Introduction: In an attempt to assess the effect of supply of care on care consumption, we studied patients with similar needs. We analyzed care consumptions of patients who benefited from a hip or knee arthroplasty in France. According to WHO \citep{BIBTEXIDa} , 9.6% of men and 18.0% of women aged over 60 years have symptomatic osteoarthritis worldwide. Additionally, 80% of those with osteoarthritis experience limitations in movement, and 25% cannot perform their major daily activities of life requiring an arthroplasty. It is a common and cost-effective procedure \cite{Bozic_2009}. However there are variations in the uptake \citep{Kurtz_2011} and cost of services for knee arthroplasty in high-income countries. Annually, it is estimated that 290,000 hip and knee prostheses are being implanted in France \citep{Astagneau_2009}. Post-operatively, patients may develop complications which might retard their recovery and increase healthcare utilisation \citep{Khan_2006}.The high demand for arthroplasty and incidence of complications especially in the first three months post-operatively may increase the substitutability of healthcare consumption. The decrease in hospital length of stay is likely to contribute to patients continuously seeking care from rehabilitation centres for long durations or when discharged home, increases in ambulatory healthcare consumption for longer periods would be observed. Post-surgery health care consumption in form of physiotherapy rehabilitation is critical as it maximises functionality and minimises the risk of complications \citep{Bitar_2005}. Although physiotherapy rehabilitation is essential, the need for this service increases for females, older age, high level of co-morbidity, patients with long acute care length of stay and those with poor pre-operative functioning capacity \citep{Wang_2016}. We therefore have a sample of patients with a similar level of needs. Where some would consume more of a certain type of health care because of a larger supply of that health care, we will conclude of an effect of supply on consumption. More interestingly, we focus on cases where there might be some complementarity or substitutability of health care supply. Literature has shown that where there is more supply of health care, there is more consumption  \citep{cook_role_2013,stange_how_2014}. For example, \citet{stange_how_2014} shows that where states allow more autonomy to Nurse Practitioners (NP) and Physician Assistants (PA), an increase in the supply of these professionals causes an increase in the use of primary care services. Where there are hard to reach populations increases in supply may benefit the former \cite{kovandzic_access_2011}. Ambulatory care access is associated to more use \citep{buja_out--hours_2015} and better health \cite{fichera_how_2016,villalbi_evaluation_1999}. Where access to screening is widened, more population is reached, giving another illustration of the role of supply in increasing consumption \citep{odesanmi_comparative_2013,andersen_effectiveness_2001}.In France, some of the consumption of health care is linked to patients complementary insurance cover; The latter covers out-of-pocket payment. At the hospital,some of the out-of-pocket payment are the accommodation daily fixed rate. In consequence, length of stay of patients may depend on the type of complementary cover patients may have. Hospital supply of care, in France, is provided by three hospital types. Public; for profit; not for profit. \citet{Weeks_2014} have shown that, overall, there is no induced demand from hospitals. In this paper, we focus on the follow-up care after hospital surgery in an ambulatory setting. We are interested in whether, different types of supply influence consumption of health care and which supplies complement or substitute each other. MethodsA retrospective study was conducted on the relationship between health care supply and health care consumption within 90 days after hip or knee arthroplasty (HKA).PopulationHealth care consumptions were extracted from the permanent beneficiaries sample of the whole French National Health Insurance Cross-Schemes Information System (NHI-CIS), the so-called EGB for Echantillon Généraliste des Bénéficiaires. EGB is a representative cross-sectional sample of the population covered by National Health Insurance, which has monitored beneficiaries’ health care consumption over a period of 20 years since 2004 \citep{Tuppin_2010}. It was created using a systematic sampling method (1/97) on the two-digit control key of beneficiaries’ national identification number and is composed of around 660,000 individuals. Health care consumptions included hospital discharge record of the arthroplasties and post-discharge ambulatory care data.Elderly patients (>60 years old) who underwent hip or knee arthroplasty between Jan 1st 2011 and Dec 31st 2011 were included based on surgical procedures identified in the hospital discharge record by a hierarchical, structured, fine-grained, multiaxial procedure nomenclature, namely the French Classification Commune Des Actes Medicaux (CCAM or Common Classification of Medical Procedures) \citep{Trombert_Paviot_2003}. The codes for hip or knee arthroplasty are: NEKA010, NEKA011, NEKA012, NEKA013, NEKA014, NEKA015, NEKA016, NEKA017, NEKA018, NEKA019, NEKA020, NEKA021, NFKA006, NFKA007, NFKA008, NFKA009, NFMA013. Patients who died after the surgery (n=13) were removed. For comparison purposes, only patients discharged to home or rehabilitation centre after an hospital length of stay under10 days were included. In total, care consumptions data of 855 patients were analyzed.Health care consumption dataHospital discharge data included the following covariates: age, gender, primary and secondary diagnosis, surgery procedures, length of stay, discharge mode. Length of stay (LOS) was categorized into 2 classes [0-9[ days and  [9-16[ days. Charlson’s comorbidity index \citep*{Charlson_1987} was computed from the primary and secondary diagnosis. Patients re-hospitalized within 90 days with primary or secondary diagnosis enlisted as possibly associated with a surgical complication were identified. Surgical site infections were detected using a specific algorithm validated by  \citet{Grammatico_Guillon_2014} and \citet{Le_Meur_2016}. Re-hospitalization for pain, mechanical complication, hematoma, thrombosis or pulmonary embolism were estimated using ad hoc algorithms based on primary or secondary diagnosis and associated surgical procedures (See Supplementary Material for details).Ambulatory care consumptions included information on outpatient visits and pharmacy purchases of prescribed medications. The outcome variables were the number of visits to a general practitioner (GP), the number of visits to or by a nurse, the number of visits to a physiotherapist, and the number of visits to a osteoarthritis specialist (i.e., rheumatologist or an orthopedist surgeon). The number of osteoarthritis drugs (i.e., analgesics, anti-inflammatory and anti-rheumatism drugs, topics for articular or muscular pain) purchased per patient within the 90 days’ post-discharge were computed. This variable was used as a covariate for the nurse and physiotherapist models only to assess a potential substitution mechanism.Health care supply dataHospital characteristics were extracted from the Annual Statistics of Healthcare Establishments (SAE) website \cite{Drees2018a} for the year 2011. The collected information were the number of beds for Medicine, Surgery, Obstetric, Long Stays, Psychiatry, Very Long Stays and the number of places for Hospitalization at Home, the number of private or public health care establishments. Ambulatory care supplies were extracted for the year 2011 from the website of La Direction de la Recherche des Etudes Evaluation et Statistiques \cite{Drees2018}. The collected variables were the density of health care professionals calculated using a Two-Step Floating Catchment Area (2SFCA) adapted to French ambulatory care \cite{Barlet_2012,Wang2005}. The care professionals of interest were the GP, physiotherapists, specialists (total of dentists, ophtalmologists, psychiatrists), and nurses. Thus we have direct supply of GPs, physiotherapists and nurses but we proxy the density of osteoarthritis specialist by other type of specialists. Socio-economic dataSocio-economic data was extracted for the year 2011 from the National Institute of Statistics and Economic Studies (INSEE) website \cite{Insee2018}. The variables collected were the 15 to 64 years old population size, the proportion of unemployed, the proportion of the population with higher education, the proportion of blue collars, and the proportion of elderly leaving alone. Average income level per household was obtained from the Direction Générale des finances \cite{Dgfip2018}. Statistical analysisFor this study, we stratified our population into two groups: the patients discharged home (n=407) and the patients discharged to rehabilitation centre (n=448). Patients’ characteristics from the two groups were compared using a logistic regression.  A p-value threshold of 5% was applied for significant differences.Negative binomial models were applied to each group of patients to assess the association between the outcome variables and the covariates listed above. Automatic stepwise approaches were used to compute the most informative models. Quantitative variables were scaled by their standard deviation to facilitate the interpretation. For instance, when modeling the number of visits to GPs, an observed coefficient X for a covariate will mean that for a variation of 1 standard deviation of this covariate the number of visits to the GP will increase by X visits \citep*{cameron_regression_2013}.All data management and statistical analyses were performed using the R statistical software (version 3.3.0).ResultsPatients’ characteristics All other variables being equal, patients discharge to rehabilitation centres are, on average, older than those discharge home (Table 1). In addition,  a female is more likely to be transferred to a rehabilitation centre. However, the comorbidity status and the length of stay for arthroplasty surgery does not differ between home and rehabilitation centre discharge.Table 1. Characteristics of the patients who benefited from a hip or knee arthroplasty in 2011, in France, and were discharged home or to a rehabilitation centre. Sources: EGB