Potential hospital care accessibility scores: association with 1 healthcare utilization and non-hospital care service accessibility

1 Background : Optimal healthcare access improves people's health status and 2 decreases health inequalities. Many studies demonstrated spatial access importance in 3 health outcomes. Recent studies assessed spatial healthcare access using the enhanced two- 4 step floating catchment area (E2SFCA) method. The aim of this study was to build a hospital 5 facility access indicator at a fine geographic scale and to determine whether there is a 6 complementarity between non-hospital and hospital care accessibility by investigating the 7 length of hospital stays (LOS). 8 9 Methods : This study focused on the ≥75-year-old population of the Nord 10 administrative region of France. Hospital spatial accessibility was computed with the E2SFCA 11 method, and then the LOS score was calculated from the French national hospital activity 12 and patient discharge database. Linear regression models were used to analyze the 13 relationship between LOS and spatial accessibility to hospital-based care and to the three 14 types of non-hospital care services (general practitioners, physiotherapists, and home- 15 visiting nurses). 16 17 Results : Overall, there were 19.0 beds in Medical, Surgical and Obstetrics (MCO) 18 facilities and 5.58 beds in Postoperative and Rehabilitation Care facilities (SSR) per 10,000 19 inhabitants, but with important geographic variations. Accessibility to hospital services was 20 higher for people in large urban areas, despite the dense population and the higher demand. In 2014, the mean LOS scores were 0.26 for MCO and 0.85 for SSR, with a non-homogeneous geographical repartition. Linear regression analysis revealed a strong negative and significant 23 association between hospital and non-hospital care accessibility. 1 Conclusions : This is the first study to measure spatial accessibility to hospital-based cares in 2 France using the E2SFCA method, and the first to investigate the relationship between 3 spatial accessibility to hospital-based care facilities and three types of non-hospital care 4 services and healthcare utilization (LOS). Our findings should help to take decisions about 5 deploying additional beds and to identify the best locations for non-hospital care services. 6 Moreover, they should also help to improve access, and to ensure the best coordination and 7 sustainability of inpatient and outpatient services, in order to better cover the population’s 8 healthcare needs. Other international studies using multiple consensual indicators of 9 healthcare outcomes and accessibility and sophisticated modeling methods should be 10 developed. 11 13 our suggest and non-hospital in a way. on policy and areas new research approaches to understand the underlying mechanisms and processes that explain the interaction between hospital-based and non-hospital care services with the ultimate objective of better organizing and allocating medical resources. This research should help to take decisions about deploying additional beds and identifying the best locations for non-hospital care services, and also to improve access, to ensure the best coordination and to contribute to the sustainability of inpatient care and outpatient services, in order to better the health needs of the population.

9 a threshold drive time from the hospital center j (i.e. catchment area j) was estimated.
1 Then, the bed-to-population ratio within the catchment area j was determined with where Pk is the patient population in the FGC area k the centroid of which falls within the 5 catchment area j (i.e. dkj < dmax), Sj is the number of beds available in the hospital center j, 6 and dkj is the driving time between the FGC area k and the hospital center j, and w() is a 7 weighted decay function that depends on the driving time dkj.

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Step 2: For each population location i, all MCO or SSR facility locations j that were within the Equation (2) where Rj is the bed-to-population ratio of the hospital center j, and dij is the driving time 14 between the FGC area i and the hospital center j.

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All driving times from i to j were obtained using Google Maps and then computed by SAS 17 version 9. 3 [45]. The E2SFCA accessibility score was calculated with the MYSQL program. The 18 definition of the decay function w() and time thresholds were previously explained [32].

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Briefly, when the travel time to a MCO and to a SSR facility was longer than 41 and 69 20 minutes, respectively, that hospital was considered too distant to be accessible. These 1 distance decay parameters were used as cut-off distances to define the catchment areas. The LOS was defined as the mean hospital stay length of elderly people (≥75 years of age) 5 relative to the total ≥75-year-old population in a given FCG (Equation 3). In this equation, 6 g represents the three groups of ≥75-year-old people (75-84, 85-94 and >95 years), and Pg 7 the corresponding total population for that age group. The numerator represents the 8 average length of stay of each age group, standardized to the total population for that age 9 group (inpatients or not) in the denominator.  respectively. Almost 25% of the population had access to fewer than 10 beds in MCO and 4 1 beds in SSR. located in the northern part of the studied territory, close to Dunkerque, and also in the 10 center, around Lille, Roubaix and Tourcoing. Conversely, the lowest values were observed 11 mostly in the southern part and around Hazebrouck. The highest ISA scores for SSR ([6.05; 12 7.14] and [7.14; 9]) were concentrated in the middle part of the region, whereas access was 13 lower in the north and south. These findings showed that accessibility to hospital services is 14 higher for people in large urban areas, despite the dense population and consequently the 15 higher demand. 16 17

Elderly population and LOS spatial distribution 18
The elderly population was not homogeneously distributed over the studied territory. The around Tourcoing, Roubaix, Lille and Orchies, LOS scores were lower. This suggests the 9 existence of spatial dependencies in LOS distribution within the studied territory. This 10 hypothesis was confirmed with the Moran test (p-value = 0.000 for both MCO and SSR LOS 11 scores). 12 13

Determinants of MCO and SSR LOS 14
To investigate the determinants of MCO and SSR LOS scores separately, two independent 15 least square regression models were implemented at the FGC scale, including the covariates 16 presented in the Data sources section. The LOS variable was log transformed to normalize its 17 distribution. 18

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The three APL variables were based on the activity level of these self-employed general 20 practitioners and on the healthcare utilization rates in function of the inhabitant age group 21 in order to estimate more precisely the healthcare supply and demand in a given territory. A 22 composite APL was integrated in the Linear Regression Model to better describe the overall 23 non-hospital care service accessibility. This analysis revealed a strong negative and 24 significant association between the composite APL and the MCO and SSR LOS (Table 3). 25 Furthermore, the MCO ISA showed that LOS were shorter for patients living in areas where 1 people had easier access to a MCO facility. To our knowledge, the present study is the first one to investigate the relationship between 8 spatial accessibility to hospital-based care facilities (ISA index) and to three types of non-9 hospital care services (APL index for general practitioners, physiotherapists, and home-10 visiting nurses) and healthcare utilization based on a national hospital database (LOS). One 11 of its main strengths is the cross-referencing of different data sources that allowed us to 12 address several major public health issues.  Conversely, although no MCO facility was located in or close to Bailleul, the ISA value for this 7 area was quite high. This finding is coherent with the fact that the ISA index provides a 8 summary measure of two important and related components of accessibility: the volume of 9 services available relative to the population size, and the proximity of services available 10 relative to the population location. Therefore, although 400 MCO beds were located close to 11 Valenciennes, the population's size was too important to obtain a high accessibility score. 12 13 Then, we examined the association between the healthcare utilization indicator (LOS) and 14 two accessibility scores (ISA and APL). Our analysis revealed a significant and negative 15 association between LOS and spatial accessibility to the three non-hospital care services 16 (general practitioners, physiotherapists, and home-visiting nurses). In other words, a better 17 accessibility to these non-hospital services corresponded to shorter hospital stays. This similar study design, comparison with the international literature was difficult. However, we 20 could find few studies that investigated one or two of these aspects. First, although this is 21 the first French study measuring hospital spatial accessibility using the E2SFCA method, 22 other countries, for instance China [52] and Japan [44], already developed hospital 23 accessibility scores following a similar approach. Second, other studies estimated the LOS to 24 assess how primary care could contribute to reduce the demand of secondary care. In 1 France, a study used the LOS for public-sector psychiatric facilities to investigate whether the 2 development of alternatives to full-time hospitalization (such as ambulatory care, part-time 3 hospitalization, and full-time outpatient care) may reduce the LOS [15]. They found a 4 significant negative association and concluded that their study was the first to provide 5 nation-wide evidence of the benefits of alternatives to full-time hospitalization in psychiatry. 6 Similarly, our study is the first to show that non-hospital care services may reduce the MCO 7 and SSR LOS. Our findings and those of this study in psychiatry suggest that in some cases, 8 non-hospital care services may constitute an alternative to hospitalization. Our results were 9 obtained by modeling the association between healthcare utilization and accessibility to two 10 types of healthcare services. These preliminary quantitative results should be supplemented 11 by data on other healthcare outcomes frequently associated with the quality of care, such as 12 unplanned readmission or mortality, as well as other aspects of accessibility (e.g. multiple 13 consensual indicators of spatial/non-spatial healthcare access). Additional studies using 14 sophisticated modeling methods should also be developed. The goal is to develop a 15 consolidated approach to facilitate the spatial organization of non-hospital medical services 16 in the territory with the aim of complementing hospital services and increasing healthcare 17 efficiency. 18 19

Limitations 20
As we used aggregated data at the FGC scale to assess associations between spatial 21 accessibility to hospital and to three types of non-hospital care services and healthcare 22 utilization, our findings may be subject to an ecological bias [32]. In addition, as previously 23 explained, while the ISA index was estimated at the census block scale, the two other 24 indicators (LOS and APL) were only available at the FGC scale, a cruder spatial scale. Thus, we 1 could not take into account the spatial accessibility heterogeneity at the census block scale. 2 For future research, we want to construct a LOS indicator at a finer scale using 3 disaggregation techniques that take into account the population density. 4

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In our analysis, we did not use statistical techniques that consider spatial autocorrelation. 6 However, at the FGC scale, the Moran's indicator revealed the presence of spatial 7 autocorrelation for both MCO and SSR LOS. To investigate more precisely the association of 8 healthcare accessibility and utilization, the next step could be to consider the specificity of 9 the study area by including its topological, geometric and geographic properties using spatial

CONCLUSION 18
This is the first study to measure spatial accessibility to MCO and SSR facilities in France 19 using the E2SFCA method and to investigate the relationship between spatial accessibility to 20 hospital-based care facilities and to non-hospital care services. It provides a basic 21 understanding of the status of inpatient care within the studied area by showing the 22 accessibility score variation across the territory and highlighting some areas with poor 23 accessibility. This type of information is important to guide policy makers and local 24 managers. Moreover, our findings suggest that hospital-based and non-hospital care services 1 (general practitioners, physiotherapists, and home-visiting nurses) interact in a 2 complementary way. Based on this research, policy makers and local managers could 3 identify areas where additional beds or healthcare professionals should be allocated in 4 priority.

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Additional studies in other areas characterized by their own specificity have to be developed 7 in order to confirm our results. It is also crucial to design new research approaches to 8 understand the underlying mechanisms and processes that explain the interaction between 9 hospital-based and non-hospital care services with the ultimate objective of better 10 organizing and allocating medical resources. This research should help to take decisions 11 about deploying additional beds and identifying the best locations for non-hospital care 12 services, and also to improve access, to ensure the best coordination and to contribute to 13 the sustainability of inpatient care and outpatient services, in order to better cover the 14 health needs of the population. All data generated or analyzed during this study are included in this published article. If 13 readers need supplementary information, they can contact me (fei.gao@ehesp.fr). 14 15

COMPETING INTERESTS 16
The authors declare that they have no competing interests.