END_REF][START_REF] Morgan | Association of a Best-Practice Alert and Prenatal Administration With Tetanus Toxoid, Reduced Diphtheria Toxoid, and Acellular Pertussis Vaccination Rates[END_REF][START_REF] Niccolai | Practice-and Community-Based Interventions to Increase Human Papillomavirus Vaccine Coverage: A Systematic Review[END_REF][START_REF] Okoli | Interventions on health care providers to improve seasonal inuenza vaccination rates among patients: a systematic review and meta-analysis of the evidence since 2000[END_REF][START_REF] Rey | on behalf of the Baromètre santé 2016 Group, Vaccine hesitancy in the French population in 2016, and its association with vaccine uptake and perceived vaccine riskbenet balance[END_REF].

A limitation of our research is the use of survey data, so social desirability or conformity biases cannot be ruled out. Another limitation is that we consider only a set of three mediators (work-related stress, use of e-health tools and enrolment in an MGP), while other factors, such as consultation length or trust in institutions, may be of importance both in prevention activities and vaccination. While the choice of mediators is justied by our conceptual framework, existing literature and data availability, further studies are needed to consider a broader set of mediators and/or outcome variables related to the quality and quantity of care.

To conclude, this study shows that an enrolment in MGP as a response to a decreasing medical density, although disappointing in terms of quantity of care supplied, has the potential to improve the quality of care provided to the patients. While a previous study that investigated the performance of GPs in MGP during

Covid-19 pandemics found that GPs in MGP ensured better follow-up of patients with chronic conditions during the lockdown than those practicing outside MGP [START_REF] Zaytseva | United, can we be stronger? Did French general practitioners in multi-professional groups provide more chronic care follow-up during lockdown?[END_REF], our results strengthen the evidence of better qualitative performance of GPs when considering their regular practice styles, such as their vaccination recommendation practices. Thus, further development of integrated primary care appears benecial to the patients located in the underserved areas and even more so since one of the requirements to establish an MGP is the participation in public health, prevention, health education and social activities of their choice in their catchment area.

Figure 1 :••

 1 Figure 1: The direct and indirect eects between GP density and quantity and quality of care

  waves of the survey with data collected respectively between October 2018 and April 2019 (rst questionnaire), December 2019 and March 2020 (dummy variable described below) and October 2020 and November 2020 (second questionnaire). All the questionnaires were pilot-tested for clarity and face validity; they were collected either online or by professional interviewers using computer-assisted telephone interviews. GPs received compensation equivalent to one consultation fee (25 euros) for their participation in each survey.First questionnaire dealt with GPs' perceptions regarding the evolution of availability of medical services in their practice area. More precisely, it collected information about (1) their perception of the GP density of their practice area (from 1=very insucient to 4=completely sucient); (2) perceived diculties when dealing with patients' requests (3 items): whether they werethese diculties resulted in refusing new patients (both enrolled or casual) or increasing waiting times; (3) work-related stress (3 items): whether the working hours adapted well to their personal commitments, they worked longer than desired or cut on training time and (4) use of e-health tools (3 items): electronic patient records, e-prescribing software and secured email service. We constructed a dummy variable to isolate the GPs reporting a practice in an area with 'very insucient' GP density.

  This score was constructed by the French National Institute of Health and Medical Research (Inserm) from National Institute of Statistics and Economic Studies (Insee) data on four dimensions: (1) the unemployment rate in the active population aged 15-64; (2) the percentage of blue-collar workers in the active population aged 15-64; (3) the percentage of high school graduates in the population aged over 15 years old and (

Figure 2 :Figure 3 :••

 23 Figure 2: Unstandardized direct eects of paths of the multiple mediation model on demand absorption capacity and vaccine recommendation frequency (Model 1)

  ) we do not nd a signicant impact of enrollment in MGP on the demand absorption capacity. A dierence between their work and ours might stem from the sample of GPs that are included in both research papers. The study population of[START_REF] Cassou | General practitioners' income and activity: the impact of multi-professional group practice in France[END_REF] is restricted to MGPs accredited by Social

Table 1 :

 1 Sample characteristics, national panel of French GPs (n=1,209) GPs: general practitioners; MGP: multi-professional group practices Source: DREES, ORS and URPS Provence-Alpes-Côte d'Azur and Pays de la Loire, 4 ème Panel d'observation des pratiques et des conditions d'exercice en médecine générale de ville.

	%

* p < 0.1, ** p < 0.05, *** p < 0.01 Note: weighted data.

Table 2 :

 2 Dependent variables, national panel of French GPs (n=1,209)

	Demand absorption capacity	%		No	Yes
	Does not refuse new patients (enrolled)	Total in MGP		55.62 49.88	44.38 50.12
	Does not refuse new patients (casual)	Total in MGP		42.97 48.6	57.03 51.40
	Does not increase waiting times	Total in MGP	53.66 67.61***	46.34 32.39***
	Vaccine recommendations	%	Never Sometimes Often Always
	MMR for non-immune adolescents (catch-up)	1.42 in MGP 0.18 Total	13.80 14.81	24.90 21.30	59.89 63.71
	Pertussis postpartum †	7.73 in MGP 5.01 Total	10.76 10.81	20.05 22.27	61.46 61.90
	Meningococcal C for 12-month-old infants	1.19 in MGP 0.37*** Total	6.80 2.33***	12.17 6.03***	79.84 91.27***
	HPV for children aged 1114	3.31 in MGP 3.15 Total	14.85 7.82	42.26 41.10	39.58 47.93
	Hepatitis B for adolescents (catch-up)	1.97 in MGP 2.20 Total	23.25 21.71	37.10 39.54	37.68 36.56
	Seasonal inuenza for adults under 65 with chronic condition	0.09 in MGP 0.18 Total	6.71 5.75	37.88 40.29	55.31 53.78

* p < 0.1, ** p < 0.05, *** p < 0.01 GPs: general practitioners; MGP: multi-professional group practices; MMR: Measles, mumps, and rubella; HPV: Human papillomavirus Source: DREES, ORS and URPS Provence-Alpes-Côte d'Azur and Pays de la Loire, 4 ème Panel d'observation des pratiques et des conditions d'exercice en médecine générale de ville. Note: weighted data.

We thank our panel of GPs as well as the bureau de professions de santé of DREES, French Ministry of Health for 1

(0,062) (0,049) (0,043) (0,036) Explanatory variable Perceived GP density -0,371** -0,371*** 0,034 0,053 0,210*** 0,211*** 0,037 0,039 0,078** (0,040) (0,043) (0,035) (0,039) (0,042) (0,047) (0,035) (0,039) (0,032) Control variables Female -0,179*** -0,171*** 0,142*** 0,134*** -0,081 -0,062 -0,047 -0,053 -0,055 (0,042) (0,044) (0,038) (0,040) (0,046) (0,038) (0,047) (0,039) (0,032) Age (ref. <50 years) 50-59 0,062 0,070 -0,024 -0,023 0,005 -0,003 -0,166*** -0,155*** -0,179*** (0,042) (0,046) (0,038) (0,045) (0,046) (0,037) (0,050) (0,039) (0,033) ≥ 60 0,132*** 0,159*** -0,070 -0,064 -0,054 -0,067 -0,394*** -0,370*** -0,191*** (0,044) (0,041) (0,044) (0,036) (0,049) (0,037) (0,043) (0,036) (0,030) Complementary medicine (ref.No) 0,056 0,054 -0,087** -0,086** 0,029 0,012 -0,049 -0,050 0,022 (0,039) (0,041) (0,035) (0,037) (0,043) (0,035) (0,044) (0,037) (0,030) Deprivation index>0 -0,024 -0,038 -0,051 -0,061 -0,030 -0,016 0,078** 0,066 0,150*** (0,039) (0,048) (0,035) (0,043) (0,043) (0,035) (0,051) (0,042) (0,035) Workload (ref.Q1) Q2-Q3 -0,038 -0,037 0,061 0,064 0,085 0,095 0,073 0,077 0,054 (0,046) (0,051) (0,041) (0,043) (0,050) (0,041) (0,051) (0,044) (0,036) Q4 -0,001*** 0,016 0,146*** 0,145*** 0,216*** 0,230*** -0,012*** -0,030 -0,025 (0,049) (0,031) (0,042) (0,037) (0,051) (0,042) (0,042) (0,045) (0,085)