InterCriteria Analysis applied to data from Euro Health Consumer Index for comparing the healthcare systems’ performance in time

Euro Health Consumer Index provides assessments for consumer services satisfaction of national healthcare systems. The healthcare rankings for the years 2014, 2015, 2016 and 2018 are observed. Intercriteria analysis is applied over the healthcare datasets for providing comparison to the Euro Health Consumer Index in the years. Summarized application over the healthcare rankings using the Aggregated ICA method is presented. Thereafter the results of Intercriteria analysis for consumer satisfaction from healthcare systems in the years 2014, 2015, 2016 and 2018 are discussed separately.


Introduction
The Health Consumer Powerhouse (HCP) published Euro health consumer index reports for investigating the consumer-related healthcare in Europe. Euro health consumer index datasets present measurements for the performance of national healthcare systems by evaluating accessibility, patient rights and information, treatment results, range and reach of services, prevention score and pharmaceutical use. The healthcare rankings evaluate the health systems of 35 countries by 6 sub-disciplines. The countries are the following: The 6 sub-disciplines in Euro Health Consumer Index have the following form: 1) Patient rights and information score; 2) Accessibility (waiting times for treatment) score; 3) Outcomes score; 4) Range and reach of services score; 5) Prevention score; 6) Pharmaceuticals score.
The sub-disciplines are based on 46 indicators evaluated by the three grade scale: green score, amber score and red score representing the states for good score-3 points, immediate score-2 points and not good score-1 point. The country score of sub-disciplines is calculated as a percentage of the maximum possible. Thereafter, the sub-discipline scores were multiplied by the weight coefficients. The methodology is presented in [10][11][12][13]15].
InterCriteria analysis (ICA) [5,6,8] is based on the theories of intuitionistic fuzzy sets [4,7] and index matrices [3]. The aim of the selected method is to investigate the possible relationships between the object according to the selected criteria. Pairwise comparison of pairs of values in the input matrix is made. Two counters are incrementing depending on the type of the relation: "<" or ">". Thereafter the degree of membership and the degree of non-membership are calculated. The steps of the procedure of applying the InterCriteria Analysis are described in [6]. The results are determined according the following scale ( Figure 1): Figure 1. Scale for determination of the type of the correlations between the criteria ICA is successfully applied in investigations from different science topics: evaluating of university rankings [18,19], neural networks preprocessing procedure [21], genetic algorithms [16,20], the global competitiveness reports [9], chemical research [24,25] and etc. In [26] an application of the ICA approach to data connected with health-related quality of life was presented. Health-related quality of life has been used in medicine and public health as a reliable outcome measure and a needs assessment frame [1,2,22,27]. In [23] the ICA method is applied for studying some statistical data for registered patients with oncological diseases for 2018 in Burgas.
2 Application of the InterCriteria Analysis to healthcare rankings for comparing the healthcare systems performance in time The first application of the Intercriteria analysis over the Euro Health Consumer Index determines relationships between the countries according to the sub-disciplines for 2018 [14]. In the current paper this investigation is continued. The Intercireria analysis is applied consequently for the years 2015, 2016 and 2018 to determine possible patterns for consumer satisfaction of the services provided by the national healthcare systems in countries. The process of discovering unseen dependencies in procedure of providing consumer services from the national healthcare systems in the countries can be helpful for their clustering. The healthcare rankings for the years 2015, 2016 and 2018 are visualized in the Fig. 2 by radar diagrams. The patient rights and information score is presented by dark blue. Outcomes score is denoted by green line. Range and reach of services score is presented by purple color. Prevention score is colored in light blue. Pharmaceuticals score is visualized by yellow/orange line.  The Aggregated InterCriteria analysis is used to investigate the three-dimensional input healthcare dataset. The method applies Stardard Intercriteria analysis over the four input tables for the years 2014, 2015, 2016, 2018. Therafter the aggregation at each value is calculated. The result includes aggregated matrix with degrees of membership and aggregated matrix with degrees of non-memberships. The application of ICA over Euro health consumer index is processed using ICrAData software [17]. The results from the Aggregated InterCriteria analysis appled to the three-dimensional dataset for healthcare systems have the following form ( Table 1):   pairs of countries in dissonance. The received outcomes from Aggregated InterCriteria analysis are visualized in the intuitionistic fuzzy triangle (Fig.4). Pink points present the pairs of countries in dissonance and weak dissonance. Green points vizualize the pairs of countries in strong positive consonance, positive consonance and weak positive consonance.

Investigating of the healthcare rankings in the years
In the current section the comparison between the national healthcare systems of the countries in the years is investigated. The aim is to observe the possible trends of dependencies or independencies between the countries in the selected years. The results of Intercriteria analysis applied to the datasets from healthcare rankings are presented in the Table 2. The pair of countries with strong dependencies in their national healthcare systems performance for 3 years is "Switzerland-Portugal". The pairs of countries in strong positive consonance for 2 years have the following form:

Results
The results from the application of aggregated InterCriteria Analysis over three-dimensional representation of the healthcare rankings are investigated. The comparison between the countries is made. The following conclusions are obtained:

Results about national healthcare system of Slovakia
The outcomes for Slovakia from the application of Aggregated InterCriteria analysis over threedimensional healthcare dataset have the following form. Portugal -Slovakia. The consumer service of national healthcare system of Slovakia is the most similar to the national healthcare systems of Switzerland, Austria and Portugal. The most independent behavior according to the investigated sub-disciplines is found between the national healthcare systems of Slovakia and Ireland.
Via the comparison of the results over the period of research (2018, 2016, 2015) the following outcomes are obtained:  The pairs of countries "Switzerland-Portugal" has been in strong positive consonance for three years. The relationships between the countries are strong. The countries Switzerland and Portugal have dependencies in their healthcare systems providing consumer services.  16 pairs of countries have been in strong positive consonance for 2 years. The behaviour of these national healthcare systems is stable with respect to the process of providing consumer services in time.
 The pairs of countries "Sweden-Ireland" is the most independent one over the years. This pair of countries appears two years in strong dissonance. The national healthcare systems functioning in these countries are different.

Conclusion
The InterCriteria Analysis is used to find some hidden patterns in the data from Euro Health Consumer Index. Ratings of European healthcare systems are compiled over the years. The data is analyzed to identify the best correlations between the countries, to discover dependent and independent countries and the relationships between them. The comparison can help describing the behaviour of the analysed countries and their assessment. In the next research, the authors will analyze the indicators of sub-disciplines individually. In the future research works, the authors will analyze the dependencies in Euro health index and Euro diabetes index.