Calculation and Validation of a New Synthetic and Autocorrelate Index to Measure the Health Status of a Population

The status of health of an individual and - more broadly - of a community or population is dened by the status of their determinants of health. A “systemic” approach to dene the health determinants is necessary in order to explore the complex relations existing among them. This study is aimed at identifying a ‘composite systemic’ index of health to measure the impact of socioeconomic factors on public health at local level and to analyze possible spatial autocorrelations between neighboring regions. Methods A Composite Index of Health (CIH) was constructed on the basis of known indicators of socio-economic well being by using the COMIC (COMposite Indices Creator) Software and was validated on the Italian population and a nationwide comparison has been performed. approach, the simple aggregation of indicators


Abstract Background
The status of health of an individual and -more broadly -of a community or population is de ned by the status of their determinants of health. A "systemic" approach to de ne the health determinants is necessary in order to explore the complex relations existing among them. This study is aimed at identifying a 'composite systemic' index of health to measure the impact of socioeconomic factors on public health at local level and to analyze possible spatial autocorrelations between neighboring regions.

Methods
A Composite Index of Health (CIH) was constructed on the basis of known indicators of socio-economic well being by using the COMIC (COMposite Indices Creator) Software and was validated on the Italian population and a nationwide comparison has been performed.

Results
Analysis of the determinants showed a signi cant direct correlation between health, environment, work and wealth and inverse correlation between health and social distress. The analysis of data from Italian provinces con rmed the South-North gradient of well-being.

Conclusions
The CIH is a reliable and robust index to evaluate the health of a local population. Although it was validated on Italian data, the index can be easily adapted to any Country.

Background
The status of health of an individual and -more broadly -of a community or population is defined by the status of their determinants of health. Their unequal distribution is a wellknown problem of public health [1,2]. Despite clear recommendations on how to best address these inequalities, there is still a lack of clarity on how to target political interventions. This can be due, at least in part, to the imperfect knowledge of what data should be considered as health indicators and, within the known factors, the role that socioeconomic indicators play in the determination of the general status of health of a population. Several Authors have highlighted the obvious strict causal relation existing between socioeconomic factors and status of health, where inequalities of the first would lead to disparities in the latter [3]. The study of single determinants may not be considered completely reliable, so public health researchers are turning their attention towards a complex systems approach at local and national level, which can explain interlinked social and health inequalities [4,5]. Such a systemic approach may allow us to study the different components of the complex health system and to get to the bottom of their intricate relationships, while obtaining the wide picture on how the system -as a whole -works [4].
This would also prompt public health professionals and politicians to plan the right interventions to tackle disparities and inequalities at local and national level.
The present study is aimed at identifying a 'composite index of health' (CIH) to measure the impact of socioeconomic factors on public health at provincial level through the ESWB (Equitable and Sustainable Well-Being) methodology and to analyze possible spatial autocorrelations between different regional areas.
In fact, data measured in a specific area (or province) can be influenced by what happens in nearby areas, generating what is commonly called "spatial autocorrelation" or "spatial interdependence". In this regard, the LISA indicators (Local Indicator of Spatial Association) provide a local framework to the measure of autocorrelation, enabling each spatial unit (i.e., the province) to assess the degree of spatial association and similarity with the surrounding elements.
In the case of positive autocorrelation, these associations can be of the High-High type (high values observed in a territorial unit and high values also in its vicinity) or Low-Low type (low values observed in a territorial unit and low values also in its neighboring areas).
Conversely, in the case of negative self-correlation, the associations will be of the High-Low or Low-High type. In all other cases, there will be no autocorrelation or non-significant autocorrelation.

Methods
For simplicity, the CIH has been constructed on the basis of the Italian provinces but can be easily adapted to any other Country.
The method of construction of the index followed these steps: 1) analysis of the theoretical framework, methodology used and indicators; 2) choice of the statistical methodology 3) statistical analysis: in order to assess the robustness of the identi ed method and, therefore, improve decision-making, we also completed an in uence analysis to analyze the most signi cant indicators

Process to calculate the indicator
To evaluate the status of health of a community, it is necessary to identify and analyze the various determinants that affect health and, when negative, the lack of health. It is a complex set of factors relative to the individual and to their role in the society: personal factors such as gender and age, personal behavior and lifestyle, social factors, living conditions, work, access to health services, nancial status and environment.
The approach used involves the construction of macro areas (pillars) by aggregating elementary indicators. Both pillars and elementary indicators have been considered non-replaceable. To construct the synthetic CIH, we adopted the indicators and polarity considered in the 2015 document "Fair and sustainable wellbeing in towns" [7] published by ISTAT and de ned in Table 1.

Methodology
The matrix of data on Italian provinces was divided into four progressive steps: Missing values were attributed via the hot-deck imputation and, where not possible, were considered overlapping Italy's average value.
The choice of the method of synthesis is based on the assumption of a formative measurement model, in which it is believed that the elementary indicators are not replaceable, which is to say, cannot compensate each other.
The exploratory analysis of input data was performed by calculating mean, average standard deviation and frequency, as well as building up a correlation matrix and performing a principal component analysis. Since this is a non-compensatory approach, the simple aggregation of elementary indicators was carried out using the correct arithmetic average with a penalty proportional to the "horizontal" variability.
Normalization of primary indicators took place by conversion into relative indexes compared to the variation range (min-max).
Attribution of weights to each elementary indicator has followed a subjective approach, opting for the same weight for each of them. Since, in some cases, the elementary indicators showed different polarity, it was necessary to reverse the sign of negative polarities by linear transformation.
Calculation of the CIH has been performed with the Adjusted Mazziotta-Pareto Index (AMPI), which is

Strength of the obtained results
An in uence analysis was also performed to assess the robustness of the method and to verify if and with which intensity the composite index rankings change following elimination from the starting set of a primary indicator. This process allowed us also to analyze the most signi cant indicators.
The analysis was conducted with the COMIC software, that allows the calculation of synthetic indices and rankings, as well as the comparison of different synthetic methods to select the most suitable among them and write an effective report based upon results.
Approval by an Ethical Committee was not necessary as this study did not involve human participants but only widely available population data. For this reason, the principles of the Declaration of Helsinki [8] do not apply to this study. Table 2 shows signi cant correlations between the analyzed indicators of the macroareas, especially the "direct" correlations between health and environment (r = 0.81), work (r = 0.61) and material well-being (r = 0,57) and the "reverse" correlation between health and social distress (r =-0,48). The in uence analysis describes the indicators that most in uence the composition of rosters in health of Italian provinces. In Figure 1 it is evident how variables of work (s = 10.96) and health (s = 9.15) are the most signi cant.

Results
The cartographic representation of the nal CIH value, alongside with the descriptive analysis of data, yields the usual dualistic pattern South vs Center-North of Italy as in other domains of ESWB and shows how the health of the Italian population is closely related to the socio-economic components.
The best CIH performances ( Figure 2) are grouped in Tuscany (Florence, Prato and Pisa) and Lombardy (Lecco, Monza and Como), but the "healthiest" province is Trento (CIH = 111.36 -CIH for Italy = 100), thanks mainly to the cultural (123.58) and employment (117.30) indexes which in that region (Trentino) "weigh" more than the more strictly sanitary variables. Frosinone (Lazio) occupies the last position in the ranking list (CIH = 83.22), even though it is the whole South to be heavily penalized (55% of the provinces below the average belong to the South of Italy).
Our results show a good spatial interaction between neighbouring provinces (Moran's index = 0.39) ( Figure 3). This is particularly true in the South, where is a de nite positive autocorrelation between 12 provinces, with low values observed in a province and low values in the surrounding areas (Low-Low Blue Color) (Figure 4).

Discussion And Conclusions
The 'composite index of health' (CIH) combines statistical rigor with high level of communicability and is useful to facilitate comparison and analysis of the status of health of a population at local and national level. However, in-depth studies need the analysis of single indicators.
The evident North-South CIH gradient is a further demonstration of the well-known social, cultural and nancial disparities within the Country. Despite being quite autonomous social and political entities, neighbouring provinces often share the same cultural background in particular in the South. It is therefore possible to identify spatial patterns able to describe areas of "multidirectional dependence", where contiguous areas show similar levels of the same phenomenon.
Improving the general status of health of the population would entail tackling the disparities by means of "upstream" changes directed to change the social-environmental determinants of health rather than health itself [3], although an improvement of local healthcare system would also act as a driver to increase the social wellbeing and would back up the improvement of the other indicators.
The governance framework to the global determinants of health should have a "systemic" and conjoined approach involving all the stakeholders and all the national and local policies [3]. Improving the determinants of health would be of great advantage not only to the individuals but also, we may say "mostly", to the society in terms of improved productivity, increased tax revenue and lower welfare and healthcare costs [9]. The UK Marmot Report clearly identi ed six objectives of the political choices: (a) improving the health of children, (b) maximizing each person capabilities, at every age, (c) creating good work environments, (d) ensuring healthy lifestyles, (e) improving the status of the environment, (f) creating policies and procedure for medical prevention.
Clearly, reaching these objectives would require a thorough knowledge of the determinants of health within the society and within each layer of it.
The CIH would be useful to have an idea of the general status of health as determined by social and nancial factors and to guide government actions on non-health issues which may yield positive health outcomes.
In conclusion, the CIH is a good indicator of the status of health of a population at local and national level and may be extremely useful to explore the relations between health and socioeconomic factors and also to evaluate the in uence of proximity with high or low-performing regions on the health of citizens of a speci c region or province. Although hereby validated on the Italian population, the CIH can be easily generalised to any Country.

Declarations
Ethics approval and consent to participate: Approval by an Ethical Committee was not necessary as this study did not involve human participants but only widely available population data. For this reason, the principles of the Declaration of Helsinki [8] do not apply to this study. Furthermore, as this study did not involve any patient, informed consent was not necessary.

Consent for publication: not applicable
Competing interests: the Authors declare that they have no competing interest to disclose.
Funding: no funding was available for this manuscript Authors' contributions: Both DT and GT conceived and planned this study; DT retrieved and analysed the data; GT reviewed the analysis of data; both DT and GT discussed the data, drafted the manuscript and approved its nal version. Both DM and GT are equally accountable for this paper.  In uence Analysis: of the shifts for basis indicator of macro areas Moran's Index.

Figure 4
Spatial autocorrelation -LISA Cluster map Index. (in square brackets the number of provinces)