The Sensitivity of the Healthy Life Years Indicator: Approaches for Dealing with Age-Specific Prevalence Data


The Sensitivity of the Healthy Life Years Indicator: Approaches 
for Dealing with Age-Specifi c Prevalence Data*

Vanessa di Lego, Markus Sauerberg

Abstract: The Healthy Life Years (HLY) indicator is the offi cial European Union 
indicator and a cornerstone of many health policies used in over 15 countries in 
the EU region to set national health plans and monitor targets. It is also used to 
investigate trends over time in the proportion of total life years spent in good or 
poor health, socioeconomic inequalities in health and mortality and the male-female 
health survival paradox. Based on the Global Activity Limitation Indicator (GALI) 
included in the European Union Statistics on Income and Living Conditions (EU-
SILC), a great amount of effort has been directed at harmonising and making HLY 
comparable across countries. Nonetheless, the characteristics of the age-specifi c 
prevalence distribution are still rarely accounted for, regardless of the fact that 
patterns of prevalence often fl uctuate considerably by age. In addition, the impact 
of assumptions used at very young ages on HLY estimates are seldom discussed, 
despite the fact that the majority of policies and initiatives at the EU level use HLY 
at birth, while data on health is only available after age 16. In this paper, we assess 
whether smoothing the age-specifi c prevalence distributions by different methods, 
extrapolating to older ages and changing assumptions at younger ages affect HLY 
estimates. Overall, assumptions made before age 15 are the most important and 
affect women and men differently, thus affecting HLY at birth for some countries. 
Estimates at age 65 are very slightly impacted. Generalised linear models (GAMs) 
seem promising for harmonising and extrapolating to older ages, while using 
polynomials or aggregating into 5-year age groups seem best for younger ages. As 
most EU policies use HLY at birth and by sex for developing and monitoring health 
policies, caution is needed when estimating HLY at birth.

Keywords: Healthy Life Years · Sensitivity · Age-Specifi c Prevalence · Life Table · 
Sullivan Method · GALI · Smoothing · Gender differences

Comparative Population Studies
Vol. 48 (2023): 117-150 (Date of release: 06.04.2023)

Federal Institute for Population Research 2023 URL: www.comparativepopulationstudies.de
      DOI: https://doi.org/10.12765/CPoS-2023-06
      URN: urn:nbn:de:bib-cpos-2023-06en7
    

* This article belongs to a special issue on “Levels and Trends of Health Expectancy: Understanding 
its Measurement and Estimation Sensitivity”.

** This article has an Online Appendix with supplementary material URL: http://www.
comparativepopulationstudies.de/index.php/CPoS/article/view/476/374.

https://www.comparativepopulationstudies.de/index.php/CPoS/article/view/476/374
http://www.comparativepopulationstudies.de
https://doi.org/10.12765/CPoS-2023-06


•    Vanessa di Lego, Markus Sauerberg118

1 Introduction

 The Healthy Life Years (HLY) indicator is one of the most important indicators for 
monitoring population health, developing policies and addressing different research 
questions. It is the offi cial European Union indicator for developing strategies for 
national health plans and monitoring health policy targets such as the 2000 Lisbon 
Strategy and the European Innovation Partnership on Active and Healthy Ageing to 
increase the average HLY of Europeans by two years by 2020 (Robine et al. 2013; 
Bogaert et al. 2018; Eurostat 2020). It has also been used to  investigate important 
research questions, such as trends over time in the proportion of total life years 
spent in good or poor health (the “compression-expansion debate”), socioeconomic 
inequalities in health and mortality, compositional effects of education on health 
indicators across regions and the male-female health survival paradox (Murray et al. 
2002; Bocquet-Appel 2008; Ekholm/Brønnum-Hansen 2009; Nusselder et al. 2010, 
2019; Van Oyen et al. 2013; Jagger et al. 2013; Füssenich et al. 2019; di Lego et al. 
2020; Welsh et al. 2021; Sauerberg 2021).

The HLY is a disability-free life expectancy (DFLE) indicator based on the Global 
Activity Limitation Indicator (GALI) included in the European Union Statistics on 
Income and Living Conditions (EU-SILC) (Robine et al. 2003). It combines mortality 
information from period Eurostat life tables with the disability prevalence data 
obtained from EU-SILC (Saito et al. 2014). Even though several other methods are 
available for estimating health expectancy indicators for different contexts and 
health data (Robine/Mathers 1993; Lynch/Brown 2005, 2010; McCallum/Mathers 
2008; Crimmins et al. 2009; Nepomuceno/Turra 2015), the approach developed by 
Sullivan is the most employed up until now (Sullivan 1971; Mathers et al. 2001; Saito 
et al. 2014). This is mainly due to its parsimonious approach and requirement for 
age-specifi c prevalence data that are readily available from cross-sectional surveys 
(Robine/Jagger 2003; Yokota et al. 2019). In addition, the Sullivan method and the 
GALI instrument have been extensively tested for consistency and comparability 
across European countries (Robine/Jagger 2003; Van Oyen et al. 2006; Berger et al. 
2015), with a wide range of sensitivity analyses performed to attest its harmonised 
features (Cox et al. 2009; Jagger et al. 2010; Rubio-Valverde et al. 2019). 

However, the sensitivity of the age pattern of disability in the context of the HLY 
has been less explored. The distribution of age-specifi c prevalence is very uneven, 
with a profi le that often fl uctuates across ages and with alternating last-age intervals. 
Since information on disability is usually derived from population surveys, health 
information is limited to specifi c ages and subject to specifi c survey characteristics, 
such as individual responsiveness, sample design and reporting behaviour (Jürges 
2007; Peracchi/Rossetti 2012; Hardy et al. 2014; Cigolle et al. 2018; Spitzer/Weber 
2019). Hence, the age pattern may also be sensitive to particular technical features 
that directly affect age-specifi c prevalence estimates, which in turn can impact the 
HLY indicator. For instance, despite many health policies in the EU region using 
HLY at birth as the main indicator, the EU-SILC survey includes only people above 
age 16. In addition, the last open age interval available for most countries is 80+, 
with some countries not only having different last age intervals available, but also 



The Sensitivity of the Healthy Life Years Indicator    • 119

experiencing changes over time, like Germany, which starting from 2015 only has 
data available for ages 74+ (GESIS 2022). Therefore, assumptions for very young 
and old persons are required. The conventional approach used by Eurostat for the 
offi cial estimates assumes that the prevalence of being unhealthy for individuals 
younger than age 15 is half of the prevalence of the 16-19 age group (Eurostat 2020; 
Welsh et al. 2021). Further, a common strategy to deal with the erratic behaviour 
of age-specifi c prevalence is to aggregate data into 5-year age groups prior to 
combining it with abridged life tables, which is the current procedure adopted by 
Eurostat. In this case, it assumes a constant proportion of unhealthy individuals 
in each age group as a means to deal with single-age inconsistencies.  Although 
a number of issues related to the sensitivity of health expectancy indicators have 
been addressed and discussed (Crimmins et al. 1994; Robine et al. 2001; Mathers 
2002), the majority of the effort has been directed at evaluating the role of the GALI 
instrument, harmonisation issues and comparability across countries (Van Oyen et 
al. 2006; Berger et al. 2015). Nonetheless, the characteristics of the age-specifi c 
prevalence distribution is not as often considered when empirically analysing levels 
and trends of health expectancy and their role when interpreting the results. In part, 
this is due to the fact that age-specifi c prevalence is usually combined with mortality 
data in order to derive health expectancy indicators, so little attention is given to the 
age pattern of prevalence prior to combining it with mortality. 

In this paper, we assess whether adopting different age-specifi c prevalence 
distributions and changing the most commonly used assumptions prior to 
combining the health information with the mortality data may affect HLY estimates. 
First, instead of simply aggregating age-specifi c prevalence into 5-year age groups, 
we evaluate whether smoothing the age prevalence distribution of disability by 
different methods as measured by the GALI instrument has any implication on 
the posterior HLY estimates. Second, as HLY is estimated using survey data that 
only has health information available after the age of 16, we test whether changing 
assumptions of the prevalence proportions before that age affects the distributions, 
as well as computing prevalence by single age intervals. Third, as the last age 
interval available from health surveys varies and is limited to either age 80+ or 
74+, we extrapolate the maximum observed age to 100+ using a generalised 
additive model (GAM), in order to test whether extrapolating the age profi le has any 
impact on the HLY estimates and whether this is a viable strategy for computing 
HLY at older ages. We then compute HLY at birth and at age 65 for all smoothing 
and extrapolation methods using period life tables from Eurostat. Estimates are 
for the year 2017 and for all the EU-28 countries (in this year it includes United 
Kingdom as part of the EU member states), as well as Switzerland, Norway and 
Iceland as non-members. We fi nally estimate the proportion of total life expectancy 
spent in healthy life years for each method and discuss implications of these results 
when estimating HLY. By further exploring the sensitivity of the HLY indicator 
with regard to the characteristics of age-specifi c prevalence, we seek to address 
the extent to which differences in health status across European countries are 
vulnerable to these technical features. The standard practice of combining age-
specifi c prevalence proportions with person-years lived without proper attention 



•    Vanessa di Lego, Markus Sauerberg120

to the distribution profi le of the former may affect the estimation of healthy life 
years. Overall, differences are small, but oftentimes they are not trivial and vary by 
smoothing method, country, sex and age. This suggests that it is important to be 
more cautious with the age distribution of health prevalence prior to combining it 
with mortality data, especially when the indicator of interest is estimated at birth. 
Further research is needed to understand what the optimal strategy would be to 
deal with the age-specifi c prevalence and this will more likely depend on the data 
available and the purpose in using the indicator. However, according to the results 
of the sensitivity analyses presented in this paper, we suggest a routine practice 
as regards estimating the HLY, as summarised in the fl owchart in Figure 9, which 
includes fi rst and foremost considering whether HLY is to be estimated at birth or 
age 65. Second, plot the age-specifi c disability prevalence and evaluate its pattern, 
as well as whether aggregating into 5-year age groups already smooths the pattern. 
GAMs adjust well at ages 65 and older and their impact on HLY is very small, but 
they can impact HLY at birth. In this case, either just estimating HLY based on the 
usual aggregation by 5-year age groups or smoothing by a polynomial fi t can be 
best. Most importantly, always test age profi les for women and men separately, 
as well as country-specifi c patterns. The most important recommendation is to 
consider the purpose of the indicator carefully beforehand and to assess its pattern 
by age before combining it with the person-years lived by age.

2 Data and methods

The observed prevalence of limitations in activities of daily living (ADLs) is obtained 
from the GALI. The exact wording of the GALI is: “For at least the past 6 months, to 
what extent have you been limited because of a health problem in activities people 
usually do? Would you say you have been (1) severely limited, (2) limited but not 
severely, or (3) not limited at all?”. This is the offi cial Eurostat indicator used to 
monitor health status, where individuals are defi ned as healthy if they report no 
limitations at all (Jagger et al. 2013; Eurostat 2020). The advantage of using the GALI 
instrument in order to estimate health expectancy is that it has been systematically 
assessed in order to ensure the highest level possible of harmonisation and 
comparability of health dimensions, age and time across European countries 
(Van Oyen et al. 2006; Jagger et al. 2010; Berger et al. 2016). We employ the most 
commonly used approach for estimating the HLY and also the one offi cially adopted 
by the European Union, which is the Sullivan method (Imai/Soneji 2007; Saito et al. 
2014; Sullivan 1971). Sullivan applies the age-specifi c prevalence (proportions) of a 
population in an unhealthy state to the age-specifi c person-years lived from the life 
table. In this way, the total life years in each age interval can be partitioned into years 
spent in good and poor health. Before we combine the age-specifi c prevalence with 
the person-years lived using Eurostat life tables, we employ a series of smoothing 
techniques and extrapolations methods as shown in Table 1. We choose this set of 
smoothing techniques because they are fl exible, demand few or no assumptions 



The Sensitivity of the Healthy Life Years Indicator    • 121

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•    Vanessa di Lego, Markus Sauerberg122

about the age distribution but at the same time have slightly different approaches 
and smoothing parameters allowing for different test setups. 

The polynomial smoothing provides us with a single model for the data, while 
the splines approach gives us a piecewise continuous function composed of many 
polynomials to model age-specifi c prevalence (Eilers/Marx 1996; Gu 2014; James 
et al. 2021). The smoothing splines are set both with and without penalty and the 
polynomial fi t is of fourth degree, as suggested by previous applications of this 
approach to age-specifi c health prevalence (Aubert 2021). Lastly, Generalised Linear 
Models (GAMs) were computed for each country and by sex in order to smooth and 
extrapolate the last age interval until 100+.1 GAMs have the advantage that the 
shape of the predictor functions are fully determined by the data, allowing for a more 
fl exible estimation while still capturing underlying patterns (Rigby/Stasinopoulos 
2005; Wood 2006). We used the population size at each age as weights in the model 
to account for age structure and the binomial link to constrain the prevalence into 
the interval [0,1]. The estimates were performed using the mgcv package in R. In 
addition, three different assumptions regarding the age-specifi c prevalence below 
age 15 were tested: 1. The offi cial EU assumption that the prevalence between ages 
0-15 is half of the observed in the age group 16-19 (Eurostat 2020); 2. The prevalence 
between ages 0-15 is zero and so there is no observed disability below age 15; 
and 3. Smooth increase since birth for the cases where age-specifi c prevalence 
was extrapolated and smoothed using GAMs. These three alternative scenarios of 
disability at younger ages allow for evaluating the sensitivity of the HLY indicator 
when estimated at birth. 

In order to choose the smoothing parameter that best fi ts the data, we used 
restricted maximum likelihood (REML) for the GAMs and generalised cross-
validation (GCV) for the splines. Likewise, in order to compare the estimated outputs 
across all smoothing methods, we used the root mean square error (RMSE). The 
RMSE is defi ned as the square root of the mean of the square of all of the errors and 
it measures how far predicted values are from observed values or how concentrated 
the data is around the best fi t (Christie/Neill 2022). Smaller RMSE score values 
indicate that the estimated curve is closer to the true curve and used as an indicator 
of best fi t. We use this approach since we compare different methods and the RMSE 
is advised as a general purpose approach to assess error metrics when performing 
comparisons, including across different smoothing methods (Malloy et al. 2009; 
Ben Ghoul et al. 2019). For a more detailed explanation of the REML used for GAMs 
and the RMSE for comparing all approaches, refer to the Technical Note in the 
Appendix (scores for each method and all countries by sex, considering the offi cial 
EU assumption that the prevalence between ages 0-15 is half of the observed in the 
age group 16-19 are presented in Table A7 in the Appendix).

1 We tested whether the same methods usually employed to extrapolate mortality would also 
work with health, in addition to using more fl exible approaches. Several attempts to extrapolate 
the age pattern of disability using Kannisto-Makeham, Gamma-Gompertz and Gompertz 
mortality models were employed, but yielded unsound results as shown in Figures A6 and A7 
in the Appendix.



The Sensitivity of the Healthy Life Years Indicator    • 123

Because the age-specifi c prevalence in disability in the EU-SILC survey is only 
available until 80+, we recalculated Eurostat life tables adopting a new open-
ended age interval of 80+ for most countries – as the offi cial life tables close at 
age 85+ – using the standard approach by Preston et al. (2001). One exception 
was Germany, where we close the life table at age 74+ (because for Germany the 
last age observed in the EU-SILC starting from 2015 is 74+). For the case of age-
specifi c prevalence that we smoothed and extrapolated until age 100+ using GAMs, 
we also extrapolated the life tables until 100+ using the Makeham mortality law. 
After smoothing the estimated age-specifi c prevalence πi+ni from the surveys and 
adjusting the open-end age interval from life tables accordingly, we combined the 
many different distributions with the person-years lived by age Li+ni adjusted from 
the Eurostat life tables to estimate the disability-free life expectancy êDF, or in this 
case, the HLY, following the formulation by Imai and Soneji (2007):

Differences in our estimates and the offi cial HLY may occur not only because 
we are computing the estimates for single ages, while Eurostat computes for 5-year 
age group intervals, but also because we are using life tables with different open-
age limits. The health data Eurostat has available to estimate HLY may also be 
slightly different from the EU-SILC microdata we have access to. Nonetheless, the 
calculations are internally consistent with the method for each variant of smoothing 
and extrapolation we use, which allows for performing the comparisons across the 
scenarios we have built between smoothed/unsmoothed and extrapolated/non-
extrapolated. As our goal in this paper is not to provide a direct comparison between 
our estimates and the offi cial ones across countries, but to showcase the sensitivity 
of the indicator for different smoothing methods, we present the results for single 
ages, the case of highest fl uctuation and sensitivity possible. Nonetheless, in the 
Appendix we have added the analysis with the 5-year age group intervals so that 
the reader can evaluate the consistency in our estimates, which are in this case very 
close or the same as the offi cial estimates.

All results were computed for the year 2017 since that is the latest year for which 
we can compute the estimates including the most comprehensive set of the EU-28 
Member States that included UK as well as Switzerland, Norway and Iceland as non-
members, but before the COVID-19 pandemic, which can cause an additional layer 
of sensitivity that would be diffi cult to isolate. As our particular aim in this paper is 
to test the sensitivity of age-specifi c prevalence to various smoothing techniques, 
we believe that the specifi c choice of year is not of particular importance to test the 
sensitivity of the indicator itself. 

^

x

1 1  (1)



•    Vanessa di Lego, Markus Sauerberg124

3 Results

3.1 The Sensitivity of Age-specifi c Health Prevalence

The fi rst set of results refers to the prevalence data by different smoothing and 
extrapolation methods. Across countries two overall major clusters of age-specifi c 
patterns of disability were identifi ed: an exponential-like and a linear-like. We 
separated the results into selected countries to emphasise the two clusters of age 
patterns that were observed. One interesting exception is Germany, which falls in 
the middle of these two clusters. We will present its results separately. As presented 
in Figure 1, Spain, France and Finland have a more exponential-like pattern – 

Fig. 1: Prevalence for women and men aged 0-80+, by different smoothing 
methods, year 2017, selected EU countries

Finland France Spain

W
om

en
M

en

0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

0.0

0.2

0.4

0.6

0.0

0.2

0.4

0.6

Denmark Netherlands Sweden

W
om

en
M

en

0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

0.0

0.2

0.4

0.6

0.0

0.2

0.4

0.6

Age

Type Obs. half disability
Obs.
 no disability Penalty Polynomial

Spline half
the disability

A
ge
−S

pe
ci

fic
 P

re
va

le
nc

e

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument



The Sensitivity of the Healthy Life Years Indicator    • 125

especially Spain and France –, while Denmark, the Netherlands and Sweden have 
a linear pattern with remarkable stability over most ages for Sweden (overall, 
most countries fall within these two patterns by age. Refer to country-specifi c age 
patterns for all countries in Fig. A1 in the Appendix). For all countries and for both 
sexes, the polynomial fi t is the smoothing that most evens out the distribution. In 
addition, for some countries, like Spain and France, the visual difference between 
the assumption of no disability below age 15 and half the disability is smaller for both 
sexes than in other countries, particularly women in Finland and the Netherlands. 
For Danish men, the age-specifi c pattern of prevalence shows signs of decline from 

Fig. 2: Heatmap of age-specifi c prevalence for women and men, by different 
smoothing methods, year 2017, EU-28* countries and Switzerland, 
Norway and Iceland

Obs.
 no disability

Obs.
 half disability Penalty Polynomial

Spline half
the disability

W
om

en
M

en

0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

Germany
Austria

Belgium
Bulgaria
Croatia
Cyprus

Czechia
Denmark

Estonia
Finland
France
Greece

Hungary
Iceland
Ireland

Italy
Latvia

Lithuania
Luxembourg
Netherlands

Norway
Poland

Portugal
Romania

Serbia
Slovakia
Slovenia

Spain
Sweden

Switzerland
United Kingdom

Germany
Austria

Belgium
Bulgaria
Croatia
Cyprus

Czechia
Denmark

Estonia
Finland
France
Greece

Hungary
Iceland
Ireland

Italy
Latvia

Lithuania
Luxembourg
Netherlands

Norway
Poland

Portugal
Romania

Serbia
Slovakia
Slovenia

Spain
Sweden

Switzerland
United Kingdom

Age

0.00 0.25 0.50 0.75
Prevalence

C
ou

nt
rie

s

* Germany until 74+, EU-28 in 2017 still includes United Kingdom.
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument



•    Vanessa di Lego, Markus Sauerberg126

around age 65 on. It is diffi cult to infer from these patterns alone whether this shape 
is due to data or period artifacts, sample size, selectivity or a real effect (Engberg et 
al. 2008; Lin et al. 2012).

Figure 2 presents an overview for all EU-28 countries in 2017, together 
with Switzerland, Norway and Iceland. The heatmap shows the observed and 
smoothed age-specifi c prevalence, placing countries in perspective. It shows 
how the proportion of disability is higher among women for most countries and 
in some contexts at relatively younger ages (see Iceland, Netherlands, Finland and 
Denmark). In general, the smoothing methods perform well in retaining the original 
structure of observed data, with the exception of smoothing splines, which appear 
to be extremely fl exible for some countries and most likely overfi tting the data (see 

Fig. 3: Age-specifi c prevalence by sex smoothed by different methods and 
extrapolated to age 100+ by GAM, year 2017, selected EU countries

Finland France Spain

W
om

en
M

en

0 25 50 75 100 0 25 50 75 100 0 25 50 75 100

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

Denmark Netherlands Sweden

W
om

en
M

en

0 25 50 75 100 0 25 50 75 100 0 25 50 75 100

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

Age

Type GAM extrapolated Obs. half disability Penalty Polynomial

A
ge
−S

pe
ci

fic
 P

re
va

le
nc

e

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument



The Sensitivity of the Healthy Life Years Indicator    • 127

Luxembourg, women in Finland and men in Serbia). In Figure 3, we present the 
same set of countries but now extrapolating by fi tting a GAM model and predicting 
until age 100 with the respective confi dence intervals, as shown in the shaded area. 
We use the fi t from the penalty spline and polynomial smoothing to predict age-
specifi c values until age 80+. 

Fig. 4: Prevalence for women and men aged 0-74+, by different smoothing 
methods, year 2017, Germany

Women Men

G
erm

any

0 20 40 60 75 0 20 40 60 75
0.0

0.1

0.2

0.3

0.4

Age

Type Obs. half disability
Obs.
 no disability Penalty Polynomial

Spline half
the disability

A
ge
−S

pe
ci

fic
 P

re
va

le
nc

e

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument

Fig. 5: Age-specifi c prevalence by sex smoothed by different methods and 
extrapolated to age 100+ by GAM, year 2017, Germany

Women Men

0 25 50 75 100 0 25 50 75 100
0.00

0.25

0.50

0.75

Age

Type GAM extrapolated Half Disability Penalty Polynomial

A
ge
−S

pe
ci

fic
 P

re
va

le
nc

e

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument



•    Vanessa di Lego, Markus Sauerberg128

Figure 3 presents these estimates in comparison with the offi cial assumption 
used by the EU to estimate HLY, which considers that below age 15 the prevalence 
of disability is half of the observed in the age group 16-19. The model extrapolates 
reasonably well until age 100 and retains most of the pattern observed until age 80+. 
Denmark and Sweden have the most uncertainty with regard to the extrapolation 
after age 80 and before age 15 for men, as shown by the wider confi dence intervals. 
The same is observed for Finnish women before age 15. Overall, similar to what was 
observed in Figure 1, countries for which smoothing the age pattern seem to show 
the largest differences are Finland (especially at younger ages for women), Denmark 
and Sweden. 

Fig. 6: Total person-years lived and person-years lived without disability, by 
smoothing method and sex, selected EU countries age 80+, 2017

Finland France Spain

W
om

en
M

en

0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

20000

40000

60000

80000

100000

20000

40000

60000

80000

100000

Denmark Netherlands Sweden

W
om

en
M

en

0 20 40 60 80 0 20 40 60 80 0 20 40 60 80

40000

60000

80000

100000

40000

60000

80000

100000

Age

Type Obs. Person−Years Lived  no disability
Person−Years lived 
 no disability Penalty

Person−Years lived 
 no disability Polynomial

Person−Years lived 
 no disability Splines Total Person−Years lived

P
er

so
n−

Ye
ar

s 
Li

ve
d 

(L
x)

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 
Eurostat



The Sensitivity of the Healthy Life Years Indicator    • 129

We present the case of Germany separately due to the particularity of its age 
pattern and the last observed age available in the EU-SILC change from year 2015. 
Before 2015, Germany had the last age available at 80+. However, from year 2015 
on, the age changed to 74+ affecting not only the comparability with other countries 
where the available ages remain 80+, but also the comparability of Germany across 
the years. Interestingly, as Figure 4 shows, the age pattern for Germany is neither 
as linear-like as in Denmark, the Netherlands and Sweden nor as exponential-like as 
Spain, Finland and France, but follows an almost linear pattern until around age 40, 
when the prevalence of disability increases. Similar to the shape for Danish men, 
the prevalence starts to decline from around ages 70 on. As shown in Figure 5, a 
GAM fi ts well to German data. The extrapolation has higher uncertainty starting 
from age 80 on but it is still a good fi t considering that no information is available 
and thus may be a good model to harmonise data at older ages.

After smoothing and extrapolating the age-specifi c prevalence, we compute the 
person-years lived without disability for the observed and smoothed age-specifi c 
prevalence, by multiplying the estimated age-specifi c prevalence subtracted from 
one (1-πi+ni) from the surveys with the total person-years lived by age Li+ni retrieved 
from the Eurostat life tables for each country, following Equation 1. In Figure 6, 
we present the total person-years lived and person-years lived without disability, 
considering each smoothing method, until age 80+.

In terms of person-years lived without disability, the different smoothing 
methods yield almost the same profi les by age when compared to the observed 
values, represented by the grey line with dots. The exception is for Finnish women, 
where, as already previously noted in Figures 1-2, the smoothing splines are very 
fl exible, overfi tting the data, instead of providing a smoothed curve. Irrespective 
of smoothing methods, Figure 6 shows how the age pattern of person-years lived 

^

Fig. 7: Total person-years lived and person-years lived without disability, by 
smoothing method and sex, Germany, age 74+, 2017

Women Men

G
erm

any

0 20 40 60 0 20 40 60

60000

80000

100000

Age

Type Obs. Person−Years Lived  no disability
Person−Years lived 
 no disability Penalty

Person−Years lived 
 no disability Polynomial

Person−Years lived 
 no disability Splines Total Person−Years lived

P
er

so
n−

Ye
ar

s 
Li

ve
d 

(L
x)

Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 
Eurostat



•    Vanessa di Lego, Markus Sauerberg130

without disability is more compressed for Sweden and Spain for both sexes in 
2017, as evidenced by the shorter distance between the curve of total person-years 
lived and person-years lived without disability. In addition, men present a more 
compressed profi le than women across the majority of countries. For Denmark 
and the Netherlands, we observe an almost linear pattern in the decline of person-
years lived without disability across age, with a steeper decline in the proportion 
of person-years lived without disability as age increases, when compared to other 
countries. For Germany, as shown in Figure 7, the age pattern of person-years lived 
without disability is also more compressed for men than women and the pattern of 
decline is less steep until age 40, when the decline is steeper and linear until age 
74+. 

3.2 The Sensitivity of Healthy Life Years (HLY)

We combine the estimated and smoothed age-specifi c prevalence as presented in 
section 3.1 with the person-years lived in order to compute the HLY indicator and 
evaluate whether there are any differences by smoothing technique. Total HLY and 
the proportion of total life expectancy (LE) spent in healthy life years (%HLY = HLY/
LE) for selected countries by different smoothing technique and extrapolation by 
sex are presented in Tables 2-3, for age 0 (Table 2) and age 65 (Table 3), respectively. 
Overall, differences across smoothing methods are greater for HLY estimates at 
birth (Table 2) than at age 65 (Table 3). Furthermore, if one considers HLY estimated 
using half the disability as the benchmark for comparison, differences are greater 
for women than for men across methods for the majority of countries.

The proportion of total life expectancy in healthy state (%HLY) is barely affected 
for most smoothing approaches used, with the exception of GAMs, with varying 
magnitudes across countries. Again, using half the disability as the benchmark for 
comparison, GAMs underestimate both HLY at birth and at age 65 for all countries 
presented here. This most likely refl ects the fact that we are extrapolating age-
specifi c prevalence to ages above 100, so estimating a higher burden of prevalence 
in the population. For the splines penalty and polynomial fi ts the results are virtually 
the same, varying only in the second or third decimal.

As expected, for the HLY estimates at age 65 there are no differences between 
the no disability and half the disability assumption, as these assumptions do not 
affect estimates for HLY beyond age 0. In order to provide a clearer picture of the 
variation across methods, Table 4 summarises the absolute differences in values 
at age 0, where  differences between no disability and half the disability (columns 
(1)-(2)) range from 1.2 years at birth for women in Finland to 0.5 in Spain and 1.2 
years at birth for men in Finland to 0.6 for men in Spain (See Tables A1-A2 in the 
Appendix for the values for all countries available in EU-SILC for each smoothing 
technique and Tables A3 and A4 with the values with 95% confi dence intervals). Not 
surprisingly, for the assumption of no disability below age 15 in the population, the 
HLY is larger when compared to the assumption that the population below age 15 
experiences half of the observed disability of the age group 16-19 (columns (1)-(2)).



The Sensitivity of the Healthy Life Years Indicator    • 131

When comparing the no disability below age 15 scenario versus any of the 
smoothing methods (see differences computed for columns (1)-(2), (1)-(3), (1)-(4) 
and (1)-(5)), which were applied on half the disability curve,  GAMs present the 

Tab. 2: Healthy Life Years (HLY) and %HLY of total life expectancy at birth, 
by different smoothing methods, extrapolation and sex, selected EU 
countries, 2017

Country Assumptions and smoothing methods, HLY at age 0
No disability Half the Splines Polynomial GAM*

disability† penalty
HLY %HLY HLY %HLY HLY %HLY HLY %HLY HLY %HLY

Women
Denmark 60.4 72.7 59.8 72.0 59.9 72.0 59.9 72.0 57.4 69.1
Spain 70.3 81.6 69.8 81.0 70.3 81.6 70.3 81.6 68.8 79.9
Finland 57.8 68.4 56.6 67.0 57.5 68.0 57.4 68.0 53.4 63.2
France 66.7 77.8 66.2 77.3 66.3 77.4 66.3 77.4 65.6 76.5
Netherlands 58.0 69.6 56.9 68.3 57.4 68.8 57.4 68.9 55.2 66.2
Sweden 72.1 85.7 70.5 83.9 71.2 84.6 71.3 84.8 70.8 84.2
Germany** 68.1 81.6 67.5 80.9 67.1 80.4 67.1 80.4 66.2 79.4

Men
Denmark 59.7 75.4 59.1 74.6 59.3 74.8 59.3 74.9 57.1 72.1
Spain 69.3 86.0 68.6 85.2 68.8 85.3 68.9 85.4 68.5 85.0
Finland 59.0 74.8 57.8 73.3 58.3 73.9 58.3 73.9 57.0 72.2
France 63.8 80.1 63.5 79.8 63.6 79.9 63.6 79.9 62.8 78.9
Netherlands 62.1 77.4 61.6 76.9 61.9 77.2 61.9 77.2 60.4 75.3
Sweden 73.1 90.5 72.7 89.9 73.1 90.5 73.0 90.4 70.9 87.7
Germany** 66.1 83.9 65.7 83.5 65.3 83.0 65.3 83.0 64.8 82.4

Note: Small differences between the offi cial EU HLY indicator may occur since Eurostat 
uses life tables that close at age 85+, while we recalculate the Eurostat life tables to close 
at either 80+ or 74+ by summing the person-years lived at each age and then computing 
the life table following the conventional procedure of Preston et al. (2001). 
† Half the disability is the offi cial EU assumption for ages below 16 and more closely refl ects 
the offi cial EU statistics. However, we are using age-specifi c prevalence and Eurostat life 
tables by single years of age, while the offi cial estimates are from 5-year age groups, so 
differences may occur for some countries. Refer to the Appendix for calculations using 
5-year age groups and that match or have very little difference from the offi cial estimates. 
%HLY=HLY/LE represents the proportion of life expectancy spent in a healthy state. 
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, when 
both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 
Eurostat



•    Vanessa di Lego, Markus Sauerberg132

largest differences, with Finnish women experiencing a difference of 4.4 years. 
Noteworthily, the GAM scenario is with both the prevalence extrapolated to age 100 
and with a life table closed at age 100+, which can also refl ect on the absolute values. 

Tab. 3: Healthy Life Years (HLY) and %HLY of total life expectancy at age 65, 
by different smoothing methods, extrapolation and sex, selected EU 
countries, 2017

Country Assumptions and smoothing methods, HLY at age 65
No disability Half the Splines Polynomial GAM*

disability† penalty
HLY %HLY HLY %HLY HLY %HLY HLY %HLY HLY %HLY

Women
Denmark 12.0 57.7 12.0 57.7 11.9 57.3 11.9 57.1 11.4 55.0
Spain 12.5 53.3 12.5 53.3 12.9 55.3 12.9 55.1 11.3 48.5
Finland 9.5 42.8 9.5 42.8 10.3 46.8 10.2 46.3 8.8 39.8
France 12.2 51.5 12.2 51.5 12.3 51.8 12.2 51.6 11.8 49.6
Netherlands 9.6 45.5 9.6 45.5 10.1 47.5 10.0 47.4 9.3 43.9
Sweden 15.7 72.8 15.7 72.8 16.3 75.6 16.3 75.8 15.2 70.7
Germany** 13.2 62.1 13.2 62.1 12.8 60.2 12.8 60.3 11.8 55.8

Men
Denmark 11.0 60.4 11.0 60.4 11.3 62.0 11.3 62.0 10.7 58.6
Spain 12.3 63.9 12.3 63.9 12.4 64.1 12.4 64.0 11.7 60.5
Finland 8.8 47.8 8.8 47.8 9.2 49.7 9.1 49.6 8.5 46.0
France 10.1 51.7 10.1 51.7 10.2 52.0 10.1 51.6 9.9 50.7
Netherlands 10.1 54.2 10.1 54.2 10.3 55.3 10.3 55.1 9.7 51.7
Sweden 15.1 78.9 15.1 78.9 15.6 81.4 15.6 81.2 14.9 77.8
Germany** 11.9 65.7 11.9 65.7 11.5 63.6 11.5 63.5 10.8 59.6

Note: Small differences between the offi cial EU HLY indicator may occur since Eurostat 
uses life tables that close at age 85+, while we recalculate the Eurostat life tables to close 
at either 80+ or 74+ by summing the person-years lived at each age and then computing 
the life table following the conventional procedure of Preston et al. (2001). 
† Half the disability is the offi cial EU assumption for ages below 16 and more closely refl ects 
the offi cial EU statistics. However, we are using age-specifi c prevalence and Eurostat life 
tables by single years of age, while the offi cial estimates are from 5-year age groups, so 
differences may occur for some countries. Refer to the Appendix for calculations using 
5-year age groups and that match or have very little difference from the offi cial estimates. 
%HLY=HLY/LE represents the proportion of life expectancy spent in a healthy state 
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, when 
both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 

Eurostat



The Sensitivity of the Healthy Life Years Indicator    • 133

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-y
e
ar

s 
liv

e
d

 a
t 

e
ac

h
 a

g
e
 a

n
d

 t
h

e
n

 c
o

m
p

u
ti

n
g

 t
h

e
 l

if
e
 t

ab
le

 f
o

llo
w

in
g

 t
h

e
 

co
n

v
e
n

ti
o

n
al

 p
ro

ce
d

u
re

 o
f 

P
re

st
o

n
 e

t 
a
l.
 (

2
0
0
1
).

†  
H

al
f 

th
e
 d

is
ab

ili
ty

 i
s 

th
e
 o

ffi
 c

ia
l 

E
U

 a
ss

u
m

p
ti

o
n

 f
o

r 
ag

e
s 

b
e
lo

w
 1

5
 a

n
d

 m
o

re
 c

lo
se

ly
 r

e
fl 

e
ct

s 
th

e
 o

ffi
 c

ia
l 

E
U

 s
ta

ti
st

ic
s.

 H
o

w
e
v
e
r,
 w

e
 a

re
 u

si
n

g
 a

g
e

-
sp

e
ci
fi 

c 
p

re
v
al

e
n

ce
 a

n
d

 E
u

ro
st

at
 li

fe
 t

ab
le

s 
b

y
 s

in
g

le
 y

e
ar

s 
o

f 
ag

e
, w

h
ile

 t
h

e
 o

ffi
 c

ia
l e

st
im

at
e
s 

ar
e
 f
ro

m
 5

-y
e
ar

 a
g

e
 g

ro
u

p
s,

 s
o

 d
if

fe
re

n
ce

s 
m

ay
 o

cc
u

r 
fo

r 
so

m
e
 c

o
u

n
tr

ie
s.

 R
e
fe

r 
to

 t
h

e
 A

p
p

e
n

d
ix

 f
o

r 
ca

lc
u

la
ti

o
n

s 
u

si
n

g
 5

-y
e
ar

 a
g

e
 g

ro
u

p
s 

an
d

 t
h

at
 m

at
ch

 o
r 

h
av

e
 v

e
ry

 li
tt

le
 d

if
fe

re
n

ce
 f
ro

m
 t

h
e
 o

ffi
 c

ia
l e

st
im

at
e
s.

*  
Fo

r 
th

e
 H

LY
 e

st
im

at
e
s 

p
e
rf

o
rm

e
d

 b
y
 s

m
o

o
th

in
g

 a
n

d
 e

x
tr

ap
o

la
ti

n
g

 t
h

e
 a

g
e

-s
p

e
ci
fi 

c 
p

re
v
al

e
n

ce
 u

si
n

g
 G

A
M

, w
e
 e

x
tr

ap
o

la
te

d
 t

h
e
 E

u
ro

st
at

 li
fe

 t
ab

le
s 

to
 

ag
e
 1

0
0
+

 u
si

n
g

 t
h

e
 M

ak
e
h

am
 L

aw
 o

f 
M

o
rt

al
it

y.
**

 F
o

r 
G

e
rm

an
y,

 e
x
ce

p
ti

o
n

al
ly

, 
th

e
 c

lo
se

o
u

t 
ag

e
 w

as
 7

4
+

 i
n

 a
ll 

v
ar

ia
n

ts
 e

x
ce

p
t 

G
A

M
, 

w
h

e
n

 b
o

th
 t

h
e
 a

g
e

-s
p

e
ci
fi 

c 
p

re
v
al

e
n

ce
 a

n
d

 t
h

e
 l

if
e
 t

ab
le

s 
ar

e
 

e
x
tr

ap
o

la
te

d
 t

o
 a

g
e
 1

0
0
+

. 
S

o
u

rc
e
: 

O
w

n
 c

al
cu

la
ti

o
n

s 
u

si
n

g
 E

U
-S

IL
C

 p
re

v
al

e
n

ce
 d

at
a 

b
as

e
d

 o
n

 t
h

e
 G

A
LI

 in
st

ru
m

e
n

t;
 E

u
ro

st
at



•    Vanessa di Lego, Markus Sauerberg134

Again, the overall differences between half the disability and GAMs are larger for 
women than for men, with the exception of France and Sweden. When considering 
the offi cial assumption of half the disability (presented in columns (2)-(3), (2)-(4), (2)-
(5)), the differences invert signs for splines with penalty and polynomial fi t for some 
countries, meaning that the smoothed HLY values are slightly higher than without 
smoothing, but the differences are very small. Between the splines with penalty 
and polynomial fi t there is virtually no difference in the smoothed HLY, so that the 
difference between these two smoothing methods and the offi cial assumption is 
very similar, with differences in the second or third decimal order (not shown as the 
values are all rounded to one decimal only). The difference for splines with penalty 
(columns (2)-(3)) is -0.9 and -0.6 years for Finnish and Swedish women respectively, 
while it is -0.8 for both Swedish and Finnish women for the polynomial (columns 
(2)-(4)). For all other countries, the differences between splines with penalty and 
polynomial are the same. Comparing the offi cial assumption of half disability with 
GAMs (columns (2)-(5)), the signs are positive again with Finnish women leading 
the greatest difference of 3.2 years, followed by German women with 2.4 years. For 
men, the magnitude of these differences is smaller than for women, but is also the 
highest across all approaches, with Danish men experiencing a difference of 1.9 in 
HLY at birth when comparing half the disability with GAM (columns (2)-(5)), followed 
by Swedish men (1.7 years). 

Unsurprisingly, when considering HLY at age 65, there are no differences between 
estimating HLY with no disability and half the disability for any country and for any 
of the smoothing and extrapolation approaches, as shown in columns (1) and (2) 
of Table 5. The assumptions of no disability and half the disability for ages below 
16 do not affect HLY estimates at age 65, so there is no difference between these 
two scenarios. As with the HLY estimates at birth, there is almost no difference 
between splines with penalty and polynomial fi t across countries for both sexes, 
with differences appearing only in the second decimal. In addition, the differences 
between HLY estimates at age 65 and at birth are smaller across all smoothing 
methods. The largest differences observed are between either no disability at 
birth and half the disability and GAMs extrapolated to age 100+ for both sexes in 
Germany, with differences of 1.3 years for women and 1.1 for men (columns (1)-(5) 
and (2)-(5)). However, unlike for HLY estimates at birth, the difference between the 
assumption half the disability and GAMs is not higher than for other smoothing 
methods. While for women in Germany, Denmark, Spain and France this is true, 
for women in Finland, Netherlands and Sweden the differences are actually higher 
between the assumption half the disability and polynomial or penalty fi ts (columns 
(2)-(3) and (2)-(4)), albeit in the negative direction (i.e., considering half the disability 
as the benchmark, HLY estimated with the smoothing methods is higher than the 
assumption of half the disability). For men in Denmark and Finland, the magnitude 
of the difference between half the disability and GAMs and half the disability and 
penalty or polynomial at age 65 is the same, but in opposite directions (i.e., HLY 
estimated by GAM is higher, by the other methods it is lower than the assumption 
half the disability).



The Sensitivity of the Healthy Life Years Indicator    • 135

C
o

u
n

tr
y

A
ss

u
m

p
ti

o
n

s,
 s

m
o

o
th

in
g

 a
n

d
 e

x
tr

a
p

o
la

ti
o

n
m

e
th

o
d

s,
 H

LY
 a

t 
a
g

e
 6

5

N
o

H
a
lf

 t
h

e
S

p
lin

e
s

P
o

ly
n

o
m

ia
l 

G
A

M
*

A
b

s.
 D

if
f 

H
LY

d
is

a
b

ili
ty

d
is

a
b

ili
ty

†
p

e
n

a
lt

y

(1
)

(2
)

(3
)

(4
)

(5
)

(1
)-

(2
)

(1
)-

(3
)

(1
)-

(4
)

(1
)-

(5
)

(2
)-

(3
)

(2
)-

(4
)

(2
)-

(5
)

W
o

m
e

n
D

e
n

m
a
rk

12
.0

12
.0

11
.9

11
.9

11
.4

0
.0

0
.1

0
.1

0
.6

0
.1

0
.1

0
.6

S
p

a
in

12
.5

12
.5

12
.9

12
.9

11
.3

0
.0

-0
.5

-0
.4

1.
1

-0
.5

-0
.4

1.
1

F
in

la
n

d
9

.5
9

.5
10

.3
10

.2
8

.8
0

.0
-0

.9
-0

.8
0

.7
-0

.9
-0

.8
0

.7
F

ra
n

ce
12

.2
12

.2
12

.3
12

.2
11

.8
0

.0
-0

.1
0

.0
0

.4
-0

.1
0

.0
0

.4
N

e
th

e
rl

a
n

d
s

9
.6

9
.6

10
.1

10
.0

9
.3

0
.0

-0
.4

-0
.4

0
.3

-0
.4

-0
.4

0
.3

S
w

e
d

e
n

15
.7

15
.7

16
.3

16
.3

15
.2

0
.0

-0
.6

-0
.7

0
.4

-0
.6

-0
.7

0
.4

G
e

rm
a
n

y
**

13
.2

13
.2

12
.8

12
.8

11
.8

0
.0

0
.4

0
.4

1.
3

0
.4

0
.4

1.
3

M
e

n
D

e
n

m
a
rk

11
.0

11
.0

11
.3

11
.3

10
.7

0
.0

-0
.3

-0
.3

0
.3

-0
.3

-0
.3

0
.3

S
p

a
in

12
.3

12
.3

12
.4

12
.4

11
.7

0
.0

0
.0

0
.0

0
.7

0
.0

0
.0

0
.7

F
in

la
n

d
8

.8
8

.8
9

.2
9

.1
8

.5
0

.0
-0

.4
-0

.3
0

.3
-0

.4
-0

.3
0

.3
F

ra
n

ce
10

.1
10

.1
10

.2
10

.1
9

.9
0

.0
-0

.1
0

.0
0

.2
-0

.1
0

.0
0

.2
N

e
th

e
rl

a
n

d
s

10
.1

10
.1

10
.3

10
.3

9
.7

0
.0

-0
.2

-0
.2

0
.5

-0
.2

-0
.2

0
.5

S
w

e
d

e
n

15
.1

15
.1

15
.6

15
.6

14
.9

0
.0

-0
.5

-0
.4

0
.2

-0
.5

-0
.4

0
.2

G
e

rm
a
n

y
**

11
.9

11
.9

11
.5

11
.5

10
.8

0
.0

0
.4

0
.4

1.
1

0
.4

0
.4

1.
1

T
a

b
. 

5:
 

H
e

a
lt

h
y
 L

if
e
 Y

e
a
rs

 (
H

LY
) 

a
t 

a
g

e
 6

5
 a

n
d

 a
b

so
lu

te
 d

if
fe

re
n

ce
s 

a
cr

o
ss

 d
if

fe
re

n
t 

a
ss

u
m

p
ti

o
n

s,
 e

x
tr

a
p

o
la

ti
o

n
 a

n
d

 
sm

o
o

th
in

g
 m

e
th

o
d

s,
 b

y
 s

e
x

, 
se

le
c
te

d
 E

U
 c

o
u

n
tr

ie
s,

 2
01

7

N
o

te
: 

S
m

al
l 

d
if

fe
re

n
ce

s 
b

e
tw

e
e
n

 t
h

e
 o

ffi
 c

ia
l 

E
U

 H
LY

 i
n

d
ic

at
o

r 
m

ay
 o

cc
u

r 
si

n
ce

 E
u

ro
st

at
 u

se
s 

lif
e
 t

ab
le

s 
th

at
 c

lo
se

 a
t 

ag
e
 8

5
+

, 
w

h
ile

 w
e
 r

e
ca

lc
u

la
te

 
th

e
 E

u
ro

st
at

 l
if

e
 t

ab
le

s 
to

 c
lo

se
 a

t 
e
it

h
e
r 

8
0
+

 o
r 

7
4
+

 b
y
 s

u
m

m
in

g
 t

h
e
 p

e
rs

o
n

-y
e
ar

s 
liv

e
d

 a
t 

e
ac

h
 a

g
e
 a

n
d

 t
h

e
n

 c
o

m
p

u
ti

n
g

 t
h

e
 l

if
e
 t

ab
le

 f
o

llo
w

in
g

 t
h

e
 

co
n

v
e
n

ti
o

n
al

 p
ro

ce
d

u
re

 o
f 

P
re

st
o

n
 e

t 
a
l.
 (

2
0
0
1
).

† 
H

al
f 

th
e
 d

is
ab

ili
ty

 i
s 

th
e
 o

ffi
 c

ia
l 

E
U

 a
ss

u
m

p
ti

o
n

 f
o

r 
ag

e
s 

b
e
lo

w
 1

5
 a

n
d

 m
o

re
 c

lo
se

ly
 r

e
fl 

e
ct

s 
th

e
 o

ffi
 c

ia
l 

E
U

 s
ta

ti
st

ic
s.

 H
o

w
e
v
e
r,
 w

e
 a

re
 u

si
n

g
 a

g
e

-
sp

e
ci
fi 

c 
p

re
v
al

e
n

ce
 a

n
d

 E
u

ro
st

at
 li

fe
 t

ab
le

s 
b

y
 s

in
g

le
 y

e
ar

s 
o

f 
ag

e
, w

h
ile

 t
h

e
 o

ffi
 c

ia
l e

st
im

at
e
s 

ar
e
 f
ro

m
 5

-y
e
ar

 a
g

e
 g

ro
u

p
s,

 s
o

 d
if

fe
re

n
ce

s 
m

ay
 o

cc
u

r 
fo

r 
so

m
e
 c

o
u

n
tr

ie
s.

 R
e
fe

r 
to

 t
h

e
 A

p
p

e
n

d
ix

 f
o

r 
ca

lc
u

la
ti

o
n

s 
u

si
n

g
 5

-y
e
ar

 a
g

e
 g

ro
u

p
s 

an
d

 t
h

at
 m

at
ch

 o
r 

h
av

e
 v

e
ry

 li
tt

le
 d

if
fe

re
n

ce
 f
ro

m
 t

h
e
 o

ffi
 c

ia
l e

st
im

at
e
s.

 
* 

Fo
r 

th
e
 H

LY
 e

st
im

at
e
s 

p
e
rf

o
rm

e
d

 b
y
 s

m
o

o
th

in
g

 a
n

d
 e

x
tr

ap
o

la
ti

n
g

 t
h

e
 a

g
e

-s
p

e
ci
fi 

c 
p

re
v
al

e
n

ce
 u

si
n

g
 G

A
M

, w
e
 e

x
tr

ap
o

la
te

d
 t

h
e
 E

u
ro

st
at

 li
fe

 t
ab

le
s 

to
 

ag
e
 1

0
0
+

 u
si

n
g

 t
h

e
 M

ak
e
h

am
 L

aw
 o

f 
M

o
rt

al
it

y.
 

**
 F

o
r 

G
e
rm

an
y,

 e
x
ce

p
ti

o
n

al
ly

, 
th

e
 c

lo
se

o
u

t 
ag

e
 w

as
 7

4
+

 i
n

 a
ll 

v
ar

ia
n

ts
 e

x
ce

p
t 

G
A

M
, 

w
h

e
n

 b
o

th
 t

h
e
 a

g
e

-s
p

e
ci
fi 

c 
p

re
v
al

e
n

ce
 a

n
d

 t
h

e
 l

if
e
 t

ab
le

s 
ar

e
 

e
x
tr

ap
o

la
te

d
 t

o
 a

g
e
 1

0
0
+

. 
S

o
u

rc
e
: 

O
w

n
 c

al
cu

la
ti

o
n

s 
u

si
n

g
 E

U
-S

IL
C

 p
re

v
al

e
n

ce
 d

at
a 

b
as

e
d

 o
n

 t
h

e
 G

A
LI

 in
st

ru
m

e
n

t;
 E

u
ro

st
at



•    Vanessa di Lego, Markus Sauerberg136

In other words, if we consider the assumption of half the disability the benchmark 
for comparison, GAMs tend to underestimate HLY at birth and at age 65 while 
penalty and polynomial tend to slightly overestimate HLY for all countries. However, 
at age 65, the magnitude of these differences is smaller.

The magnitude of these differences across HLY estimates are in line with what 
was observed by visual inspection in Figures 1-3, where, for example, the distribution 
of the observed prevalence by age for countries like Spain is already relatively 
smoother than the profi les of Denmark, Finland and the Netherlands, with seemingly 
shorter distances between the observed values and the smoothed curves. In any 
case, the differences are larger for HLY at birth. Indeed, the confi dence intervals for 
those estimates are also wider so they have more uncertainty than the estimates for 
HLY at age 65, as shown in Tables 6 and 7 (See Tables A3 and A4 for all countries).

Tables 6 and 7 show how while the confi dence intervals for HLY estimates at birth 
can be as high as 8 years within the selected countries (women in Finland, 57.5 (95% 
CI 53.5-61.4) and men in Denmark, 59.3 (95% CI 55.0-63.0, both splines penalty), the 
interval for HLY estimates at age 65 does not exceed 2.6 years (women in Finland, 
10.3 (95% CI 9.1-11.6) splines penalty). The estimates with the wider confi dence 
intervals are splines with penalty while GAMs present lower uncertainty in the 
measures. Irrespective of method and whether the prevalence was extrapolated or 
not, the estimates for HLY at age 65 have lower uncertainty. 

As a means of comparatively assessing the performance across the methods, 
we estimated the root mean square error (RMSE) as presented in Table 8 (see Table 
A7 for all countries). Indeed, with the exception of Denmark for both sexes and 
for Finnish women where GAMs deviate more strongly from the other models, for 
most countries the performance of the models are similar, with GAM presenting 
slightly higher scores. The higher the score, the poorer the performance of the 
method, relatively. Nonetheless, other factors are important to account for in order 
to evaluate performance and which method is more appropriate. Even though the 
smoothing splines present the lowest scores in most cases, this may in part be 
due to the extreme fl exibility, which can lead to overfi tting the data (as Fig. 1  and 
2 show for the case of Finland). As shown in Tables 6 and 7 they also yield the 
widest confi dence intervals and the most uncertainty when estimating HLY at birth, 
suggesting that at least for some countries smoothing age specifi c prevalence with 
a very fl exible model yields overfi tted results. Alternatively, splines with penalty 
and polynomial provide a similar result with an adjustment that is not as fl exible 
as smoothing splines, also shown in Figures 1 and 3, and with lower uncertainty in 
the estimates. However, these methods are still sensitive to variations throughout 
the age structure, for example capturing the decreasing prevalence after age 75 
in Denmark, which is not guaranteed to be a real effect or simply a data artifact 
and upticks in older ages for France. In this case, polynomials may be best when 
there is not so much variance in the data, as their estimated HLY values have lower 
uncertainty than the penalty. GAMs present the highest RMSE scores and thus have 
the highest distance from the observed data, despite the differences being small for 
the majority of countries (with the exception of Denmark and Finnish women). It is 
unclear whether this is due to the fact that GAMs seem to be particularly affected 



The Sensitivity of the Healthy Life Years Indicator    • 137

by the pattern below age 15. This effect is relatively smaller when the modelling is 
done by 5-year age groups, but not enough to eliminate this effect (see Appendix, 
Fig. A3-5 and Tables A5-6). 

As previously shown, differences across methods varied for women and men 
depending on the smoothing method and country. For example, we showed that 
for some countries the difference between half the disability and GAMs is larger for 

Tab. 6: Healthy Life Years (HLY) at birth with 95% confi dence intervals, by 
different smoothing methods, extrapolation and sex, selected EU 
countries, 2017, half-disability assumption

Smoothing and extrapolating methods, HLY at Age 0
Country Splines penalty Polynomial GAM*

HLY 95%CI HLY 95%CI HLY 95%CI

Women
Denmark 59.9 55.8 63.5 59.9 56.7 62.6 57.4 54.7 60.2
Spain 70.3 68.4 72.1 70.3 68.8 71.8 68.8 67.3 70.3
Finland 57.5 53.5 61.4 57.4 54.4 60.4 53.4 49.7 57.1
France 66.3 64.1 68.4 66.3 64.6 68.1 65.6 64.3 66.9
Netherlands 57.4 54.3 60.4 57.4 54.9 59.9 55.2 53.1 57.3
Sweden 71.2 67.6 74.7 71.3 68.6 73.9 70.8 68.5 73.1
Germany** 67.1 65.2 68.9 67.1 65.6 68.5 66.2 64.8 67.7

Men
Denmark 59.3 55.0 63.0 59.3 56.0 62.1 57.1 53.9 60.3
Spain 68.8 66.9 70.7 68.9 67.4 70.4 68.5 67.6 69.5
Finland 58.3 55.1 61.5 58.3 55.9 60.7 57.0 54.7 59.2
France 63.6 61.3 65.6 63.6 61.8 65.0 62.8 61.3 64.3
Netherlands 61.9 59.2 64.3 61.9 59.9 63.7 60.4 58.9 61.9
Sweden 73.1 70.5 75.5 73.0 71.0 74.8 70.9 68.0 73.7
Germany** 65.3 63.5 67.1 65.3 63.8 66.7 64.8 63.5 66.2

Note: Small differences between the offi cial EU HLY indicator may occur since Eurostat 
uses life tables that close at age 85+, while we recalculate the Eurostat life tables to close 
at either 80+ or 74+ by summing the person-years lived at each age and then computing 
the life table following the conventional procedure of Preston et al. (2001). However, we 
are using age-specifi c prevalence and Eurostat life tables by single years of age, while 
the offi cial estimates are from 5-year age groups, so differences may occur for some 
countries. Refer to the Appendix for calculations using 5-year age groups and that match 
or have very little difference from the offi cial estimates. 
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, 
when both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 

Eurostat



•    Vanessa di Lego, Markus Sauerberg138

women than men. Hence, in order to provide a clearer picture of these differences 
and whether existing sex gaps in HLY estimates are affected by the smoothing 
methods, we used the estimates to calculate gender differences in HLY across 
countries for all the methods used, as presented in Figure 8. The absolute gender 
differences in HLY estimates are higher at birth than at age 65 and more markedly so 
for some countries, like the Netherlands and Finland. As already shown in Tables 4 

Tab. 7: Healthy Life Years (HLY) at age 65 with 95% confi dence intervals, by 
different smoothing methods, extrapolation and sex, selected EU 
countries, 2017, half-disability assumption

Smoothing and extrapolating methods, HLY at age 65
Country Splines penalty Polynomial GAM*

HLY 95%CI HLY 95%CI HLY 95%CI

Women
Denmark 11.9 10.7 13.2 11.9 10.8 13.0 11.4 10.7 12.2
Spain 12.9 12.3 13.6 12.9 12.3 13.4 11.3 10.7 12.0
Finland 10.3 9.1 11.6 10.2 9.1 11.3 8.8 8.0 9.6
France 12.3 11.5 13.0 12.2 11.5 12.9 11.8 11.1 12.4
Netherlands 10.1 9.1 11.0 10.0 9.2 10.9 9.3 8.7 9.9
Sweden 16.3 15.2 17.3 16.3 15.4 17.2 15.2 14.4 16.0
Germany** 12.8 12.1 13.4 12.8 12.2 13.4 11.8 11.2 12.5

 Men
Denmark 11.3 10.1 12.5 11.3 10.2 12.3 10.7 9.8 11.5
Spain 12.4 11.8 12.9 12.4 11.9 12.9 11.7 11.2 12.2
Finland 9.2 8.2 10.1 9.1 8.3 9.9 8.5 7.8 9.1
France 10.2 9.5 10.9 10.1 9.5 10.7 9.9 9.3 10.6
Netherlands 10.3 9.6 11.1 10.3 9.7 11.0 9.7 9.1 10.2
Sweden 15.6 14.9 16.4 15.6 14.9 16.2 14.9 14.1 15.8
Germany** 11.5 10.9 12.1 11.5 11.0 12.0 10.8 10.2 11.4

Note: Small differences between the offi cial EU HLY indicator may occur since Eurostat 
uses life tables that close at age 85+, while we recalculate the Eurostat life tables to close 
at either 80+ or 74+ by summing the person-years lived at each age and then computing 
the life table following the conventional procedure of Preston et al. (2001). However, we 
are using age-specifi c prevalence and Eurostat life tables by single years of age, while 
the offi cial estimates are from 5-year age groups, so differences may occur for some 
countries. Refer to the Appendix for calculations using 5-year age groups and that match 
or have very little difference from the offi cial estimates. 
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, 
when both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument; 

Eurostat



The Sensitivity of the Healthy Life Years Indicator    • 139

and 5, the HLY at birth for women estimated using GAM in Finland is 3.2 years lower 
than the estimated value using the offi cial EU assumption of half the disability below 
age 15. For men, the difference is only of 0.4 years. Thus, the higher gender gap of 
-4.01 shown in Figure 8 for the GAM is driven by the HLY estimate for women (i.e., a 
higher gender gap driven by a larger underestimation of the GAM compared to the 
benchmark of half the disability), while the HLY estimates using the other methods 
are similar, varying from -1.25 (half disability) and -0.80 (penalty). In addition, the 
overall positive gender gap in Spain has its sign reversed at age 65 when comparing 
the gender gap using GAM versus the other methods for HLY estimates.

Finally, we performed some additional exercises that are presented in the 
Appendix (see section The Role of Mortality), as we found it intriguing that the 
differences between smoothed versus unsmoothed HLY estimates seemed far 
smaller than what we expected when comparing the curves of observed versus 
smoothed persons-years lived without disability in Figures 6 and 7. It appears that it 
does not matter very much whether the person-years lived, the Li+ni function, when 
weighted by the age-specifi c prevalence, has a fl uctuating pattern or not, as the 
Sullivan approach sums the persons-years lived across all ages and evens out the 
fl uctuating pattern of disability. In order to test to what extent the summing procedure 
from the Sullivan method ends up capturing the mortality pattern of the Li+ni function 
more than the health prevalence itself, we calculate HLY with standardised mortality 
information, with country-specifi c prevalence data and the EU-28 average mortality 

Tab. 8: Root Mean Square Error (RMSE) by different smoothing methods, 
extrapolation and sex, selected EU countries, 2017, half-disability 
assumption

Country Root Mean Square Error (RMSE)
Women Men

Splines Penalty Polynomial GAM* Splines Penalty Polynomial GAM*

Denmark 0.068 0.069 0.073 0.092 0.079 0.077 0.081 0.092
Spain 0.028 0.029 0.031 0.038 0.029 0.032 0.036 0.039
Finland 0.048 0.064 0.067 0.107 0.056 0.057 0.060 0.063
France 0.036 0.036 0.038 0.041 0.042 0.041 0.042 0.047
Netherlands 0.049 0.051 0.057 0.069 0.046 0.046 0.050 0.055
Sweden 0.051 0.057 0.059 0.063 0.047 0.045 0.047 0.061
Germany** 0.026 0.028 0.030 0.032 0.031 0.031 0.033 0.036

Note: Smoothing methods evaluated with the exception of GAM are until age 80+.
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, 
when both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument 

and smoothing methods; Eurostat



•    Vanessa di Lego, Markus Sauerberg140

information. Consequently, differences in these standardised HLY estimates stem 
solely from differences in country-specifi c prevalence data. In Figure A8 we show 
how EU countries would rank from best to worst after controlling for differences in 
the country’s mortality level. Among men, the country ranking is more affected by 
the mortality information, with changes of up to 8 ranks. This effect is less prominent 
for women in all countries. Changing mortality never affects rankings for women 
more than 3 points. In part, this is due to the fact that there is a larger variation in 
mortality among men across EU countries than among women. However, that is 
not the full story. Even if we replace the EU-28 standard with that of Bulgaria for 
Swedish women who rank high in terms of HLY, their change in ranking would only 
be of 3 points below. This suggests that the HLY indicator appears to refl ect mostly 
differences in GALI prevalence among women, with mortality levels playing a less 
important role, while the opposite is true for men. 

4 Discussion

 The HLY indicator is not only used by researchers to address topics related to 
health and mortality, but is also the cornerstone of many health goals and policies 

Fig. 8: Absolute differences in HLY at birth and at age 65 between women and 
men, by different smoothing methods, selected EU countries, 2017

0 65

Denmark Finland France Germany Netherlands Spain Sweden Denmark Finland France Germany Netherlands Spain Sweden

−4

−2

0

2

Country

A
bs

ol
ut

e 
D

iff
er

en
ce

 in
 H

LY
 e

st
im

at
es

 (W
om

en
−M

en
)

Type GAM Half the disability No disability Polynomial Splines Penalty

Note: Smoothing methods evaluated with the exception of GAM are until age 80+. 
* For the HLY estimates performed by smoothing and extrapolating the age-specifi c 
prevalence using GAM, we extrapolated the Eurostat life tables to age 100+ using the 
Makeham Law of Mortality. 
** For Germany, exceptionally, the closeout age was 74+ in all variants except GAM, 
when both the age-specifi c prevalence and the life tables are extrapolated to age 100+. 
Source: Own calculations using EU-SILC prevalence data based on the GALI instrument 

and smoothing methods; Eurostat



The Sensitivity of the Healthy Life Years Indicator    • 141

developed by the EU. HLY has been used by different Directorate Generals (DG) for 
a variety of initiatives and policies such as Social Protection & Social Inclusion (HLY 
at birth and age 65, by sex), European Pillar of Social Rights on Social Scoreboard 
(HLY at the age of 65, by sex), European Innovation Partnership on Active and 
Healthy Ageing: target 2020 (HLY at birth by sex) and the European Sustainable 
Development Indicator (HLY and life expectancy at birth, by sex), just to mention a 
few (Leonardi 2010; Lagiewka 2012; Bogaert et al. 2018). It is also used in the United 
Nations Active Ageing Index (HLY at the age of 65, by sex) and in over 15 countries in 
the EU region to set health targets and national plans as well as evaluate budget and 
pension policy issues (Oortwijn et al. 2007; Economic and Financial Affairs 2017). 
Hence, it is an important indicator and thus a deep understanding of its potential, 
limitations and sensitivity is key. Indeed, the HLY indicator has been recognised as 
the most suitable indicator for cross-national comparisons, with the GALI instrument 
being harmonised and developed to increase comparability across countries (Van 
Oyen et al. 2006, 2018; Jagger et al. 2010; Berger et al. 2015). Nonetheless, the 
characteristics of the age-specifi c prevalence distribution are still rarely considered 
when employing the indicator and interpreting results, regardless of the fact that 
patterns of prevalence often fl uctuate considerably by age, especially when using 
single ages. In addition, the impact of assumptions used at very young ages on 
HLY estimates are seldom discussed, despite the fact that data on health is only 
collected after age 15 and the majority of policies and initiatives at the EU level use 
HLY at birth. 

A common strategy to deal with the erratic behaviour of age-specifi c prevalence 
has often been to aggregate data into 5-year age groups and combine it with abridged 
life tables in order to estimate HLY (Eurostat 2020). Research has also been directed 
to account for uncertainty in HLY measures caused by survey characteristics (Murray 
et al. 1993; Jagger et al. 2014) and developing confi dence limits for HLY estimates 
that do not require the assumption of a constant proportion of unhealthy individuals 
in an age interval (Andreev/Shkolnikov 2010). In our exploratory analysis, we focus 
on the age-specifi c prevalence behaviour and instead of grouping data into 5-year 
age groups we test whether there is any effect on HLY estimates of smoothing and 
extrapolating the prevalence of disability by age by different methods, country, sex 
and assumptions below age 15. 

Overall, absolute differences across methods are not very substantial and 
smoothing performance is also similar, as supported by the RMSE scores. However, 
the  analyses indicate caution when handling age-specifi c prevalence, particularly 
when considering the assumptions below age 15, with differences across methods 
being in general larger for estimates of HLY at birth and larger for women than men in 
the majority of countries. When using the offi cial EU assumption of half the disability 
as a benchmark for comparison across the three main smoothing and extrapolation 
variants tested (penalty, polynomial and GAMs), the difference between methods 
compared to the benchmark was larger for HLY at birth than at age 65 and usually 
higher for women than for men, with penalty and polynomial smoothing yielding 
similar results. The GAMs extrapolated to ages 100+ provided slightly lower values 
of HLY at age 65 when compared to half the disability benchmark, but differences 



•    Vanessa di Lego, Markus Sauerberg142

between GAMs and half the disability for age 65 were small. However, differences 
between GAMs and half the disability for HLY estimates at birth were sometimes as 
high as 3 years (see women in Finland). 

In addition, the assumption of no disability before age 15 had the highest 
impact on HLY at birth, mainly because it directly impacts the younger ages with 
higher values of person-years lived. Even though the offi cial EU indicator does not 
assume no disability before age 15, comparing estimates with this scenario helps 
to demonstrate the magnitude of the impact of assumptions at younger ages. As 
expected, these assumptions have no impact on the HLY estimates at age 65.

This indicates that  assumptions made at young ages are important and that 
the strategies used to deal with this age group merits attention. Likewise, the fact 
that assumptions affect women and men differently may suggest that different 
parameters by gender are important when the aim is to design gender-specifi c 
policies. This is relevant as most EU policies use HLY at birth and by sex for 
developing and monitoring health policies, like the target by the European Innovation 
Partnership on Active and Healthy Ageing (EIP-AHA), which was set in 2011 with the 
aim of increasing healthy life years at birth by 2 years by 2020 (Jagger et al. 2008; 
Nusselder et al. 2010; Lagiewka 2012; Van Oyen et al. 2013; Luy/Minagawa 2014; 
UNECE/European Commission 2015).

Furthermore, the fact that even after extrapolating to ages 100+ and applying 
different smoothing methods did not impact HLY estimates at age 65 indicates that 
at this age the indicator is less sensitive to age patterns of prevalence than at birth. 
Hence, the Generalised Additive Model (GAM) approach may be a promising tool 
to model and harmonise age-specifi c profi les of disability for cases where there is 
limited or erratic information for older ages or where there is a break in the time series 
with changes in the coverage across ages like the case of Germany. However, it is 
important to note that the level of uncertainty with the extrapolation can be higher 
with GAMs depending from which age the extrapolation occurs. One alternative 
could be to extrapolate only 5 or 10 years in order to harmonise the data and have 
a more robust comparison across countries. This would be an interesting avenue 
for further investigation, as while there is a wide array of demographic and statistics 
methods available to interpolate, graduate and smooth mortality data both at young 
and older ages, strategies for dealing with age-specifi c prevalence are still limited 
in health research, often relying on multistate methods (van der Gaag et al. 2015). 
In part, this is due to the fact that contrary to mortality, health prevalence by age 
may not increase monotonically, as recovery from certain conditions is possible. 
In addition, health is a stock variable sensitive to past experience (Barendregt et 
al. 1997; Brouard/Robine 1992; Murray et al. 2002) and with a complex interaction 
between health and mortality, making it diffi cult to accurately model age-specifi c 
health prevalence (Riffe et al. 2016, 2017). In this regard, it has been shown that 
some relational models provide a good fi t for modelling some types of disabilities by 
age (Marshall et al. 2013), while alternative summary measures that incorporate the 
mortality history of cohorts and therefore combine health and mortality information 
have also been proposed (Sauerberg et al. 2020). However, these methods are 
more important to capture the relationship between age-specifi c prevalence of 



The Sensitivity of the Healthy Life Years Indicator    • 143

disability and various disability types rather than to harmonise and extrapolate 
prevalence at older ages. In addition, since the EU-SILC does not include individuals 
living in institutions, the prevalence of being unhealthy at older ages is likely to 
be systematically biased downwards. Since health data for the institutionalised 
population at a European level is not easy to obtain, extrapolating prevalence data 
to higher ages might be one alternative to account for this issue in the lack of more 
reliable information.

5 Conclusions and recommendations 

The standard practice of combining age-specifi c prevalence proportions with 
person-years lived without proper attention to the distribution profi le of the former 
may affect the estimation of HLY. Although the overall differences seem to be small, 
oftentimes they are not trivial and vary by smoothing method, country, sex and 
age. This suggests that it is important to be more cautious with the age distribution 
of health prevalence prior to combining it with mortality data, especially when 
the indicator of interest is estimated at birth. We have shown in what ways and 
in which direction HLY is sensitive to some assumptions at younger ages and the 
age-specifi c prevalence. However, further research is needed to understand what 
the optimal strategy would be to deal with the age-specifi c prevalence and this will 
more likely depend on the data available and the purpose in using the indicator. 
According to the results of the sensitivity analyses presented in this paper, we 
suggest a routine practice as regards estimating the HLY, as summarised in the 
fl owchart in Figure 9 below. First, as the main sensitivity in the results refers to HLY 
at birth, it is important to consider whether HLY is to be estimated at birth or age 65. 
Second, plot the age-specifi c disability prevalence and evaluate its pattern, as well 
as whether aggregating into 5-year age groups already smooths the pattern. GAMs 
adjust well at ages 65 and older and their impact on HLY is very small, but they 
can impact HLY at birth. In this case, either just estimating HLY based on the usual 
aggregation by 5-year age groups or smoothing by a polynomial fi t can be best. 
Most importantly, always test age profi les for women and men separately, as well 
as country-specifi c patterns. The most important recommendation is to consider 
the purpose of the indicator carefully beforehand and to assess its pattern by age 
before combining it with the person-years lived by age.

It is noteworthy to mention that this recommendation is based on very fl exible 
smoothing methods that we chose since they do not require any assumptions about 
the pattern of prevalence by age. However, future research is needed to develop 
techniques that employ a more robust treatment of those profi les and test whether 
standard demographic procedures used for adjusting age-specifi c distributions are 
equally suitable for health.



•    Vanessa di Lego, Markus Sauerberg144

Acknowledgements
We would like to thank two anonymous reviewers who contributed to improving the 
fi rst version of this paper. This project received funding from the European Research 
Council under the EU’s Horizon 2020 Research and Innovation Programme, Grant 
Agreement No. 725187 (LETHE). This paper is based on data from Eurostat, European 
Union Statistics on Income and Living Conditions European Health Interview Survey 
(EU-SILC), cross-sectional 2017, version release 2 in 2020.

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Source: Own elaboration

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Dr. Markus Sauerberg. Federal Institute for Population Research (BiB). Wiesbaden, 
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Date of submission: 23.01.2022  Date of acceptance: 05.01.2023

https://doi.org/10.1007/s00038-012-0361-1
https://doi.org/10.1186/s13690-018-0270-8
https://doi.org/10.1016/j.lanepe.2020.100023
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https://doi.org/10.1093/eurpub/cky105
mailto:Vanessa.DiLego@oeaw.ac.at
https://www.oeaw.ac.at/vid/people/staff/vanessa-di-lego
mailto:markus.sauerberg@bib.bund.de
https://www.bib.bund.de/EN/Institute/Staff/Sauerberg/Sauerberg.html


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