Assessments and developments in constructing a National Health Index for policy making in the United Kingdom Anna Freni-Sterrantino

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Assessments and developments in constructing a National Health

Index for policy making, in the United Kingdom

Anna Freni-Sterrantino

The Alan Turing Institute, London, UK

E-mail: afrenisterrantino@turing.ac.uk

Thomas P. Prescott

The Alan Turing Institute, London, UK

Greg Ceely

Ofﬁce for National Statistics

Myer Glickman

Ofﬁce for National Statistics

Chris Holmes

The Alan Turing Institute, London, UK

E-mail: cholmes@turing.ac.uk

Summary.

Composite indicators are a useful tool to summarize, measure and compare changes among different

communities. The UK Ofﬁce for National Statistics has created an annual England Health Index (starting

from 2015) comprised of three main health domains - lives, places and people - to monitor health

measures, over time and across different geographical areas (149 Upper Tier Level Authorities, 9 regions

and an overall national index) and to evaluate the health of the nation. The composite indicator is deﬁned

as a weighted average (linear combination) of indicators within subdomains, subdomains within domains,

and domains within the overall index. The Health Index was designed to be comparable over time,

geographically harmonized and to serve as a tool for policy implementation and assessment.

We evaluated the steps taken in the construction, reviewing the conceptual coherence and statistical

requirements on Health Index data for 2015-2018. To assess these, we have focused on three main

steps: correlation analysis at different index levels; comparison of the implemented weights derived from

factor analysis with two alternative weights from principal components analysis and optimized system

weights; a sensitivity and uncertainty analysis to assess to what extent rankings depend on the selected

set of methodological choices. Based on the results, we have highlighted features that have improved

statistical requirements of the forthcoming UK Health Index.

Keywords: Composite Indicator; Health Index; Weights; Robustness assessment; Sensitivity analysis;

Uncertainty

1. Introduction

A composite index (CI) is a way to summarize several indicators in one number and provide a tool

for policy-making. Besides the known health-related indices like Healthy Life Expectancy [vdWPB96]

or Disability-Adjusted Life Years [HPM12,SLTF+12], in the United Kingdom (UK) there has been a

long tradition of health-related indices; the ﬁrst ‘Health Index’ was developed in 1943 as a surveillance

system for population health at national level, based on mortality and morbidity annual data [Sul66].

Kaltenthaler et al. [KMB04], in their systematic review conducted in 2014, evaluated 17 population

level health indexes and found that three were composed for the UK population. The ‘Health and

material deprivation in Plymouth’ [ABPS92] a modiﬁcation of Townsend’s ‘Overall Health Index’

[TPB88] and the most popular ‘Index of Multiple Deprivation’ [DotEtR00]. However none of them

or any of the other health-population indexes seemed to fulﬁl the desiderata for a health index:

proper health coverage indicators; routinely collected and updated data; indices at local and national

level; and statistical coherence. These ﬁndings were later conﬁrmed by Ashraf et al. [ANTG19] in

a systematic review. They concluded that most of the indices measured population’s overall health

arXiv:2210.05154v1 [stat.AP] 11 Oct 2022

2Chris Holmes

outcomes, but only few gave focus to speciﬁc health topics or the health of speciﬁc sub-populations.

They urged the development of population health indices that can be constructed systematically and

rigorously, with robust processes and sound methodology.

Recently, to ﬁll this gap, the Oﬃce for National Statistics of the UK (ONS) developed an annual

(experimental) composite index to quantify health in England, to track changes in health across the

country and to compare health measures across diﬀerent population subgroups.

The Health Index (HI) expands the WHO deﬁnition of health: ‘a state of complete physical, mental

and social well-being and not merely the absence of disease and inﬁrmity’ [Gra02], to include health

determinants that are known to inﬂuence people’s health. Therefore, the HI is characterized by three

main domains: Healthy People, Healthy Lives and Healthy Places, split across 17 subdomains, for

a total of 58 indicators. For example, life expectancy and the standardized number of avoidable

deaths deﬁne the subdomain ‘Mortality’ and prevalence at Upper Tier Local Authority (UTLA)

level of dementia, musculoskeletal, respiratory, cardiovascular, cancer and kidney conditions deﬁne

the subdomain ‘Physical health conditions’ within the Healthy People domain. Healthy Places is

structured over 14 indicators (access to public and private green space, air and noise pollution, road

safety, etc.) split in 5 subdomains: Access to green space, Local environment, Access to housing,

Access to services and Crime.

The construction of a new composite indicator is a lengthy process that takes into account several

steps and choices. From the wide literature on composite indicators [BDWL19,Fre03,JSG04], it

emerges that there is no gold-standard, with every method having its own drawbacks and advantages

[GITT19] relative to the purpose of each CI and its future use in policy making.

In recent years, extensive work was carried out by many institutions, such as Eurostat [Eur17],

the Organisation for Economic Co-operation and Development (OECD) [C+08], the Joint Research

Centre (JRC) [ST02] and speciﬁc working groups at the European Commission [JRC], to provide

statistical guidance on CI construction. The cumulative eﬀort has provided a framework to deﬁne CI

principles [NSST05], outlining the essential steps, introducing sensitivity and uncertainty analysis as

a core part of composite indicators [SST05] and advancing composite indicators methodology [MN05].

With no current unanimous approved checklist for evaluating composite indicators, we relied on

two main sources to guide us into assessing the Health Index. The ﬁrst is based on the COIN step-list

from the JRC [JRC], which includes observations from the OECD handbook [C+08]. These elements

provide a framework that will guide us on the statistical (quantitative) methodological choices and

statistical analysis. The second source is based on previous work carried out in an audit format by the

JRC composite indicators expert group [SP12,CB+22], where they have evaluated other composite

indicators.

In this paper, in an eﬀort to fulﬁll transparency requirements, we evaluated the steps taken

and arising issues that come into the design of the ONS HI. We highlight areas of improvement or

which warrant further investigation, based on our ﬁndings, aiming for a statistically and conceptually

coherent index, that will be integrated in the future HI release. This paper is structured as follows.

We start by describing the beta ONS HI for 2015-2018 structure and steps taken in its construction,

in section 2. In section 3, we provide an in-depth correlation analysis which will be useful for the

weights system selection that we introduce in section 4. The index validity is evaluated by sensitivity

and uncertainty analysis in section 5. At the end of each section we conclude with features that could

be improved or are worthy of further considerations. Finally, we provide discussion and conclusions,

in section 6.

2. The ONS Health Index

The ONS Health Index (HI) is a composite index (CI) structured in three main domains: ‘Healthy

People’, ‘Healthy Lives’ and ‘Healthy Places’, see Figure 1. These domains are based on 17 subdomains,

which are in turn based on 58 indicators, collected for the 149 Upper Tier Level Authorities (UTLA)

in England, from 2015 to 2018. See Table 1for full indicator and subdomain detailed descriptions (see

also Table 1 in Supplementary Material). The choice of the indicators, and the deﬁnition of the 17

subdomains and three domains, were based on a comprehensive review of contents of existing indices

and frameworks; cross-referenced with existing accepted deﬁnitions of health; and then consulted

on by an expert group with members from central government, local organisations, think tanks and

academia to evaluate the proposal[Cee20]. The methodology was based on the 10 steps reported in

UK Health Index 3

Fig. 1. The Health Index structure.

the COIN guidance promoted by the European Joint Research Center [JRC]. After collating raw data

for the indicators at UTLA level, the steps taken to construct the Health Index were:

(a) data imputation;

(b) data treatment and normalization;

(d) arithmetic aggregation with equal weights across subdomains and domains.

The index is computed for each UTLA, aggregated geographically to correspond to English regions,

and further aggregated into an overall national ﬁgure. The index values are calculated for each year

from 2015 to 2018 inclusive, with a normalised value anchored at the baseline year 2015. Full details

are provided in Supplementary Material (SM).

The Health Index is built starting from a tensor Xof raw data, with elements xcit. Here, each

c∈Cis an upper tier local authority (UTLA), for the set Cof |C|= 149 UTLAs; each i∈Iis an

indicator, for the set Iof |I|= 58 indicators; and each t∈T={2015,2016,2017,2018}denotes the

year. We are also given a partition of the set of UTLAs, C, into a set Rof |R|= 9 regions, r∈R,

which are disjoint subsets r⊆Cof UTLAs.

2.1. Data Imputation

We ﬁrst note that Xis 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.

4Chris Holmes

Table 1. Health Index structure: domains, subdomains and indicators

Health Domains:

People (Pe) Lives (Li) Places (Pl)

Pe.1 Mortality: life

expectancy, avoidable deaths

Li.1 Physiological risk factors:

diabetes, overweight and

obesity in adults, hypertension

Pl.1 Access to green space:

public green space, private

outdoor space

Pe.2 Physical health

conditions: dementia,

musculoskeletal conditions,

respiratory conditions,

cardiovascular conditions,

cancer, kidney disease

Li.2 Behavioural risk factors:

alcohol misuse, drug misuse,

smoking, physical activity,

healthy eating

Pl.2 Local environment: air

pollution, transport noise,

neighbourhood noise, road

safety, road traﬃc volume

Pe.3 Diﬃculties in daily life:

disability that impacts daily

activities, diﬃculty completing

activities of daily living

(ADLs), frailty

Li.3 Unemployment:

unemployment

Pl.3 Access to housing:

household overcrowding, rough

sleeping, housing aﬀordability

Pe.4 Personal well-being: life

satisfaction, life

worthwhileness, happiness,

anxiety

Li.4 Working conditions:

job-related training, low pay,

workplace safety

Pl.4 Access to services:

distance to GP services,

distance to pharmacies,

distance to sports or leisure

facilities

Pe.5 Mental health: suicides,

depression, self-harm

Li.5 Risk factors for children:

infant mortality, children’s

social, emotional and mental

health, overweight and obesity

in children, low birth weight,

teenage pregnancy, child

poverty, children in state care

Pl.5 Crime: personal crime

Li.6 Children and young

people’s education: young

people’s education,

employment and training,

pupil absence, early years

development, General

Certiﬁcate of Secondary

Education achievement

Li.7 Protective measures:

cancer screening, vaccination

coverage, sexual health

UK Health Index 5

2.2. Data treatment and normalization

Once the missing data has been imputed, the completed tensor X= (xcit) is decomposed into |I|= 58

ﬂattened data sets, Xi={xcit :c∈C, t ∈T}for each i∈I. Using the data transformations

filisted in Supplementary Table 3 for each indicator, i, the raw indicator data is transformed to

Yi={ycit =fi(xcit) : c∈C, t ∈T}. The assignment of each transformation, fi, to an indicator, i, is

selected to minimise the absolute values of skewness and kurtosis of Yi, aiming for absolute skewness

≤2 and absolute kurtosis ≤3.5. By minimising (absolute) skewness and kurtosis, we aim to ensure

that the transformed data Yiis approximately normally distributed. For 18 indicators, the skewness

and kurtosis of Xiwere 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 ycit of Yinto z-scores,

zcit = (−1)δiycit −µi

σi,

which then deﬁne the elements of the tensor Z= (zcit). For each indicator, i, we specify δi= 0 or

δi= 1 to ensure that larger positive values for zcit correspond to improved health, a property which we

term as being health directed. Note that the mean and standard deviation µiand σifor each indicator,

i, are taken to be the population-weighted mean and standard deviation of ycit for the chosen baseline

year across UTLAs c∈C, ﬁxing t= 2015. Finally, given the z-scores zcit forming the tensor Z, the

ONS Health Index presents the z-scores as Health Index values,

hcit =H(zcit) = 100 + 10zcit,

which are translated and rescaled z-scores, such that hcit = 100 means that the transformed value,

ycit, for indicator iin the UTLA cin year tis equal to the weighted mean, µi.

2.3. Subdomain weights computation: a time-series factor analysis

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 [DL13].

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 ZCT = (zct) are collapsed by year and then rescaled to (0,1),

next given d∈D, a factor analysis on the indicators i∈dwas carried out and the weights were chosen

as the ﬁrst loading factor, taken in absolute value. The weights wifor indicators i∈Iare chosen

by running factor analysis for each subdomain, d∈D, in turn, allowing for one factor estimated

using a maximum likelihood method. For example, for a subdomain d={i1, i2}comprised of two

indicators, suppose the factor loadings are 0.5 and 0.75. We would then set the weights wi1= 0.4

and wi2= 0.6. In supplementary material, we address the weights constraints taking into account the

diﬀerent aggregation levels.

2.4. Arithmetic aggregation with equal weights across subdomains and domains

The ﬁnal step is the arithmetic aggregation of the index, where there are equal weights for subdomains

wsand domains wd, 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

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AssessmentsanddevelopmentsinconstructingaNationalHealthIndexforpolicymaking,intheUnitedKingdomAnnaFreni-SterrantinoTheAlanTuringInstitute,London,UKE-mail:afrenisterrantino@turing.ac.ukThomasP.PrescottTheAlanTuringInstitute,London,UKGregCeelyOfceforNationalStatisticsMyerGlickmanOfceforNationalStati...

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