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The timing of the transition from mortality
compression to mortality delay in Europe,
Japan and the United States
Fanny Janssen
1,2*
and Joop de Beer
2
* Correspondence: f.janssen@rug.nl
1
Population Research Centre,
Faculty of Spatial Sciences,
University of Groningen, P.O. Box
800, 9700, AV, Groningen, The
Netherlands
2
Netherlands Interdisciplinary
Demographic Institute, P.O.Box
11650, 2502, AR, The Hague, The
Netherlands
Abstract
Previous research found evidence for a transition from mortality compression (declining
lifespan variability) to mortality delay (increasing ages at death) in low-mortality countries.
We specifically assessed the year at which increases in life expectancy at birth transitioned
from being predominantly due to mortality compressiontobeingpredominantlydueto
mortality delay in 26 European countries, Japan, and the United States of America (USA),
1950–2014.
To unsmoothed age- and sex-specific death rates from the Human Mortality Database, we
applied the CoDe (compression and delay) mortality model.
Among women, the transition first occurred in the USA around 1950, then in North-Western
Europe (1955–1970) and Southern Europe (1970–1975), and still later in Eastern Europe.
Among men, the transition occurred about 10 years later and is still incomplete in
Eastern Europe. We identified four stages: (1) predominance of compression mainly
due to mortality declines at young ages, (2) declining importance of mortality
compression due to the decreasing impact of mortality declines at young ages, (3)
delay becomes predominant due to the increasing impact of mortality delay and
the counterbalancing effects of mortality compression/expansion at different ages,
and (4) strong predominance of delay accompaniedbystrongadultmortality
declines and declining compression at old ages.
Our results suggest that life expectancy and maximum lifespan will increase further.
With mortality delay, premature mortality and old-age mortality are shifting towards
older ages.
Keywords: Mortality, Life expectancy, Transition, Modal age at death, Mortality
compression, Mortality delay, Shifting mortality
Introduction
Within mortality research, a paradigm shift has occurred: rather than studying trends in
the expected average age at death, or life expectancy at birth (e0), researchers are increas-
ingly studying changes over time in the full age-at-death distribution. To describe the
changes over time in the age-at-death distribution, two scenarios have been distinguished,
which, empirically, can operate simultaneously (Kannisto 2001): (1) mortality compression
(Fries 1980), which results from more people dying at the same ages and is indicative of
declining lifespan variability or declining lifespan disparities (Bergeron-Boucher et al. 2015);
Ge
n
us
© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International
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Janssen and de Beer Genus (2019) 75:10
https://doi.org/10.1186/s41118-019-0057-y
and (2) mortality delay, or the shifting of mortality, whereby the shape of the age-at-death
distribution remains intact but shifts to the right, which results in higher ages at death (Kan-
nisto 2001; Bongaarts 2005; Canudas-Romo 2008;Vaupel2010). Whereas mortality delay
results from a decline in mortality across all ages, differences in the rates of decline across
ageswillcauseachangeintheshapeoftheagepattern of mortality: either mortality com-
pression or, sometimes, even mortality expansion (increasing lifespan variability). Mortality
delay at older ages is described by an increase in the modal age at death (=the age at which
most deaths are occurring)(Canudas-Romo 2008).
By means of decomposition techniques, changes in life expectancy can be decom-
posed into mortality compression and mortality delay (Rossi et al. 2013;Bergeron-
Boucher et al. 2015; de Beer and Janssen 2016). Examining the relative roles of
these two types of change and of the potential changes in these developments over
time provides us with crucial information not only about the determinants of past
mortality trends but also about future trends in both the average and the max-
imum human lifespan. As long as the delaying of mortality to older ages continues,
and, consequently, the modal age at death continues to increase, a limit to life
expectancy is unlikely to be reached in the near future, since the ongoing shift in
the age pattern of mortality will result in further increases in life expectancy.
Moreover, the decrease in death probabilities in old age is contributing to a strong
increase in the number of centenarians (Robine and Caselli 2005). This development in
turn increases the likelihood that some of these centenarians will survive to very old ages,
and thus that the maximum individual lifespan will rise (de Beer et al. 2017).
Previous studies on the changes over time in the age-at-death distribution among
low-mortality countries showed that the relative importance of compression
(measured by declining variability in the age at death) and of delay (measured by
an increase in the modal age at death) to changes in life expectancy are changing
over time. Historically, compression of mortality has played the dominant role in
low-mortality countries (e.g. Wilmoth and Horiuchi 1999; Kannisto 2000,2001;
Robine 2001; Canudas-Romo 2008, Cheung et al. 2009; Smits and Monden 2009;
Engelman et al. 2010; Ouellette and Bourbeau 2011; Bergeron-Boucher et al. 2015).
Since the 1950s, the pattern has been changing (Kannisto 1996; Wilmoth and
Horiuchi 1999;Kannisto2000,2001;Robine2001; Bongaarts 2005; Edwards and
Tuljapurkar 2005; Canudas-Romo 2008;Cheungetal.2008; Cheung et al. 2009;
Thatcher et al. 2010; Ouellette and Bourbeau 2011). A number of scholars who have exa-
mined the long-term changes for low-mortality countries have found evidence that a transi-
tion from mortality compression to mortality delay has been taking place (Cheung et al.
2005; Canudas-Romo 2008; Ouellette and Bourbeau 2011;Bergeron-Boucheretal.2015),
with Japan leading the way in this transition (Cheung et al. 2009; Ouellette and
Bourbeau 2011). Recent formal analysis for low-mortality countries has confirmed that
delayisovertakingcompressioninthechangeinlifeexpectancy(Janssenetal.2015;
Bergeron-Boucher et al. 2015; de Beer and Janssen 2016). Janssen et al. (2015)showed
that the contribution of mortality compression to the overall gain in remaining life
expectancy at age 50 between 1956 and 2009 was consistently less than 50% for the
ten examined European low-mortality countries. Bergeron-Boucher et al. (2015)
found that from 1965 onwards, more than 70% of the increase in e0 among Swedish
women was caused by delay. De Beer and Janssen (2016)showedthattwothirdsof
Janssen and de Beer Genus (2019) 75:10 Page 2 of 23
the increase in e0 between 1950 and 2010 in Japan, France, the USA, and Denmark
was due to delay.
Until now, however, no studies have examined the existence and the timing of a
transition from changes in e0 being predominantly due to mortality compression
to changes in e0 being predominantly due to mortality delay simultaneously for a
large number of countries, including Eastern European countries, or the role of
compression at different ages in this potential transition.
Previous cross-national studies have demonstrated that there have been large diffe-
rences between countries in the extent of delay and compression (e.g. Wilmoth and
Horiuchi 1999; Edwards and Tuljapurkar 2005; Smits and Monden 2009;
Canudas-Romo 2008; Cheung et al. 2008; Engelman et al. 2010; Thatcher et al. 2010;
Shkolnikov et al. 2011; Ouellette and Bourbeau 2011; Gillespie et al. 2014;
Bergeron-Boucher et al. 2015; Janssen et al. 2015; Muszyńska and Janssen 2016). For
example, one study that examined mortality compression for an Eastern European
country (Shkolnikov et al. 2003) observed that the variability in the age at death
increased after 1950 in Russia, a trend that is indicative of mortality expansion
rather than mortality compression. Other research has shown that there are large
differences in variability among countries with similar levels of life expectancy
(Smits and Monden 2009) and that the variability in the age at death increased in
the USA in the 1980s and the early 1990s (Shkolnikov et al. 2011). Thus, it is
likely that the timing of the transition from mortality compression to mortality
delay differs between countries as well.
Recent studies have acknowledged the importance of distinguishing between com-
pression at different ages (e.g. Zhang and Vaupel 2009; Bergeron-Boucher et al.
2015; de Beer and Janssen 2016). In their study of the “dynamic process of mortality
compression”, Zhang and Vaupel (2009) clearly demonstrated that overall mortality
compression depends on the different processes that occur at younger versus older
ages. Vaupel et al. (2011) also emphasised that whereas a reduction in premature
deaths diminishes lifespan disparities, a reduction in old-age mortality increases life-
span disparities. Goldstein and Cassidy (2012) showed that slowing of senescence, i.e.
more reduction of death rates at older ages than at middle age, results in expansion
of mortality, while an equal reduction in death rates across all ages results in a
shift of the age-at-death distribution.
Also, the results of previous studies on compression seem to depend heavily
on whether these analyses examined compression over all ages, or for a selection
of ages only. For example, previous studies that focused on overall compression
(e.g. Wilmoth and Horiuchi 1999;Robine2001;Yashinetal.2001;
Bergeron-Boucher et al. 2015) generally found that compression of mortality had
been stable at least since the 1970s; whereas, the studies that focused on com-
pression above the modal age at death showed that compression continued
through the 1970s and the 1980s (Thatcher et al. 2010; Kannisto 2001; Cheung
et al. 2008), and that stagnating trends have only recently been observed in
some countries (Cheung et al. 2009).
In this paper, we will assess the timing of the point at which increases in e0 transi-
tioned from being predominantly due to mortality compression to being predominantly
due to mortality delay in 26 European countries and in Japan and the USA over the
Janssen and de Beer Genus (2019) 75:10 Page 3 of 23
1950–2014 period. We will also examine the role mortality compression at young,
adult, and old ages that plays in this transition.
Data and methods
For our analysis, we used unsmoothed age-specific death rates from the Human
Mortality Database (2017) by single year of age (up to age 100), by year (1950–2014),
and by sex for all European countries with data from at least 1959 onwards, as
well as for Japan and the USA. After excluding Estonia, Iceland, and Luxembourg
because of data issues, our sample consisted of 26 European countries, Japan, and
the USA.
We divided the European countries into four main regions: Northern Europe
(Denmark, Finland, Ireland, Norway, Sweden, United Kingdom (UK)), Western Europe
(Austria, Belgium, Switzerland, West Germany, France, the Netherlands), Southern
Europe (Italy, Portugal, Spain), and Eastern Europe. We based these geographic cat-
egories on those of the United Nations (2016), although we made some adjustments to
enable that countries with similar e0 values and/or e0 trends were grouped together.
That is, unlike the United Nations, we placed Latvia and Lithuania in Eastern Europe
and distinguished between eastern Germany (Eastern Europe) and western Germany
(Western Europe). We then subdivided the Eastern European countries into the follow-
ing categories: former Soviet republics (Belarus, Russia, and Ukraine), Baltic countries
(Lithuania and Latvia), and remaining Eastern European countries (Bulgaria, the Czech
Republic, East Germany, Hungary, Poland, and Slovakia).
For our modelling exercise, we used the parametric CoDe mortality model
(Compression and delay mortality model), which has been previously described,
validated, and discussed (de Beer and Janssen 2016). We have chosen the CoDe
model because in addition to providing a good model for fitting the full age
pattern of mortality (de Beer and Janssen 2016),itenablesustodistinguish
between mortality delay and mortality compression, and—in doing so—between
mortality compression at young, adult, and old ages. Previous models describing
the full age pattern of mortality (the Thiele model, the Heligman-Pollard model,
the Siler model, the Rogers & Little model, and the Kostaki adaptation of the
Heligman-Pollard model) could not capture mortality delay and mortality compres-
sion (de Beer and Janssen 2016). Previous models that included mortality delay did
not fit the full age pattern of mortality, but instead fitted only adult mortality
(Bongaarts 2005; Horiuchi et al. 2013). The few previous studies that assessed the
relative contributions of mortality delay and mortality compression did not distin-
guish between mortality compression at young, adult, and old ages (Rossi et al. 2013
using the method developed by Rousson and Paccaud 2010; Bergeron-Boucher et al. 2015
using the Siler model; Börger et al. 2018 in their classification system).
The CoDe mortality model uses five additive terms representing mortality at
successive life stages (child mortality, teenage mortality, and mortality during
young adult, middle, and old age) and includes the modal age at death as a
parameter to account for the delay in mortality. The model describes child and
teenage mortality with two simple functions and uses a mixed logistic model with
different slopes for young adult, middle, and old ages. The CoDe mortality model
is defined by:
Janssen and de Beer Genus (2019) 75:10 Page 4 of 23
qxðÞ¼ A
xþBþae x−16ðÞ
1þex−16ðÞ
þIx≤M−hðÞ
b1eb1x−MðÞ
1þb1
geb1x−MðÞ
2
6
6
4
3
7
7
5
þIM−h<x≤MðÞ
b2eb2ðx−MÞ
1þb2
geb2ðx−MÞ
þc1
2
6
6
4
3
7
7
5
þIðx>MÞb3eb3ðx−MÞ
1þb3
geb3ðx−MÞ
þc2
2
6
6
4
3
7
7
5
ð1Þ
where q(x) is the death probability at age x,Areflects infant mortality, Baffects
the decline in mortality with age at young ages, areflects the level of teen morta-
lity. To distinguish the different life stages after teen mortality, we used an indica-
tor function I(.), with Mthe modal age at death and hassumed to be 30, and
added constants c
1
and c
2
—which are calculated from the other parameters—to
enable smooth patterns over age. b
1
and b
2
determine the increase in mortality
with age at ages representing adult premature mortality and b
3
determines the
increaseinmortalitywithageabovethemodalage.Weassumethatg, the upper
bound of q(x), equals 0.7 (de Beer and Janssen 2016).
Appendix 1 illustrates the effects of the main parameters of the CoDe model on
the age-at-death distribution. An increase in the modal age Mdescribes the delay
in mortality, i.e. the shift in the mortality age pattern from younger to older ages—
while the age-at-death distribution retains its shape—that results in increasing life
expectancy at birth (e0). The increase in the modal age also implies that the nor-
mal age at death increases. Without changes in old-age mortality compression, a
delay in mortality also implies a higher maximum age at death. Declines in the
level of infant mortality Aand teen mortality aresult in compression of mortality:
as mortality declines at these ages, a higher concentration of deaths around the
modal age at death occurs. This compression of mortality due to mortality declines
at young ages (hereafter referred to as compression at young ages) results in in-
creases in e0. An increase in the parameters b
1
,b
2
,andb
3
affects the slope of the
age curve of death probabilities and results in an increase in the steepness of the
age-at-death distribution at adult (b
1
,b
2
)andoldages(b
3
), relative to the modal
age at death and, consequently, in declining lifespan variability (=mortality com-
pression). Compression below the modal age as a result of an increase in b
1
and
b
2
results in fewer deaths at ages far below the modal age and more deaths at ages
just below the modal age, which in turn results in an increase in e0. This compres-
sion below the modal age at adult ages is hereafter referred to as compression at
adult ages. Compression of deaths at young ages combined with compression of
deaths at adult ages, and thus all compression below the modal age, is referred to
as compression of premature mortality. Compression of deaths above the modal
age due to an increase in b
3
results in fewer deaths at very old ages, but more
deaths at ages slightly above the modal age. In this case, e0 declines. Compression
of deaths at ages above the modal age also means that relatively fewer people are
achieving exceptional longevity. This compression above the modal age is hereafter
referred to as compression of old-age mortality.
Janssen and de Beer Genus (2019) 75:10 Page 5 of 23
The CoDe model takes into account that premature mortality and old-age mortality
are relative concepts. The ages that are considered “premature”and “old”depend on
the modal age at death. We, therefore, go beyond previous research that studied
age-specific mortality trends only, or that distinguished between premature and late
deaths using a fixed age of either 65 or 75. Unlike in Zhang and Vaupel (2009), our
threshold age is directly linked to the modal age at death, which enables us to compare
our results with the findings of previous studies that focused on compression above the
modal age. On the other hand, as illustrated in the last paragraph of the “Country and
sex differences in the timing of the transition from mortality compression to mortality
delay”section, this also means that when there is a large decline in the modal age at
death, the likelihood of observing mortality compression at adult ages and mortality ex-
pansion at older ages is larger. Similarly, when there is a large increase in the modal
age at death, the likelihood of observing mortality compression at old ages is more
likely than mortality expansion.
We estimated the model parameters in R, using non-linear minimization (nlm), and
using as starting values for Mthe observed modal age at death, above age 30, and a range
surrounding that age (−3, −2, −1.5, −1, −0.5, −0.25, + 0.25, + 0.5, + 1, + 1.5, + 2, + 3)
and selected the outcome with the lowest weighted least squares (WLS), where we
weighted the squared errors in death probabilities, the logarithm of death probabi-
lities, and the density of the age-at-death distribution by their standard errors (de
Beer and Janssen 2016). Based on a careful analysis of the WLS and visual inspec-
tion of the resulting trends in the parameters, we decided to omit the estimates for
Bulgaria in 1950 and 1951, and for Latvia in 1959, and to use linear interpolation of
the estimates in another 11 single cases. In all remaining cases, the model fit of the
CoDe model turned out to be good. From the last column in Table 1, it can be
observed, for example, that the absolute residual effect was in general low and on
average 0.17 years for men and 0.10 years for women over an average change in e0
over 1980–2014 of 7.1 and 5.9 years, respectively. For 1950–2014, the average
absolute residual effect was respectively 0.21 for men and 0.19 for women over an
average change of 12.1 and 13.5 years, respectively.
We decomposed the change in fitted e0 from 1950 to 2014 into changes in the
modal age and changes in mortality compression at young, adult, and old ages. In
doing so, we distinguished between the sub-periods of 1950 to 1979 and 1980 to
2014, and separate 10-year sub-periods from 1950 and 1955 onwards. Our decision to
divide our observation period into the 1950–1979 and 1980–2014 sub-periods was
basedonourfindingthatthetrendsinMbefore and after 1975–1980 were quite
distinct (see the first paragraph of the “Results”section) and on our wish to divide the
overall period into sub-periods that were as equal as possible. Our decomposition
involved the cumulative adjustment of the subsequent parameters to the final level,
while keeping the remaining parameters at the starting level. We used the following
order: A+B,a,M,b
1
,b
2
,andb
3
, to enable that indeed compression is measured rela-
tive to the modal age at death. We eliminated the effect of c
2
in compression below
the modal age (b
1
,b
2
) to ensure that a decline in the probability of dying before
reaching the modal age does not affect the probability of dying after reaching the
modal age. Similarly, the effect of c
1
was eliminated from compression at young adult
ages (b
1
). Unweighted average contributions were calculated for the different regions.
Janssen and de Beer Genus (2019) 75:10 Page 6 of 23
In order to determine in a robust manner the timing of the transition from changes
in e0 being predominantly due to mortality compression to changes in e0 being
predominantly due to mortality delay, we assessed the 5-year period in which the con-
tribution of delay to the change in e0 became larger than the contribution of compres-
sion. We did so by smoothing the yearly contributions of delay and compression to the
change in e0 by means of 3-year moving averages (resulting in yearly contributions
from 1951-1952 up until 2012–2013) and subsequently summing these yearly contribu-
tions over the 5-year periods (1951–1955, 1955–1960,…,2005–2010, 2010–2013). To
ensure that the change was long-lasting, we considered a minimum of two consecutive
5-year periods that had to last until the end of the observation period. We allowed the
long-lasting change to be interrupted by a single 5-year period in which compression
was still more important than delay, but only if before and after this 5-year period there
were two subsequent periods in which the delay was more important than compression.
Results
Past trends in the modal age at death
Figure 1shows the trends over time (1950–2014) in the estimated modal age at death
(M) for the different countries. The figure clearly displays the different trends in Mbe-
fore and after 1975–1980, particularly for men. Among men, Mhardly increased up to
1975–1980. However, from 1975–1980 onwards, Mamong men increased strongly in
the non-Eastern European countries; whereas, in the Eastern European countries, M
among men stagnated and underwent significant temporal declines. Only recently have
increases in Magain been observed among men in Eastern Europe. Among women, M
increased quite linearly throughout the 1950–2014 period in the non-Eastern European
countries but increased less strongly in the Eastern European countries up to 1975–
1980. As a result, women in Eastern Europe clearly had lower levels of Mthan women
in non-Eastern Europe from 1975–1980 onwards.
Relative importance of compression and delay in the trends in life expectancy
Figure 2shows the relative effects of mortality compression and mortality delay on
the trends in life expectancy at birth (e0) over the 1950–2014 period, divided into
1950–1979 and 1980–2014. In the 1950–1979 period, the changes in e0 were
largest among Japanese women and smallest among Eastern European men.
Whereas the increase in e0 tended to be greater among women in 1950–1979, it
tended to be greater among men in 1980–2014. Mortality compression generally
played a bigger role than mortality delay up to 1980, which suggests that the in-
creases in e0 occurred primarily because of declining disparities in the ages at
death that resulted from large declines in infant and child mortality. From 1980
onwards, however, mortality delay was more important than compression, which
indicates that declines in mortality across all ages led to a shift in the distribution
of deaths towards older ages. On the contrary, among Eastern European men, delay
contributed less than compression to the change in e0 also over the 1980–2014
period. This can be related to the significant temporal declines in Mfrom 1975
onwardsamongmeninmanyEasternEuropeancountries(Fig.1). Among men in
Bulgaria, Lithuania, Latvia, Belarus, and Ukraine, these declines resulted in substan-
tial negative effects on e0 over the 1980–2014 period (Table 1).
Janssen and de Beer Genus (2019) 75:10 Page 7 of 23
Table 1 Contributions (in years) of changes in the modal age at dying (M) and of mortality
expansion/compression at young, adult, and old ages in the change in life expectancy at birth (e0)
between 1980 and 2014*, by country and sex
Observed Observed Observed Effect Effect compression/expansion Effect
e0 1980 e0 2014 Change e0 Change M Before M After M Residual
1980–2014 Total Young Adult Old age
Men
Japan 73.38 80.52 7.14 6.70 0.47 1.09 −0.47 −0.15 −0.03
USA 69.99 76.66 6.67 8.17 −1.23 1.90 −2.58 −0.56 −0.26
Denmark 71.17 78.55 7.38 7.75 −0.22 1.98 −1.48 −0.72 −0.15
Finland 69.23 78.12 8.89 9.48 −0.43 1.07 −0.79 −0.71 −0.17
Ireland 69.93 79.16 9.23 10.20 −0.73 1.39 −1.46 −0.66 −0.24
Norway 72.34 80.02 7.68 7.74 −0.08 1.82 −1.12 −0.78 0.02
Sweden 72.78 80.35 7.57 6.60 1.05 0.84 0.63 −0.43 −0.08
UK 70.51 79.01 8.49 10.13 −1.52 1.65 −2.50 −0.67 −0.11
Austria 68.97 78.92 9.95 8.23 1.91 2.62 −0.39 −0.33 −0.20
Belgium 69.88 78.57 8.70 8.97 −0.11 2.16 −1.71 −0.56 −0.17
The Netherlands 72.44 79.88 7.44 8.41 −0.99 1.67 −1.77 −0.89 0.02
Germany, West 69.87 78.67 8.80 8.08 0.97 2.30 −0.94 −0.40 −0.25
France 70.16 79.27 9.11 8.94 0.61 1.92 −0.85 −0.46 −0.43
Switzerland 72.23 80.93 8.70 9.05 −0.25 2.28 −1.86 −0.68 −0.10
Italy 70.67 79.72 9.05 8.08 1.09 1.95 −0.30 −0.56 −0.12
Portugal 68.11 77.93 9.82 7.36 2.91 4.09 −0.82 −0.37 −0.44
Spain 72.39 80.10 7.71 6.64 1.34 1.90 −0.27 −0.28 −0.28
Bulgaria 68.44 70.31 1.87 −1.26 3.26 1.70 1.00 0.56 −0.13
Czech Republic 66.81 75.72 8.91 6.94 2.03 1.89 0.18 −0.04 −0.07
Germany, East 68.71 77.42 8.71 8.20 0.92 2.43 −1.29 −0.22 −0.41
Hungary 65.52 72.26 6.74 0.04 6.82 2.04 3.42 1.37 −0.12
Poland 65.76 73.66 7.90 1.41 6.51 2.29 3.22 1.00 −0.01
Slovakia 66.71 73.25 6.54 1.69 4.80 1.21 2.94 0.64 0.05
Lithuania 65.58 68.52 2.94 −4.99 8.24 2.05 4.58 1.61 −0.31
Latvia 63.74 69.25 5.52 −1.78 7.55 3.51 2.77 1.26 −0.25
Belarus 65.95 67.81 1.85 −4.27 6.11 1.82 3.26 1.04 0.01
Russia 61.39 65.26 3.87 1.05 2.98 2.04 0.54 0.40 −0.16
Ukraine 64.62 66.31 1.69 −3.17 4.97 1.56 2.37 1.04 −0.11
Janssen and de Beer Genus (2019) 75:10 Page 8 of 23
Considerable differences in the relative importance of compression and delay in the
change in e0 from 1980 to 2014 showed (1) between the regions, with Southern Europe
experiencing more compression than Northern and Western Europe; (2) between the
sexes, with more delay among men especially in Northern and Western Europe and
the USA; and (3) between the individual countries (Fig. 2, Table 1).
Table 1 Contributions (in years) of changes in the modal age at dying (M) and of mortality
expansion/compression at young, adult, and old ages in the change in life expectancy at birth (e0)
between 1980 and 2014*, by country and sex (Continued)
Observed Observed Observed Effect Effect compression/expansion Effect
e0 1980 e0 2014 Change e0 Change M Before M After M Residual
1980–2014 Total Young Adult Old age
Women
Japan 78.75 86.89 8.13 7.70 0.28 0.69 −0.28 −0.13 0.14
USA 77.48 81.48 4.00 3.56 0.47 0.73 −0.06 −0.20 −0.03
Denmark 77.18 82.67 5.50 3.41 1.99 0.43 1.63 −0.08 0.10
Finland 77.86 83.84 5.99 6.00 0.04 0.66 −0.30 −0.32 −0.05
Ireland 75.38 83.24 7.87 7.63 0.03 0.86 −0.43 −0.41 0.21
Norway 79.18 84.09 4.91 4.57 0.51 0.78 −0.03 −0.24 −0.16
Sweden 78.85 84.06 5.20 4.32 1.03 0.46 0.82 −0.24 −0.15
UK 76.57 82.78 6.21 5.54 0.57 0.82 0.10 −0.35 0.10
Austria 76.06 83.75 7.69 6.76 0.96 1.33 −0.08 −0.29 −0.02
Belgium 76.66 83.53 6.87 6.18 0.80 1.22 −0.16 −0.26 −0.11
the Netherlands 79.13 83.30 4.16 4.01 0.22 0.79 −0.29 −0.28 −0.06
Germany, West 76.62 83.35 6.72 5.83 1.04 1.29 −0.01 −0.24 −0.15
France 78.41 85.45 7.05 6.16 0.95 1.20 −0.07 −0.18 −0.06
Switzerland 78.85 85.12 6.27 5.31 0.86 1.06 0.06 −0.26 0.10
Italy 77.42 84.47 7.04 5.76 1.31 1.25 0.30 −0.25 −0.03
Portugal 75.21 84.15 8.94 6.67 2.25 2.68 −0.10 −0.32 0.01
Spain 78.55 85.65 7.10 5.96 1.06 1.16 0.17 −0.27 0.08
Bulgaria 73.90 77.26 3.35 3.61 −0.32 1.37 −1.43 −0.27 0.07
Czech Republic 73.93 81.73 7.80 7.04 0.93 1.19 −0.03 −0.23 −0.17
Germany, East 74.64 83.42 8.78 7.65 1.21 1.25 0.19 −0.23 −0.09
Hungary 72.76 79.25 6.50 5.04 1.82 1.55 0.34 −0.06 −0.36
Poland 74.22 81.43 7.21 5.82 1.52 1.76 −0.08 −0.16 −0.13
Slovakia 74.26 80.32 6.06 4.90 1.17 1.13 0.10 −0.06 −0.02
Lithuania 75.64 79.34 3.70 3.67 0.17 1.43 −0.82 −0.43 −0.15
Latvia 74.11 78.73 4.63 3.66 1.21 1.77 −0.36 −0.19 −0.25
Belarus 75.61 78.43 2.83 1.90 0.88 1.39 −0.12 −0.38 0.04
Russia 72.97 76.48 3.51 2.96 0.58 1.20 −0.46 −0.17 −0.02
Ukraine 74.06 76.21 2.15 1.88 0.22 1.06 −0.67 −0.18 0.04
*2010 for Bulgaria; 2012 for Italy; 2013 for UK, Lithuania, Latvia, and Ukraine
Janssen and de Beer Genus (2019) 75:10 Page 9 of 23
Timing of the transition from a predominance of compression to a predominance of delay
The transition from a predominance of compression to a predominance of delay in the
increases in e0 started earlier among women than among men and occurred earlier in
Northern and Western Europe than in Southern and Eastern Europe (Table 2).
Among women in the USA, the effect of delay was larger than the effect of com-
pression throughout the period. The onset of the transition occurred between 1955
and 1970 among women in Japan and in most other Northern and Western
European countries, between 1970 and 1980 in the three Southern European coun-
tries and between 1970 and 1995 in all of the Eastern European countries, except
Belarus (2000) and Latvia (2005). Among men, the transition from a predominance
of compression to a predominance of delay occurred later, from 1965 onwards.
Like the transition among women, the transition among men started relatively early
in the USA, Northern and Western Europe, and in Japan, albeit surprisingly late in
Denmark, Norway, and the Netherlands. Among men in Southern Europe, the
Fig. 1 Past trends in the estimated modal age at death (M), 1950–2014, by sex and region
Janssen and de Beer Genus (2019) 75:10 Page 10 of 23
transition started between 1975 and 1985, and even later in Eastern Europe.
Among men in Lithuania, Latvia, and Belarus, there is no evidence that the transi-
tion from compression to delay has occurred.
The importance of compression at young, adult, and old ages in the transition
In the 1950s in non-Eastern Europe, the predominance of mortality compression
was caused by the large contribution of mortality decline at young ages to the
increase in e0 (Fig. 3). In addition, among men, the modal age was either only
marginally increasing or even declining (Fig. 1). For women in non-Eastern Europe,
delay was already contributing on average 44% of the increase in e0.
Between the 1950s (1950–1959) and the 1960s (1960–1969), the decline in the
relative role of compression in the increase in e0 was mainly due to a decrease in
the importance of mortality declines at young ages. This trend occurred across
Europe among both men and women.
Between the 1960s and the 1970s (1970–1979), the role of mortality delay increased
considerably in non-Eastern Europe (Fig. 3). Mortality delay first became predominant
from 1970 onwards among women in North-Western European countries and later
became predominant among women in Southern Europe and among men (see as well
Appendix 2). In this period in which delay was becoming predominant, the positive
contribution of compression of mortality at young ages to the change in e0 was coun-
terbalanced by the negative contributions of expansion at adult ages and compression
at old ages, especially among men (Fig. 3).
In Eastern Europe (see Appendix 2), the period from 1975 to 1995 is charac-
terised by expansion of adult mortality among women, and, among men, large
negative contributions from a decline in the modal age at death only partly coun-
terbalanced by compression at adult ages and expansion at old ages. From 1975
onwards for women and 1995 onwards for men, a clear increase in the contri-
bution of delay can be observed, coupled with compression of old-age mortality,
Fig. 2 Contributions (in years) of mortality delay (or declining Mwhen negative) and mortality compression (or
expansion when negative) to changes in life expectancy at birth (e0), 1950*-1979 and 1980–2014
#
, by sex.
*1952 for Belarus, 1956 for East and West Germany; 1958 for Poland; 1959 for Belarus, Lithuania, Russia and
Ukraine; 1960 for Latvia.
#
2010 for Bulgaria; 2012 for Italy; 2013 for UK, Lithuania, Latvia, and Ukraine. JP Japan,
US United States, NEur Northern Europe, WEur Western Europe, SEur Southern Europe, EEur Eastern Europe
Janssen and de Beer Genus (2019) 75:10 Page 11 of 23
resulting in a predominance of delay from 1990 onwards among women, and from
1995 onwards among men.
In more recent years, in non-Eastern Europe, delay remained highly predominant, and
at about the same relative level, despite some fluctuations in its contribution because of
fluctuations in the contribution of young age mortality, in particular teenage mortality
(Fig. 3;Appendix 2). Whereas, the negative contributions of expansion of adult mortality
Table 2 Five-year period in which the contribution of mortality delay to the increase in life
expectancy at birth became persistently larger than the contribution of mortality compression, by
sex and country, 1951–2013
Country Men Women
Japan 1965–1970 1965–1970
USA 1965–1970 1951–1955*
Denmark 1980–1985 1995–2000
Ϯ
Finland 1965–1970 1965–1970
Ireland 1985–1990 1975–1980
Norway 1980–1985 1965–1970
Sweden 1965–1970 1955–1960*
UK 1965–1970 1960–1965*
Austria 1970–1975* 1970–1975
Belgium 1970–1975 1970–1975
The Netherlands
#
1975–1980 1955–1960
Germany, West 1970–1975 1970–1975
France 1965–1970 1960–1965
Switzerland 1965–1970 1965–1970
Italy 1985–1990 1975–1980
Portugal 1985–1990 1975–1980
Spain 1975–1980 1970–1975
Bulgaria
#
2000–2005 1975–1980
Czech Republic
#
1990–1995* 1985–1990
Germany, East
#
1990–1995
Ϯ
1975–1980
Hungary
#
1995–2000 1980–1985
Poland
#
1990–1995* 1970–1975*
Slovakia
#
1990–1995 1985–1990
Lithuania
#
N/A 1970–1975*
Latvia
#
N/A 2005-2010
Belarus
#
N/A 2000–2005
Russia
#
2005–2010
Ϯ
1995–2000
Ukraine
#
2005–2010 1995–2000
N/A = not applicable
#
At least two 5-year periods in which declines in e0 occurred, mostly only among men, but for Belarus, Latvia, Russia, and
Ukraine for both men and women
*One 5-year period in between in which the contribution of compression was larger than delay
Ϯ
Also at an earlier point in time, an extended period occurred in which absolute delay was more important than absolute
compression: DKF 1951–1980, RFM 1980–1990, DEM 1970–1980
Janssen and de Beer Genus (2019) 75:10 Page 12 of 23
have been declining among men, the positive contributions of compression of adult mor-
tality have recently emerged among women, indicating that declines in adult mortality are
particularly strong. Despite further increases in the modal age at death (Fig. 1), the small
negative contribution of compression at old-age mortality stayed either stable or declined
slightly, reflecting the absence of a further recent increase in the related parameter, with
even signs of expansion recently for some countries (see Appendix 3).
Discussion of observed results
In almost all studied 26 European countries, Japan, and the USA, a transition occurred from
increases in life expectancy at birth (e0) mainly due to compression of mortality to increases
a
b
Fig. 3 Contributions (in years) of mortality delay (or declining Mwhen negative) and mortality compression
(or expansion when negative) at young, adult, and old ages to the changes in life expectancy at birth (e0),
for the separate decades from 1950* to 2009 [results for 1955 to 2014 in Appendix 2]. aMales. b
Females.*For West Germany from 1956 onwards. For Eastern Europe from 1960 onwards
Janssen and de Beer Genus (2019) 75:10 Page 13 of 23
in e0 predominantly due to mortality delay. Delay of mortality results from a shift in the age
distribution of mortality towards older ages and implies an increase in the modal age at
death. Compression of mortality implies that the share of deaths around the modal age in-
creases and that, consequently, lifespan variability is declining. Compression can be caused
by a strong decrease in deaths at young or advanced ages, which has a positive effect on e0,
or by an increase in the share of deaths around the modal age (as a result of a decline in the
share of deaths in advanced age), which results in a negative effect on e0.
Country and sex differences in the timing of the transition from mortality compression
to mortality delay
Important differences between men and women and across countries occurred in the
timing of the point at which increases in e0 transitioned from being predominantly due
to compression of mortality to being predominantly due to mortality delay. Specifically,
we found that, for women, the transition started at or before 1950 in the USA, between
1955 and 1970 among women in Northern and Western Europe, between 1970 and
1975 among women in Southern Europe, and still later among women in Eastern
Europe. Generally, the transition occurred among men about 10 years later than among
women, although it is important to note that delay has not yet overtaken compression
among men in Lithuania, Latvia, and Belarus. Our own additional analysis using data
for American women from 1933 onwards showed that the onset of the transition began
in the 1951–1955 period and not earlier.
Generally, the transition from compression to delay appears to have occurred around
10 years later among men than among women. This observation is related to the diffe-
rences between men and women in the increase in the modal age at death (Cheung et al.
2009), which were more modest among men than among women from 1950 up to 1975
(see Fig. 1). At least among men and women in non-Eastern European countries, these
sex differences in the increase in the modal age can be partly attributed to the differential
effects of the smoking epidemic for men and women. Men—and particularly men in the
Anglo-Saxon countries and North-Western Europe—were the first to take up smoking in
large numbers (Lopez et al. 1994). Women did not start smoking until some decades after
men (Lopez et al. 1994; Janssen and van Poppel 2015). By that time, the negative effects of
smoking on health were widespread and well-known. Consequently, the smoking preva-
lence levels of women never reached the enormously high levels of men (Lopez et al.
1994; Van Poppel and Janssen 2016). In line with this hypothesis regarding the impact of
the smoking epidemic on sex differences in the increase in the modal age, Janssen and de
Beer (2016) observed for the Netherlands that the trends in the modal age at death for
non-smoking-related mortality—i.e. with the effects of smoking excluded—were roughly
the same among men and women aged 40 and older over the period 1950–2012. Simi-
larly, Janssen et al. (2015) observed that in a number of European low-mortality countries,
from 1950 to 2009, patterns in longevity extension among men and women aged 50 and
older were more similar for non-smoking-related mortality than for all-cause mortality.
For Eastern European countries, sex differences in alcohol consumption might be
important as well. Because men tend to consume more alcohol than women (Leon
et al. 2009;Mäkeläetal.2006), they also have higher levels of alcohol-attributable
mortality (e.g. Trias-Llimós et al. 2017). This gender gap is especially striking in
Eastern Europe (e.g. Trias-Llimós and Janssen 2018).
Janssen and de Beer Genus (2019) 75:10 Page 14 of 23
Differences between countries in the timing of the onset of the predominance
of delay may have also been affected by the smoking epidemic. There are clear
differences between countries in the impact and the timing of the smoking
epidemic, as described by Lopez et al. 1994 in their smoking epidemic model.
MeninAnglo-SaxonandNorth-WesternEuropean countries were the first to
take up smoking in large numbers at the beginning of the twentieth century
resulting in very high smoking-attributable mortality among these men some 30
to 40 years later. On average, men in Southern and Eastern Europe took up
smoking 35 years later, during a period when the adverse health effects of smok-
ing became increasingly known. Thus, among these men, smoking prevalence and
smoking-attributable mortality was lower, although still substantial. The women
in the abovementioned countries followed a similar pattern of tobacco use but
with a delay of several decades (e.g. Lopez et al. 1994) and experienced lower
smoking prevalence and smoking-attributable mortality than men.
It is likely, however, that our general observation that the transition occurred earlier
in Northern and Western Europe, the USA, and Japan, and later in Southern and
Eastern Europe, is mainly attributable to historic differences in socioeconomic develop-
ments and improvements in medical care, with greater improvements leading to larger
historic declines in under-five mortality in particular and to higher current life expec-
tancy values (e.g. Omran 1998; Mackenbach 2013). Higher life expectancy is known to
be associated with smaller lifespan disparities (Vaupel et al. 2011; Smits and Monden
2009), and thus with improvements resulting primarily from a shift in the distribution
of deaths towards older ages.
However, the transition from increases in e0 being predominantly due to com-
pression of mortality to increases in e0 being predominantly due to mortality delay
has not yet occurred in all European countries. Among men in Lithuania, Latvia,
and Belarus, delay has not yet overtaken compression. In these and other Eastern
European male populations, large (temporal) declines in e0 occurred from 1975
onwards. These declines are largely attributable to the health crisis in Eastern
Europe that resulted from the policies of communist regimes (McKee and
Shkolnikov 2001; Vallin and Meslé 2004;Leon2011). This health crisis affected
men and women of all ages, but particularly men and people of adult ages (McKee
and Shkolnikov 2001). In line with our expectations, we found that the health
crisis caused adult mortality to expand substantially among women in 1975–1984
and 1985–1994. However, the effects of the health crisis were larger among men,
and because the crisis affected the broader population, it resulted among men
predominantly in a decline in the normal (=modal) age at death. As the normal
age at death decreased, lifespan disparities below the modal age at death also
declined (=compression of adult mortality) simply because the distance of the
onset of adult mortality to the normal age at death became smaller, and the in-
crease in mortality with age steeper. As well as illustrating the relative concept of
compression below the modal age at death, this pattern shows that a health crisis
can result in a decline in the modal age at death, as a result of which a decline in
lifespan variability below the modal age at death does not necessarily result in a
positive effect on life expectancy. Similarly, the expansion of old-age mortality that
was observed in this period while the modal age at death was declining took place
Janssen and de Beer Genus (2019) 75:10 Page 15 of 23
because the older ages represented more ages than they did before the decline in
the modal age at death occurred, which inevitably led to a decline in the steepness
of mortality with age (=expansion of old-age mortality).
Phases in the transition from compression to delay
Distinguishing between compression/expansion at different ages allowed us to provide
a more detailed description of the overall transition from changes in e0 being predom-
inantly due to mortality compression to changes in e0 being predominantly due to
mortality delay. More specifically, we could distinguish the following phases from
1950 onwards: (1) compression played a large and predominant role mainly be-
cause of mortality compression at young ages due to large mortality declines at
young ages, while delay had very little effect; (2) mortality compression became less
important as the effects of mortality compression and mortality declines at young
ages tapered off; (3) mortality delay became more important than mortality com-
pression due to large increases in the modal age at death, as well as to the coun-
terbalancing effects of mortality compression at young ages on the one hand, and
of mortality expansion at adult ages and old-age compression on the other; and (4)
strong predominance of delay combined with larger mortality declines at adult ages
and declining mortality compression at old ages.
Our description of the different stages from 1950 onwards could supplement the
description of the current stage of the epidemiological transition theory in
low-mortality countries (Omran 1998). Based on his study of the dispersion of
lifespans in France, Robine (2001)proposedanalternativethirdstageofthe
epidemiological transition theory, i.e. instead of “the age of degenerative and
man-made diseases”,hesuggested“the age of the conquest of the extent of life”,a
stage that is characterised by increasing life expectancies combined with no or very
small reductions in lifespan dispersion. In our analysis, we could clearly discern
different subphases in the transition from mortality compression to mortality delay
that could be used to supplement the description of the third and later stages of
the epidemiological transition theory.
As mortality delay has been the main contributor to the increase in e0 in re-
cent years, the definition of premature mortality and old-age mortality has been
changing as well. As first presented by Lexis (1878) and later revived by Kannisto
(2001), the modal age at death can be seen as representing “normal”or “typical”
longevity (Cheung et al. 2005). Thus, when the modal age increases, an older age
at death becomes normal. Since premature mortality refers to mortality at an age
below the point in the lifespan at which dying is considered normal, premature
mortality is extended to higher ages. Similarly, since old-age or late mortality re-
fers to mortality at an age above the point in the lifespan at which dying is con-
sidered normal, old-age mortality is shifted to higher ages. In the 28 countries
studied here, the normal age at death among women was on average 81.4 years in
1960 (80.2 in the earliest available year) and 87.7 years in 2010 (88.4 in the latest
available year), while among men, this was 76.2 years in 1960 and 80.4 years in
2010. If Eastern European countries are excluded, the equivalent values for men
are 75.8 and 83.2. Thus, whereas age 83 was considered old in 1960, dying at
this age can now be considered normal among men and premature among
Janssen and de Beer Genus (2019) 75:10 Page 16 of 23
women in the majority of European countries. This is important information for
policy-makers who are trying to further reduce premature mortality in the con-
text of mortality delay. It is clear that policies should be adjusted to target an
older group of people than in the past.
Although mortality delay is increasing in importance, mortality compression has
also played a role in recent mortality changes. Tracking mortality compression
and mortality expansion provides us with information about declines or increases
in lifespan disparities between individuals, and this information can be indicative
of underlying inequalities, such as socioeconomic differences that could be associ-
ated with differences in smoking habits (van Raalte et al. 2011). Whereas lifespan
disparities at younger ages predominated in the past, today lifespan disparities at
adult and older ages are becoming more important.
Trends in old-age compression/expansion also have important implications for
the debate on a potential limit to life expectancy and the maximum life span. Our
observation of a strong trend towards mortality delay implies that there is no limit
to life expectancy in the near future. If we were approaching a limit to lifespan, we
would expect to see that either mortality delay (i.e. the increase in the modal age)
had slowed down or the effect of mortality compression in old age had exceeded
the effect of mortality delay. A limit to lifespan implies that the upper bound of
the age-at-death distribution is fixed. As long as mortality delay continues without
compression in old age, the upper bound of the age-at-death distribution will
continue to move to older ages. If compression in old age does occur, the upper
bound of the age distribution will increase less strongly than the modal age. Thus,
the finding that from 1980 onwards deaths above the modal age have become
increasingly concentrated within a narrow age interval does not imply that there is
a limit to life expectancy, provided mortality delay continues to play a more
important role than mortality compression at old ages. This result does, however,
indicate that the maximum lifespan has not been increasing as fast as the modal
age at dying. Compression in old age implies that the difference between the
modal age and the upper bound has been decreasing. Our observation that com-
pression of old-age mortality has recently been stable or even slightly declining
among women in non-Eastern Europe—and that there have even been signs of
mortality expansion in certain countries—indicates that the maximum lifespan
could increase further as the modal age at death increases. But if the maximum
lifespan continues to increase more slowly than the modal age, we may expect to
find that there is a limit to the increase in the modal age in the long run, as com-
pression in old age cannot continue infinitely (Cheung et al. 2005).
Conclusion and implications
The transition from a predominance of mortality compression to a predominance
of mortality delay in determining changes in e0 could be dated among women at
around 1950 in the USA, between 1955 and 1970 in Northern and Western
Europe, around 1970–1975 in Southern Europe, and still later in Eastern Europe,
withthetransitionamongmenintheseEuropean regions generally occurring
about 10 years later. Among men in Lithuania, Latvia, and Belarus, delay has not
yet overtaken compression because of the health crises they have experienced. It
Janssen and de Beer Genus (2019) 75:10 Page 17 of 23
is, however, likely that for them the transition will occur soon. Differences in the
timing of the transition could be linked to the past health crisis in Eastern
Europe, past differences in the pace of socioeconomic change and associated im-
provements in medical care, but also to differences in the timing and impact of
the smoking epidemic.
Based on our analysis of the role of compression at different ages, we distin-
guished four phases in the transition from mortality compression to mortality
delay: (1) predominance of compression due to strong mortality declines at young
ages, (2) declining importance of mortality compression due to the decreasing im-
pact of mortality declines at young ages, (3) mortality delay becomes predominant
due to strong increases in the modal age at death and the counterbalancing effects
of mortality compression/expansion at different ages, and (4) strong predominance
of delay combined with stronger mortality declines at adult ages and declining
mortality compression at old age.
Our results indicate that we are not approaching a limit to life expectancy or a max-
imum lifespan. With mortality delay, premature mortality and old-age mortality are
also shifting towards older ages.
Appendix 1
Effects of delay parameter Mand compression parameters b
1
,b
2
, and b
3
of the CoDe
model based on a hypothetical age-at-death distribution that resembles a life expectancy
at birth (e0) of 72.5 years
–Mortality delay
An increase in the modal age at death (=delay) from 85.2 to 90.86 years corresponded
with a 5-year increase in e0 from 72.5 to 77.5 years.
–Mortality compression
Janssen and de Beer Genus (2019) 75:10 Page 18 of 23
A decline in A(infant mortality) from 0.0035 to 0.0027 resulted in less lifetable
deaths up until age 15, with more lifetable deaths around the modal age at death (not
visible), which resulted in an increase in e0 of 1.0 years. A decline in a(teen mortality)
from 0.0009 to 0.00063 resulted in less lifetable deaths from age 10 up until age 45, and
slightly more lifetable deaths around the modal age at death (not visible), which re-
sulted in an increase in e0 of 0.5 years.
An increase in b
1
from 0.088 to 0.0983 combined with an increase in b
2
from
0.113 to 0.13 resulted in less lifetable deaths up until age 79 and more lifetable
deaths from age 79 up until the modal age at death (91) leading to a 1-year in-
crease in e0.
An increase in b
3
from 0.125 to 0.145 resulted in more lifetable deaths between
the modal age at death (91) and age 97 and less thereafter, which together led to a
decline in e0 of 0.2 years.
* denoted by the vertical line
Janssen and de Beer Genus (2019) 75:10 Page 19 of 23
Appendix 2
Contributions (in years) of mortality delay (or declining Mwhen negative) and
mortality compression (or expansion when negative) at young, adult, and old ages
to the changes in life expectancy at birth (e0), for the separate decades from 1955*
to 2014
#
. * For West Germany from 1956 onwards. For Eastern Europe from 1960
onwards.
#
2010 for Bulgaria; 2012 for Italy; 2013 for UK, Lithuania, Latvia, and
Ukraine
a) Males
b) Females
Janssen and de Beer Genus (2019) 75:10 Page 20 of 23
Appendix 3
Past trends in compression above the modal age at death (b
3
), 1950–2014, women, by
region (without Eastern Europe)
Abbreviations
CoDe mortality model: Compression and delay mortality model; e0: Life expectancy at birth; M: Modal age at death;
nlm: Non-linear minimization; UK: United Kingdom; USA: United States of America; WLS: Weighted least squares
Acknowledgements
We thank Shady El Gewily (econometrics, University of Groningen) for his help in programming in R.
Funding
This work was supported by the Netherlands Organisation for Scientific Research (NWO) in relation to the research
programme “Smoking, alcohol, and obesity, ingredients for improved and robust mortality projections”, under grant
no. 452–13-001. See www.futuremortality.com.
Availability of data and materials
For the analysis, data from the Human Mortality Database are used, which are available online at www.mortality.org.
All calculations are done in R.
Authors’contributions
FJ designed the study, did the analyses, and wrote the manuscript. JdB aided in interpreting the results and reviewed
the manuscript. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’sNote
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Received: 4 May 2018 Accepted: 4 February 2019
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