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

Background : Optimal healthcare access improves people's health status and decreases health inequalities. Many studies demonstrated spatial access importance in health outcomes. Recent studies assessed spatial healthcare access using the enhanced two-step floating catchment area (E2SFCA) method. The study aim was to build a hospital facility access indicator at a fine geographic scale and to assess the impact of spatial accessibility to inpatient hospital care and non-hospital care services on the length of hospital stay (LOS). Methods : This study focused on the ≥75 -year-old population of the Nord administrative region of France. Hospital spatial accessibility was computed with the E2SFCA method, and then the LOS score was calculated from the French national hospital activity and patient discharge database. Linear regression models were used to analyze the relationship between LOS and spatial accessibility to inpatient hospital care and to three types of non-hospital care services (general practitioners, physiotherapists, and home-visiting nurses). Results : Overall, there were 19.0 beds in Medical, Surgical and Obstetrics (MCO) facilities and 5.58 beds in Postoperative and Rehabilitation Care facilities (SSR) per 10,000 inhabitants, but with important geographic variations. Accessibility to hospital services was 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. The linear regression analysis revealed a strong negative and significant association between LOS and non-hospital care accessibility. Conclusions : This is the first study to measure spatial accessibility to inpatient hospital care in France using the E2SFCA method, and the first to investigate the relationship between healthcare utilization (LOS) and spatial accessibility to inpatient hospital care facilities and three types of non-hospital care services. Our findings should help to take decisions about deploying additional beds and to identify the best locations for non-hospital care services. Moreover, they should also help to improve access, and to ensure the best coordination and sustainability of inpatient and outpatient services, in order to better cover the population’s healthcare needs. Other international studies using multiple consensual indicators of healthcare outcomes and accessibility and sophisticated modeling methods should be developed.

in many countries, including developing countries [22,23], because it ensures an effective and generally faster service that covers the large majority of personal healthcare needs [24], and acts as the principal point of continuing care for patients [25]. Nevertheless, hospitals remain one of the key healthcare actors. Inpatient care provided by hospitals represents a major part of people's consumption of healthcare and medical goods, especially in Europe.
In 2017, nine of the ten countries with the highest hospital discharge rates worldwide were European Union member states [26]. Coordination and organization between inpatient hospital care and primary care are critical for a successful healthcare system. This is particularly true during pandemic situations when hospitals may reach a point of "complete saturation" due to increased patients' influx. In these situations, non-hospital resources, as the most significant primary care contributor, might anticipate and limit the number of hospitalizations and the consumption of hospital-linked resources [27,28]. A consolidated spatial organization of non-hospital medical services in the territory can complement hospital services and increase healthcare efficiency [29]. Therefore, it is essential to assess accessibility to non-hospital care and inpatient hospital care, and also to examine whether there is interactions between them [30]. However, much of the recent research on geographic healthcare access has focused on assessing the potential access to healthcare services, rather than on their utilization [31,32]. However, to address the variety of demands by patients, providers and policy makers, it is necessary to measure the potential access to and also the utilization of health services. Furthermore, healthcare utilization is linked to interactions between accessibility to non-hospital and inpatient hospital care. For instance, the length of hospital stay, one of the classical indicators of healthcare utilization, is associated with primary care supply. Kjekshus

Study setting and population
This study was carried out in the Nord administrative region that is located in the north of France, with a surface area of 5743 km 2 and a population density of 456 inhabitants per km 2 .
Moreover, it has been shown that edge effects lead to minor accessibility variations in this area [39]. The study focused on the ≥75-year-old population of this area.

Data sources and statistical unit
Multiple data sources were combined for the present study: (1) The accessibility to non-hospital care was described using the Localized Potential Accessibility (Accessibilité potentielle localisée: APL) database [40]; Based on the E2SFCA method, APL indices are available at national level but only for eight types of self-employed practitioners: general practitioners, physiotherapists, homevisiting nurses, gynecologists, dental surgeons, midwives, pediatricians, and ophthalmologists. For this study, the APL indices for general practitioners, physiotherapists, and home-visiting nurses were used because these three types of health professionals could contribute substantially to the primary care services to older adults. Furthermore, the healthcare provided by them might interact with inpatient hospital care.
(2) The number of available beds in each hospital was extracted from the Annual Statistical Survey of Healthcare Facilities 2014 database (Statistique Annuelle des Établissements: SAE) [41]. Facilities were classified in two categories: Medical, relationship between LOS and spatial accessibility to inpatient hospital care and also to the three types of non-hospital care services (general practitioners, physiotherapists, and homevisiting nurses). The final variables included in the model for further analysis and the categories of facilities for which they are available are shown in Table 1. 2.3.1. Assessing hospital care spatial accessibility using the E2SFCA method The hospital facility access indicator was built using the enhanced two-step floating catchment area (E2SFCA) method, one of the most widely used gravity-based approaches.
Based on this method, two different spatial indicators were constructed in France: the localized potential accessibility score developed by the French Research Institute in Health Economic institute (IRDES) at the municipality level in 2011 [36], and at the census block level for the Greater Paris area in 2019 [37]. In 2016, the index of spatial accessibility (ISA) at the census block level was implemented by Gao and al. [38]. However, one common limitation of these studies was the focus on non-hospital care services only. So far, no French indicator based on the E2SFCA method has measured the access to hospital care at a very fine geographic scale.
The E2SFCA method [49] was implemented in two steps, as follows: Step1: For each hospital center j with a MCO or SSR facility, the number of beds in the MCO or SSR facility was counted and the population living in the FGC area k and located within a threshold drive time from the hospital center j (i.e. catchment area j) was estimated.
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 catchment area j (i.e. dkj < dmax), Sj is the number of beds available in the hospital center j, and dkj is the driving time between the FGC area k and the hospital center j and w() is a weighted decay function that depends on the driving time dkj.
Step 2: For each population location i, all MCO or SSR facility locations j that were within the threshold driving time dmax from location i (i.e. catchment area i) were estimated, and all Rk for the catchment area were summed to calculate the Index of Spatial Accessibility (Ai) at location i (Equation 2): where Rj is the bed-to-population ratio of the hospital center j, and dij is the driving time between the FGC area i and the hospital center j.
All driving times from i to j were obtained using Google Maps and then computed by SAS version 9.3 [50]. The E2SFCA accessibility score was calculated with the MYSQL program. The definition of the decay function w() and time thresholds were previously explained [38].
Briefly, when the travel time to a MCO and to a SSR facility was longer than 41 and 69 minutes, respectively, that hospital was considered too distant to be accessible. These distance decay parameters were used as cut-off distances to define the catchment areas.
The spatial accessibility index obtained with the E2SFCA method is a special form of physician-to-population ratio, expressed as the number (N) of beds per 10, 000 inhabitants.
Higher scores indicate higher accessibility.

Measuring health service utilization using the LOS indicator
The LOS was defined as the mean hospital stay length of elderly people (≥75 years of age) relative to the total ≥75-year-old population in a given FCG ( assess the accessibility to non-hospital services. In summary, equations (1) and (2)  accessibility and accessibility to the three non-hospital services. Equation (5) is a variation of (5) equation (4)  were observed in urban areas located in the northern part of the studied territory, close to Dunkerque, and also in the center, around Lille, Roubaix and Tourcoing. Conversely, the lowest values were observed mostly in the southern part and around Hazebrouck. The highest [ISA_SSR]_hospital values ([6.05; 7.14] and [7.14; 9]) were concentrated in the middle part of the region, whereas access was lower in the north and south. These findings showed that accessibility to hospital services is higher for people in large urban areas, despite the dense population and consequently the higher demand.

Elderly population and [LOS]_non-hospital spatial distribution
The elderly population was not homogeneously distributed over the studied territory. The

Comparison with the international literature
Previous studies have paid attention to healthcare spatial accessibility and the question of whether healthcare activity could be rebalanced by expanding/strengthening the role of primary care relative to the more costly hospital (secondary) care. Most studies that focused on the use of primary care to reduce specialty/inpatient care were observational studies in which the rates of preventable hospitalizations were correlated with the self-rated access level [52] or distance [53,54] to primary care services [55]. Few studies quantified both hospital and non-hospital care spatial accessibility with the E2SFCA method, and investigated their association with the length of hospital stay. The present study fills this gap by integrating three factors: spatial accessibility (1) to inpatient hospital care facilities and (2) to three types of non-hospital care (general practitioners, physiotherapists, and home-visiting nurses), and (3) length of hospital stays. As few studies have considered all three with a similar study design, comparison with the international literature was difficult. However, we could find few studies that investigated one or two of these aspects. First, although this is the first French study measuring hospital spatial accessibility using the E2SFCA method, other countries, for instance China [56] and Japan [57], already developed hospital accessibility scores following a similar approach. Second, other studies estimated the LOS to assess how primary care could contribute to reduce the demand of secondary care. In France, a study used the LOS for public-sector psychiatric facilities to investigate whether the development of alternatives to full-time hospitalization (such as ambulatory care, part-time hospitalization, and full-time outpatient care) may reduce the LOS [21]. They found a significant negative association and concluded that their study was the first to provide nation-wide evidence of the benefits of alternatives to full-time hospitalization in psychiatry.
Similarly, our study is the first to show that non-hospital care services may reduce the length of stay in MCO and SSR facilities. Our findings and those of this study in psychiatry suggest that in some cases, non-hospital care services may constitute an alternative to hospitalization. Our results were obtained by modeling the association between healthcare utilization and accessibility to two types of healthcare services. These preliminary quantitative results should be supplemented by data on other healthcare outcomes frequently associated with the quality of care, such as unplanned readmission or mortality, as well as other aspects of accessibility (e.g. multiple consensual indicators of spatial/nonspatial healthcare access). Additional studies using sophisticated modeling methods should also be developed. The goal is to develop a consolidated approach to facilitate the spatial organization of non-hospital medical services in the territory with the aim of complementing hospital services and increasing healthcare efficiency.

Limitations
As we used aggregated data at the FGC scale to assess associations between spatial accessibility to hospital and to three types of non-hospital care services and healthcare utilization, our findings may be subject to an ecological bias [38].        LOS for Post-operative and Rehabilitation Care (SSR) centers