Applying an Extended Kernel Density 4-Step Floating Catchment Area Method to Identify Priority Districts to Promote New Publicly Financed Supply of Gastroenterology Exams

In continental Portugal, the publicly financed supply of gastroenterology exams was limited since the end of the last century, restricted to a fixed set of private providers that was hired by the Portuguese state. This way of contracting created market entry barriers and is inefficient, since prices are administratively set. Besides, it produced access inequalities, because of the way that the supply was geographically distributed. This paper applies the Extended Kernel Density 4-Step Floating Catchment Area (EKD4SFCA) method to identify priority districts for the promotion of new supply by the state, in order to choose the appropriate way of contracting new private supply, as determined by current law, and to reduce access inequalities. The applied method enables the identification of the Portuguese regions with strong competition between health care providers and where patients’ access to publicly financed gastroenterology exams is relatively low. In these regions, the state should promote public bids to stimulate new supply, exploring thereby the potential for setting lower prices and reducing access inequalities.


Introduction
The EKD4SFCA method provides a combined analysis of competition and access by incorporating the Herfindahl-Hirschman Index (HHI) and a market dominance identification technique in the Extended Kernel Density 2-Step Floating Catchment Area (EKD2SFCA) method (Polzin et al., 2014(Polzin et al., , 2016)).
As far as competition analysis is concerned, an innovation of the EKD4SFCA method is the adaptation and extension of the HHI index and of the dominance identification method of Melnik et al. (2008) for their application with small geographic units of analysis, a distance decay function and catchment areas.This way, fine-resolution results are obtained, which provide detailed information that can be useful for public policies in Portugal to manage financing of private health care provision in accordance with the legislation.Actually, since 2013, after Decree-Law 139/2013 came into effect, public financing of diagnostic exams carried out by private health care providers in continental Portugal became dependent on a prior appraisal of the existing competitive situation in health care markets.In competitive geographic markets, public bids have to be promoted to explore competition and attain lower prices.In other regions, free adhesion contracts can be signed, which may facilitate entry of new providers into concentrated markets.This paper presents an application of the EKD4SFCA method to identify priority districts for the promotion of new supply of gastroenterology exams by the state, in order to choose the appropriate way of contracting private supply, as determined by law, and to reduce existing access inequalities.
It has been acknowledged that the populations have been facing problems in obtaining colonoscopies in Portugal that lead to insufficient diagnosis and treatment of gastrointestinal diseases.If new supply capacity is not promoted, a heightening of the number of deaths due to malignant neoplasms of colon, rectum and anus should be expected, as the illustrated forecasts from 2014 until 2025 indicate in Figure 1.(Note 1)

Method
The EKD4 which are analysis.where HHI i E is the extended HHI calculated for the geographic unit i, and G refers to groups of supply points, namely the firms or economic groups that own the supply points (G=1 is the largest group, G=2 is the second largest group, and so on, until the smallest group competing in the market i, namely G=N).The expression inside the square brackets in equation ( 1) refers to the market share of group G with supply points located at l that have catchments covering i, and g(d il ,d max ) is a distance decay function, while d max is the travel time that defines the boundaries of the catchment areas.This way of calculating the HHI makes it possible to identify in a detailed way the competitive pressure between firms in each of the small geographic areas of a study region, taking into account the potential flows of the populations from their residences to the supply points.
While the HHI is applied at the industry level, the dominance identification method of Melnik et al. (2008) is applied at the firm level.It is a competition assessment method that enables the identification of market dominance by considering how existing competition limits the ability of a firm to dominate the market.It considers the market shares of all competing firms in an industry to calculate a dominance threshold.If the firm with the largest market share has a greater share than the dominance threshold, then it has a dominant position (Hellmer & Wårell, 2009;Melnik et al., 2008).
As proposed by Knoche &Thöni (2011) andMcIntosh &Hellmer (2012), this method complements any competition assessment that is initiated with the HHI.However, it presents the same four problems of the original HHI, namely problems (i) to (iv) identified above.In order to alleviate these problems, the extended version of the method uses catchment areas, small geographic assessment units and a distance decay function, as it is described by equation ( 2): (2) which is the extended calculation of the dominance threshold for the geographic unit i.The variables, the distance decay function and d max are the same ones as in equation ( 1), of the extended HHI.

Access Assessment Method
As remarked before, we adopt the EKD2SFCA method to analyze access.This method uses floating catchment areas and computes access scores for small geographic units (Polzin et al., 2014).In 2SFCA-based methods like the EKD2SFCA, the catchment areas are floating areas, because the computation of the scores depends on catchment areas centered on the centroids of each of the small geographic units of the study region.All scores are thus computed by a window that is moved across the study region (Luo & Wang, 2003;Yang et al., 2006).This is also the logic behind the extended versions of the HHI and the dominance identification method presented in the previous section.The floating catchment areas make it possible to compute HHI degrees and dominance thresholds for all small geographic units of a study region.Equation (3) summarizes the two steps of the EKD2SFCA: (3) Where is the computed overall access score of the population that resides in the geographic unit i, S l is the supply capacity of the supply point georeferenced at l, measured as the number of physicians or beds, for instance, P k is the population of the geographic unit georeferenced at k, H k is the health needs score of the population at k, d kl is the travel time between k and l, and d max is the maximum travel time that defines the size of the catchment areas.Finally, the distance decay function is represented by g(d kl ,d max ) and g(d il ,d max ), and C i refers to the commuting score of the population at i computed with representative variables of the mobility of the populations when accessing health care.
The distance decay function used in equations ( 1), ( 2) and ( 3) is the quartic function, which is applied only after an initial catchment d init until d max : The initial catchment d init is used as proposed by McGrail & Humphreys (2009, 2009, 2009), Schuurman et al. (2010) and Polzin et al. (2014Polzin et al. ( , 2016)), assuming that travel times below a predetermined threshold do not present any sensible proximity impediment to utilization.

Results
The competition analysis presented in the next section is based on an application of the extended versions of the HHI and the dominance identification technique.Table 1 presents the distribution of private facilities or supply points that provide gastroenterology exams across the 18 districts and in the whole continent of Portugal, namely the numbers with contract for publicly financed provision and total (with and without contract).(Note 2) It also shows the number of firms that own supply points in each of the districts and continent.The total number of firms of continental Portugal is not equal to the sum of the firms with supply points in the districts, because there are firms competing in more than one district.We also note that of the 502 firms competing in the continent, only 147 of them have contract for the provision of publicly financed gastroenterology exams.The distribution of supply points across the districts in quartiles is illustrated in Figure 2.

Compe
The extend are applied geographic competitio free adhesion contracts directed to new providers would be best to promote competition.In the other districts, the state could promote public bids to better manage public financing, aiming to explore competition and attain lower prices.

Access Analysis
Now, after obtaining the competition assessment results, it is possible to apply the full EKD4SFCA method and complement the analysis with an access analysis.Accordingly, in this section we produce access scores with the EKD2SFCA method presented in equation ( 3) to obtain aggregate results for the 18 districts of continental Portugal.We consider only access to the existing publicly financed private providers, in which patients pay at maximum relatively low user fees.By restricting analysis to these providers, we can identify access inequalities due to an uneven distribution of the publicly financed supply capacity to satisfy demand.
As in the case of the competition assessment, we also use floating catchment areas of 30 minutes travel time for the computation of the access scores, and the initial catchment of 10 minutes for the application of the quartic distance decay function.
For the health needs index in equation ( 3) we used five variables, namely death by malignant tumors per population, the inverse of purchasing power per capita, percentage of illiterate population, percentage of population over 65 years old, and number of inpatients treated in public hospitals per 1,000 inhabitants, with data from the 278 municipalities of continental Portugal.(Note 5) Thus, we produced 278 health needs scores, and to each postcode area we attributed the health needs score of its correspondent municipality.
The commuting index was constructed with the following variables: employed or student population that uses primarily car, bus, train or metropolitan in commuting as a proportion of the population, average travel time in commuting (minutes), population that works or studies in another municipality as a proportion of total population, and employed or student population with commuting of over 60 minutes as a proportion of total population.
The two indices are first component indices constructed with principal components analysis (PCA), as explained by Polzin et al. (2014Polzin et al. ( , 2016)), following the methodology described by Henry et al. (2003), Salmond et al. (2006) and Mooi & Sarstedt (2011).The relevant sets of variables were chosen with an iterative approach, following the Kaiser criterion and observing the specific criteria for the Kaiser-Meyer-Olkin (KMO) statistic, the Bartlett's Test of Sphericity, the communalities, and the percentage of the total variance attributed to the first component.Table 3 summarizes the complete process.
Table 3. Constructing an index with the first component of PCA After calculating the scores we apply cluster analysis for the identification of three clusters with a k-means algorithm, as in Polzin et al. (2014), and define the low access populations as the ones in the regions with scores grouped in the lowest cluster, and also the ones that cannot access publicly financed supply points in 30 minutes or less.Table 4 summarizes the results for the postcode areas, while Figure 4 illustrates the aggregated results for the districts, according to predominance in terms of affected populations.

Table 1 .
Number of private supply points and firms

Table 4 .
Distribution of the access scores across the three access levels