Assessments and developments in constructing a National Health Index for policy making, in the United Kingdom

We first note that $\mathcal{X}$ is missing data, which needs to be imputed. Missing data was of two types: either an indicator value for a given year is completely missing for all UTLAs (see Table 2 in SM), or missing only in a subset of UTLAs. Briefly, if an indicator value for only one year was available, such as for ‘access to green space’, the values were imputed to be constant across all four years. If an indicator value is missing for a given year but available before/after, then the value was the average of the years either side of the missing year. If an indicator value is missing and only the year before or after was available then the value would be imputed with that of the closest year. Full details of the data imputation are provided in the supplementary material.

Once the missing data has been imputed, the completed tensor $\mathcal{X}=(x_{cit})$ is decomposed into $|I|=58$ flattened data sets, $\boldsymbol{X}_{i}=\{x_{cit}:c\in C,t\in T\}$ for each $i\in I$. Using the data transformations $f_{i}$ listed in Supplementary Table 3 for each indicator, $i$, the raw indicator data is transformed to $\boldsymbol{Y}_{i}=\{y_{cit}=f_{i}(x_{cit}):c\in C,t\in T\}$. The assignment of each transformation, $f_{i}$, to an indicator, $i$, is selected to minimise the absolute values of skewness and kurtosis of $\boldsymbol{Y}_{i}$, aiming for absolute skewness $\leq 2$ and absolute kurtosis $\leq 3.5$. By minimising (absolute) skewness and kurtosis, we aim to ensure that the transformed data $\boldsymbol{Y}_{i}$ is approximately normally distributed. For 18 indicators, the skewness and kurtosis of $\boldsymbol{X}_{i}$ were optimal, 40 indicators have been transformed and of these 18 have been log-transformed (see Table 3 in SM).

The normalization step in the ONS Health Index accounts for time and geography, and allows indicators to be compared on the same scale, weighting by the UTLA populations. The normalization transforms elements $y_{cit}$ of $\mathcal{Y}$ into z-scores,

which then define the elements of the tensor $\mathcal{Z}=(z_{cit})$. For each indicator, $i$, we specify $\delta_{i}=0$ or $\delta_{i}=1$ to ensure that larger positive values for $z_{cit}$ correspond to improved health, a property which we term as being health directed. Note that the mean and standard deviation $\mu_{i}$ and $\sigma_{i}$ for each indicator, $i$, are taken to be the population-weighted mean and standard deviation of $y_{cit}$ for the chosen baseline year across UTLAs $c\in C$, fixing $t=2015$. Finally, given the $z$-scores $z_{cit}$ forming the tensor $\mathcal{Z}$, the ONS Health Index presents the $z$-scores as Health Index values,

which are translated and rescaled $z$-scores, such that $h_{cit}=100$ means that the transformed value, $y_{cit}$, for indicator $i$ in the UTLA $c$ in year $t$ is equal to the weighted mean, $\mu_{i}$.

The ONS has chosen to compute weights using a time-series factor analysis. The fundamental assumption of factor analysis is that there is a latent factor that underpins the variables in a group. This translates to this level of the Health Index: ONS assumed that there is a single unobserved variable that underpins the indicators within each subdomain. Highly correlated indicators within each subdomain could lead to double counting in the index, so factor analysis directly addresses this issue, accounting for the correlation between indicators in their implied weights DL (13).

To maintain the same weights for all the years considered (2015-18) a time-series factor analysis was applied. The rationale was to ensure that, by accounting for all the years jointly, they would change with each additional year of data. As such, the weights would need to be calculated for a set time period, e.g. 2015 to 2019, and these weights would be held constant until a review date. This assured that (i) the indicators selected matched the underlying factor (subdomains) over time; (ii) and then the factor loadings were scaled and used as data-driven weights.

In practice, from the normalized data $\mathcal{Z}_{CT}=(z_{ct})$ are collapsed by year and then rescaled to (0,1), next given $d\in D$, a factor analysis on the indicators $i\in d$ was carried out and the weights were chosen as the first loading factor, taken in absolute value. The weights $w_{i}$ for indicators $i\in I$ are chosen by running factor analysis for each subdomain, $d\in D$, in turn, allowing for one factor estimated using a maximum likelihood method. For example, for a subdomain $d=\{i_{1},i_{2}\}$ comprised of two indicators, suppose the factor loadings are 0.5 and 0.75. We would then set the weights $w_{i_{1}}=0.4$ and $w_{i_{2}}=0.6$. In supplementary material, we address the weights constraints taking into account the different aggregation levels.

The final step is the arithmetic aggregation of the index, where there are equal weights for subdomains $w_{s}$ and domains $w_{d}$, while indicator weights are derived from a factor analysis. All the weights have been chosen as positive and summing to one, for all the different aggregation levels. The Health Index, at the hierarchical levels of indicators, subdomains, domains and overall, is then computed for each year at geographical levels of UTLAs, regions and the nation, where the geographical aggregations at the regional and national levels are population-weighted.

For the year 2015, for each UTLA, we plot each domain’s Health Index values, ordering the UTLAs by the overall Health Index ranking, in Figure 2. It emerges that Lincolnshire, Leeds and Staffordshire have all three domain index values concentrated at the same values. In contrast, Westminster (the UTLA with the largest difference in domain indexes) presents Healthy People at 109, similar to Kensington and Chelsea, but Healthy Places at 82. Westminster and Blackpool present similar values for Healthy Places and Healthy People, but their ranking is significantly different. It is interesting to note that Healthy Lives sits within the range defined by Healthy Places and Healthy People. Similar patterns are observed for the following years, as reported in the SM (see Figures 5-7).

Before investigating the HI and carrying out further analysis: correlation and sensitivity/robustness analysis, we implemented a slight change to the original HI as presented above. As pointed out in C⁺ (08), a certain coherence in the methods needs to be preserved to create a statistically sound index. This change was done to avoid statistical misinterpretation, as not all the potential combinations of data transformation and subsequent data operations could be properly interpreted, as carried out in the ONS version.

Hence, we have computed a modified ONS HI version. We begin from the imputed matrices $\boldsymbol{X}_{i}$ for each indicator, $i$. Then, instead of directly selecting and applying transformations $f_{i}$ to ensure normality, we accounted for kurtosis and skewness using winsorization first and then by transforming. This approach resulted in only 5-7 variables per year that have been log-transformed (Table 4 in SM). We proceed to standardize using a z-score (following the ONS), and then aggregated with arithmetic mean and equal weights (see Table 5 in SM for comparison ).

We opted for less strict data transformation, as this would have not changed the aggregation formula interpretation. As it stands at the moment, the ONS data transformations included 40 indicators, with 18 indicators log-transformed. By aggregating all transformed variables using an arithmetic mean, the untransformed variables are effectively aggregated via a mix between a geometric mean (for log-transformed variables) and arithmetic mean (for other variables). As succinctly summarised by NSST (05), “when the weighted variables in a linear aggregation are expressed in logarithms, this is equivalent to the geometric aggregation of the variables without logarithms. The ratio between two weights indicates the percentage improvement in one indicator that would compensate for a one percentage point decline in another indicator. This transformation leads to attributing higher weight for a one unit improvement starting from a low level of performance, compared to an identical improvement starting from a high level of performance.”

We used this modified version as the starting point for the rest of this paper. The z-scores (see Figure 2 in SM) comparison between this modified version and the original ONS shows that several indicators have more outliers below the 25^th percentile, but overall, there are no major discrepancies in values. Indeed, this modified version generated a different ranking, that affected the UTLAs in the middle, while the top and bottom UTLAs remain unaffected (see Table 4 in SM). The biggest shift in ranking is observed for Barking and Dagenham (which moved positively 49 positions), whereas Westminster, Herefordshire and Shropshire all shifted down the rankings by, respectively, 50, 48 and 51 positions. Overall 52% of the UTLAs shifted in absolute value of within 10 ranking positions, 38% shifted between 20–30 positions and only 9% shifted more than 31 positions. Only Blackpool, Kingston upon Hull, City of Northampton and Hertfordshire kept the same ranking in comparison to the original ONS HI version. All the analysis was conducted on R version 4.2R C (22) and COINr package W (21), by Becker.

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  We suggest to adopt winsorization, as it takes care of the outliers and provides a robust approach to ensure that kurtosis and skewness are within the acceptable limits, without heavy mathematical data transformations. This also preserves the statistical coherence at aggregation level and interpretation.

We used our modified version of the Health Index to carry out a correlation analysis (Pearson) at the different levels of aggregation. The correlation analysis provides insights on the potential redundancy of those indicators with high correlation ($\rho\geq 0.9$); negative correlation ($\rho\leq-0.4$) also indicates some conceptual problems. Acceptable correlation values are for weak ($0.3<\rho\leq 0.4$) and moderate ($0.3\leq\rho<0.9$). The ideal situation would be to have indicators positively correlated among them ( 0.3- 0.9), and not highly correlated with other subdomains as this could impact weights and aggregation. In Figure 3, indicators grouped in subdomains are showing overall positive correlations. However, there are some correlations of concern. For example, public and private green space that define the subdomain ’Access to green space (Pl.1)’ show negative correlations, and in subdomain ’Access to services (Pl.4)’ distance to the nearest pharmacy and general practitioner (GP) are also highly correlated. We suspected that this could be somehow related to the urban/rural UTLA definition. Cardiovascular and respiratory prevalence are highly correlated in subdomain ’Physical health conditions (Pe.2)’. The indicators in ’Behavioural risk factors (Li.2)’ and ’Working conditions (Li.4)’ present negative and weak correlations. In this heatmap, we see also correlation among the subdomains like blocks. For example ’Risk factors for children(Li.5)’ and ’Children and young’s people education (Li.6)’ are also correlated, likewise ’Physical health conditions (Pe.2)’ and ’Difficulties in daily life (Pe.3)’.

From the subdomain correlation map (see Figure 4), we immediately see that the indicator ’Household overcrowding’ is highly correlated with the subdomains on ’Local environment (Pl.2)’. Finally, we correlated ( see Figure 3 in SM) subdomains versus domains, we found that People subdomains are overall well correlated with the other subdomains within their domain. Lives and Places are similar but present some weak correlations: ’Access to services (Pl.4)’, and ’Unemployment (L1.3)’ and ’Difficulties in daily life (Pe.3)’. This confirms what we have observed in the indicators heatmap.

The panels in Figure 5 show the scatter-plots for the three domains. It can be observed that Healthy Lives and Healthy People have a high Pearson correlation ($\rho$= 0.65), while for Healthy Lives and Healthy Places ($\rho$= -0.12) and Healthy People and Healthy Places ($\rho$= -0.39) the correlations are negative, a similar situation as described for the SSI by SP (12). Once we removed London’s UTLAs, characterized by high values of People and Lives and low on Places, the correlation for Lives and People increases ($\rho$= 0.72), null for Lives and Places ($\rho$= -0.06) and diminishes in People and Places ($\rho$= -0.25).

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  We suggest to remove the public and private green space indicators due to the high negative correlation.

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  A revision of the indicators defining ’Behavioural risk factors’. Physical activity is correlated with alcohol misuse and smoking and not with healthy eating, which is correlated with drug use. The subdomain should be split and re-organized. Drug misuse and healthy eating are pointing toward unemployment and in general to a some measure on society inequality.

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  Subdomains ’Risk factors for children’ and ’Children and young people’s education’ could be merged in a unique block, as the indicators are highly correlated.

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  Cardiovascular, respiratory and hypertension could be combined as they are highly correlated, therefore bringing redundancy.

In standard practice JRC ; MN (05), the composite indicator for time $t$ is defined as:

where $c$ indexes the indicators and $C$ is a set of indicators being composed (which, in the context of the ONS HI, may correspond to subdomains, domains, or the overall index). Thus the composite indicator is a weighted linear aggregation, where weights are (typically) constrained to sum to 1.

In the composite index literature GITT (19), weights methods are often found to be linear, geometric or multi criteria, or classified into compensatory and non-compensatory approaches. However, the major difference in weight systems boils down to defining weights either as coefficients that address the importance of a variable (indicator/subdomains/domains) or as a trade-off coefficient.

Weights that convey ‘importance’ should be used in aggregation formulae that do not allow for compensability; that is, where poor performance in some indicators can be compensated by sufficiently high values of other indicators. These definitions are also known as compensatory, because the ‘compensation’ refers to a willingness to allow high performance on one variable (subdomain/domain) to compensate for low performance on another. The weighted mean (arithmetic/geometric) is a classic example of compensatory approach, where the weight is a de facto trade-off coefficient.

Non-compensatory methods allow the weights to express ‘importance’, where the greatest weight is placed on the most important ‘dimension’ Vin (92); Van (90). These approaches have their roots in social choice theory (also known as multicriteria) and more details can be found in M⁺ (08). Briefly, in this framework, indicator (subdomain/domain) values rank the countries in different ways and contributed to define the relative performance of each country/option with respect to each of the other countries/option. This indicators-unit ranking, generates an impact matrix and a voting system must be put in place to define the overall ranking. For example the ‘plurality vote’ will rank as first the unit (UTLA) that has ranked at first place on the majority of the indicators. However, this approach comes with the price of dealing with preferences and choices on how to select the final ranking given the indicators-ranking M⁺ (08). Two popular approaches, that take the name after their authors, suggest that a Condorcet approach is necessary when weights are to be understood as importance coefficients, while a Borda approach is desirable when weights are meaningful in the form of trade-offs.

These methods, while valuable, are rather harder to implement as they require an expert panel to grade the indicators in first place, but also lack the immediate facility to explain when compared with a weighted mean. The dual notions of weighting as importance versus weighting as trade-off and their interpretation requires more consideration, to assure that selected weights are in line with the practitioner preferences. In their article, Munda and Nardo MN (09, 05) provide extensive commentary on an interesting mis-interpretation around the weights/aggregation combination that gets buried in the CI construction, but is useful to address here.

According to the OECD guidelines Fre (03): “Greater weight should be given to components which are considered to be more significant in the context of the particular composite”. As pointed out by Greco et al. GITT (19), the popular linear aggregation weights are used as if they were importance coefficients, while they are in fact trade-off coefficients.

Briefly, the authors MN (05, 09) state that in linear and geometric aggregation the weights play the role of a trade-off ratio that depends on the scale of measurement. If the weight has to be interpreted as a measure of importance, then the weights should be connected with the indicators themselves and not with their quantification; they should be invariant to the units of the indicator. This distinction between weights as trade-off ratio versus importance does not disappear even when all indicators are on the same scale. For a weight to express ‘importance’, then non-compensablity should be enforced. This issue becomes relevant when CI are composed of different data for multicriteria optimization where improvement in one domain cannot compensate for degradation in another. One way to disentangle this paradox of trade-off weights interpreted as importance weights is proposed by Becker BSPV (17). In order to derive weights as ‘explicit importance’, we need to evaluate the correlation structure and use it to understand the ‘importance’ role of the domains/ subdomains in the composite indicators, and what the influence of each indicator is on the index, generating optimized weights.

For a weighting system where weights are representing ‘explicit importance’, then different variances and correlations among indicators (subdomains/domains) mask the weights to represent importance, as shown above in the correlation analysis.

To find weights that reflect importance and not trade-off ratios, conditioned on the correlations, we follow the methods introduced by Becker BSPV (17). We recall that for the Health Index, domains and subdomains have equal weights, while indicators have data-driven weights derived by FA. If we take the equal weights choice as a way to express equal importance of the three domains, we need to account for each variable’s influence on the output, and how weights can be assigned to reflect the desired importance, ‘conditioned’ on the existing shared information among the domains. Knowing the correlation among domains can help to reduce uncertainty, as strong correlations suggest that the domains should be treated jointly, rather than individually. This can help in reassessing the weights.

A measure of importance, capturing the dependence between the CI and the effect of domains, starts from analysing the correlations ratio $S_{d}$, also known as the first order sensitivity index or main effect. We split the correlation ratio in two parts: a correlated part, $S_{d}^{c}$, and uncorrelated part, $S_{d}^{u}$, such that

where $d=1,2,3$ indicates the level of aggregation.

A large value for $S_{d}$, with a relatively low uncorrelated part $S_{d}^{u}$ such that $S_{d}\approx S_{d}^{c}$, indicates that the domain contribution to the index variance is only due to the correlation with the other domains MT (12). However, if $S_{d}^{c}$ is negative, this implies conceptual problems with one of the domains, and is not a desirable feature in composite indicators.

The optimized weights have been presented in Becker et al. BSPV (17). It is important to note that, while we have applied this approach at the domain level, the same methodology can be applied to other levels of the hierarchical structure of the Health Index, i.e. for aggregating indicators into subdomains and subdomains into domains. Briefly, first we estimate $S_{d}$ and $S_{d}^{u}$ by implementing a series of linear and non-linear regressions (using splines Woo (01)). The steps to compute the two summands of the correlation ratio, are the following:

1. 1.

   Estimate $S_{i}$ using a nonlinear regression approach

2. 2.

   Perform a regression of $x_{d}$ on $x_{\sim d}$. This can be either linear (using multivariate linear regression), or nonlinear (using a multivariate Gaussian process). Denote this fitted regression as $\hat{x}_{d}$.

3. 3.

   Get the residuals of this regression, $\hat{z}_{d}=x_{d}-\hat{x}_{d}$.

4. 4.

   Estimate $S_{d}^{u}$ by a nonlinear regression of $y$ on $\hat{z}_{d}$, using the same approach as in step (a).

5. 5.

   The correlated part then is the simple expression $S_{d}^{c}=S_{d}-S_{d}^{u}$

Using a simple numerical approach, the weights are estimated that result in the desired importance, using an optimisation algorithm. If $\tilde{S}_{d}=\frac{S_{d}}{\sum_{d=1}^{D}S_{d}}$ is the normalised correlation of $x_{d}$, then the targeted normalised correlation ratio is $\tilde{S_{d}^{\star}}$, where it is assumed that is $\tilde{S_{d}^{\star}}=w_{d}$ is the weight assumed (in our case equal weights) to reflect the importance. Once these quantities have been computed, and provided the equal weights ( or any other weight system user-provided), the optimized weights are the results of the minimizing the objective function

The results of this approach are reported in Figure 6. Our first observation is that the domains have fairly similar linear and non-linear correlation ratio $S_{d}$ estimates, indicating that linear estimates would have been sufficient to address the linear correlation among the three domains. Recall that we would like low $S_{d}^{c}$ and high $S_{d}^{u}$, both positive. What we have obtained is that the correlated part dominates in Healthy Lives, indicating that Healthy Lives has a small impact on the composite index as it is mostly imputable to the correlation with the other variable. For Healthy People both components contribute equally and both positively. Healthy Places has a negative correlated effect, which is similar to the uncorrelated part, but the negative $S_{d}^{c}$ values implies potential problems in the composite index. Somehow, we could have expected that Healthy Places could have some problematic behaviour, as we have observed in the correlation analysis.

Having unpacked the correlation among the domains, we can use this information to find a new set of weights that truly reflects the importance of each variable in the CI, but that are close to the importance distribution we have specified - in our case equal importance (each domain 0.33 weight). The optimization algorithm finds optimal weights of 0.45 for Healthy People, 0.16 for Healthy Lives, and 0.73 for Healthy Places. These weights will be used subsequently for a sensitivity and uncertainty analysis.

While there is no objective choice in selecting the weights, we concentrate on a so-called data-driven weighting system, derived from Principal Component Analysis (PCA) or Factor Analysis (FA). Now, in the context of composite indicator construction, these two methods can be applied at different steps due to their versatile interpretation: to identify dimensions, to cluster indicators and to define weights. While PCA and FA share several methodological aspects, there is a key difference between the two analyses. PCA is a data reduction method based on the correlation matrix, which re-defines a new set of uncorrelated variables as linear combinations of the original variables. In contrast, FA is a measurement model of a latent variable, where the latent factor ’causes’ the observed variables. There is a recommendation in the CI community ST (02) to use the PCA loadings as weights only if the first component accounts at least for the $70\%$ of the total variability. We applied this procedure to derive the weighting systems for subdomains. The 58 indicators are split in 17 subdomains (see Table 1), and for each of these subdomains we carried out a PCA analysis, for each year.

For most subdomains, over all four years, the first PCA component accounted for a range between 51% to 94% of the total variability. Exceptions were observed (see Table 6 in SM) for ’Mental health (Pe.4)’ with variance explained 66-69%, ’Behavioural risk factors (Li.1)’ 53-55%, ’Working conditions (Li.4)’ 50-55%, ’Risk factors for children (Li.5)’ 55%, ’Children and young people’s education (Li.6)’ 63-69% , ’Access to housing (Pl.3)’ 65-69%. We then normalized the loading coefficient and compared them over time, jointly with the weights originally derived from FA for all the years collapsed.

We have investigated the PCA weights values over time and compared them with the time-series FA analysis computed for the ONS HI. We have found that these are very similar over time, which is reassuring in terms of stability of the index weights (see Figure 7). However, when we compared PCA and FA weights, we have found that FA gave higher weights to the following indicators (difference percentage among weights): low pay (12%), self-harm (10%), difficulty completing activities of daily living (5.4%) and drug misuse (6.6%). On the contrary, PCA imposed higher weights to job-related training (7.6%), physical activity (7%), suicides (5.9%) and workplace safety (4.4%).

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  Given the negative correlation between the Healthy Places domain and the two other domains, we discourage arithmetic mean aggregation.

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  To interpret the weights as ‘importance’, optimized weights should be adopted.

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  Between FA and PCA derived weights, we recommend using PCA as the subdomain is not the ‘cause’ of the indicators, but a combination.

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  The overall index could be obtained by adopting optimized weights and a geometric mean aggregation formula. Optimized weight allow for partial substitution as correlation is accounted for; geometric mean rewards balance by penalizing uneven performance in the underlying domains.

We carried out the sensitivity analysis on the modified ONS HI and in Figure 8, we notice that for the overall index tail rankings are stable, while the middle UTLAs are the ones showing the highest variability with median rankings (green dots) above or below the provided ranking.

We then repeated the analysis for the three domains separately (see Figure 4 in SM). The estimates are more precise, as the bounds between the 5^th and 95^th centile are narrower compared to the overall index. We observed that People rankings are quite precise and concentrated and it is possible to see that they are following the Health Index. Lives and Places are displaying higher variability, with Places acting as the ‘wild card’.

The first order sensitivity and the total order sensitivity have been computed for the overall index and the three domains and we reported them in Table 7 in SM. We then plotted the main effect $S_{i}$ and the interactions $S_{T_{i}}$, see Figure 9. These values can be interpreted as the uncertainty caused by the effect of the $i$^th uncertain parameter/assumption on its own. The total order sensitivity index is the uncertainty caused by the effect of the $i$^th uncertain parameter/assumption, including its interactions with other inputs. This disentanglement shows that at domain level normalization plays a major role for all of them, with winsorization additionally being quite relevant for Places and weights being relevant for People. For the overall index, weights are the main cause of the variability with normalization and winsorization playing a minor role at interaction levels.

We assessed the absolute mean differences on the overall rank shift, by removing indicators and subdomains. At indicator level (see Figure 10), we observed the highest shifts are due to unemployment, access to private and public green space and personal crime. Moderate absolute shifts are observed for job-related training, workplace safety, disability, frailty, suicides, depression and rough sleeping.

At subdomain levels (see Figure 11), the highest impact is for ‘Access to services (Pl.4)’ and ‘Children and young people’s education (Li.6)’, followed by ‘Unemployment (Li.3)’ and ‘Working conditions (Li.4)’. The observation that Healthy Lives shows the most influence on the overall index values confirms what has already been observed in previous sections, where we note the high correlation between Healthy Lives values and the overall index values.

In summary, this analysis conducted on the 2015-18 beta Health Index served as proof on the statistical coherence and investigated choices and issues that arise in the process of building a new composite index. The aim of the ONS Health Index is to become a reliable harmonized index over time and over space, with inclusion of finer geographical level and potential stratification of population by age and sex, including Scotland and Wales. The suggestions highlighted in this article are not exhaustive due to the current evolving nature of the index, but provide a valuable tool that serves as guidance for the upcoming versions.

While we assessed the beta version, the Health Index version from year 2019 already includes the Lower Tier Local Authorities (LTLA) for England (307 LTLAs) and several suggestions have been integrated. We review the propositions made in this paper and how these have been included.

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  Data is winsorized to derive weights by factor analysis, reducing need for much other transformation to normalize. The final data, which gets aggregated later on to produce Index scores, is not winsorized so LTLAs with extreme values can still observe change over time.

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  Public green space indicator - that was negatively correlated with private outdoor space - will be removed in the 2020 Health Index.

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  The passage to LTLA relaxed the correlation seen for Behavioural risk factors, and drug misuse indicators has been changed to a different source to meet the granularity criteria.

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  Subdomains ‘Risk factors for children’ and ‘Children and young people’s education’ are now joined into a unique subdomain ‘Children and young people’.

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  Hypertension (renamed to ‘High blood pressure’) continues to show high positive correlation with cardiovascular, respiratory and musculoskeletal conditions, even at LTLA level. Currently, the ONS is exploring potential alternatives for these indicators.

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  At LTLA level data no longer present a negative correlation between Healthy Places and the other domains: they are now all positively correlated, albeit Places has a weaker correlation with the others than the Lives–People correlation.

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  The inclusion of a smaller geography as base unit and changes observed for in correlations pairs, changes the derived weights that account for the correlation. The added value of our analysis highlighted how crucial the weights are, not only in terms of value but also in terms of interpretation. The ONS is going to evaluate the possibility to have non-compensatory weights defined by expert opinion, to better capture what stakeholders rate as important among the domains and subdomains.

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  We argued that between FA and PCA derived weights, PCA should be preferred. The ONS has not implemented this proposed modification. This is due to the evolving nature of the index at this stage. The extension to additional geographical layer and population stratification will have an impact on the correlation matrices and therefore weights may undergo substantial changes, before a stable version is finalized.

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  Finally, our last suggestion promoted a geometric mean aggregation formula, that implies only partial substitution and rewards balance by penalizing uneven performance in the underlying domains. Initially, among the principle followed by the ONS in producing a composite index, there was the necessity to be able to have simple statistical methods that could be easy to explain. However, in the course of this analysis, we showed that the geometric mean offers a valid alternative, used by many other well-known and respected indexes such as the Human Development Index Pro (10). This option will be taken into account in the ONS’s upcoming methodological evaluations.

In conclusion, the ONS Health Index (2015–18) presents a summary of the health of the population of England and fills a gap in policy making and assessment tools. The index is based on a hierarchical geographical structure, starting from the Upper Tier Local Authority level, rising to National level. It provides a detailed and flexible composite measurement, that will allow policy makers to assess changes in population health, and to plan interventions by identifying areas and policy domains where interventions can provide significant, quantifiable impact. Future Health Index editions, with finer geographic granularity and population subgroups, will enrich the understanding of health determinants and guide bespoke interventions and assessments.