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 identified method and, therefore, improve decision-making, we also completed an influence analysis to analyze the most significant indicators (software COMIC - COMposite Indices Creator by Italian National Institute of Statistics – ISTAT)
4) analysis of the results with the help of a georeferenced map of the CIH of Italian provinces and a Cluster Map LISA which shows the provinces with statistically significant values of the LISA index, classified in five categories: a) Not significant (white); b) High-High (red); c) Low-Low (blue); d) Low-High (light blue); e) High-Low (light red) (software GeoDa v.1.12).
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, financial 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”  published by ISTAT and defined in Table 1.
The matrix of data on Italian provinces was divided into four progressive steps:
a) Selection of a set of basic indicators on the basis of an ad hoc evaluation model centred on the existence of quality requirements;
b) Further selection aimed at balancing the set of indicators within the theoretical framework of the structure. Outcome indicators are impact indicators as the ultimate result of an action of a stakeholder’s activity or process;
c) Calculation of synthetic indices (pillars), by making use of the more appropriate methodology to obtain usable analytical information on the health of Italian provinces;
d) Processing of a final synthetic index as a rapid empirical reference concerning the degree of health of Italian provinces.
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 used for the min-max standardization of elementary indicators, and aggregated with the mathematical average penalized by the “horizontal” variability of the indicators themselves. In practice, the compensatory effect of the arithmetic mean (average effect) is corrected by adding a factor to the average (penalty coefficient) which depends on the variability of the normalized values of each unit (horizontal variability), or by the variability of the indicators compared to the values of reference used for the normalization.
The synthetic index of the i-th unit, which varies between 70 and 130, is obtained by applying, with negative penalty, the correct version of the penalty method for variation coefficient (AMPI +/-), where: 𝐴𝑀𝑃𝐼𝑖-=𝑀𝑟𝑖- 𝑆𝑟𝑖𝑐𝑣𝑖.
𝑀𝑟𝑖 e 𝑆𝑟𝑖 are, respectively, the arithmetic mean and the standard deviation of the normalized values of the indicators of the i unit, and 𝑐𝑣𝑖= 𝑆𝑟𝑖 / 𝑀𝑟𝑖 is the coefficient of variation of the normalized values of the indicators of the i unit.
The correction factor is a direct function of the variation coefficient of the normalized values of the indicators for each unit and, having the same arithmetic mean, it is possible to penalize units that have an increased imbalance between the indicators, pushing down the index value (the lower the index value, the lower the level of health).
This method satisfies all requirements for the wellbeing synthesis:
- Spatial and temporal comparison
- Irreplaceability of elementary indicators
- Simplicity and transparency of computation
- Immediate use and interpretation of the obtained results
- Strength of the obtained results
An influence 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 significant 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  do not apply to this study.