Modal lifespan and disparity at older ages by leading causes of death: a Canada-U.S. comparison

Abstract

The U.S. elderly experience shorter lifespans and greater variability in age at death than their Canadian peers. In order to gain insight on the underlying factors responsible for the Canada-U.S. old-age mortality disparities, we propose a cause-of-death analysis. Accordingly, the objective of this paper is to compare levels and trends in cause-specific modal age at death (M) and standard deviation above the mode (SD(M +)) between Canada and the U.S. since the 1970s. We focus on six broad leading causes of death, namely cerebrovascular diseases, heart diseases, and four types of cancers. Country-specific M and SD(M +) estimates for each leading cause of death are calculated from P-spline smooth age-at-death distributions obtained from detailed population and cause-specific mortality data. Our results reveal similar levels and trends in M and SD(M +) for most causes in the two countries, except for breast cancer (females) and lung cancer (males), where differences are the most noticeable. In both of these instances, modal lifespans are shorter in the U.S. than in Canada and U.S. old-age mortality inequalities are greater. These differences are explained in part by the higher stratification along socioeconomic lines in the U.S. than in Canada regarding the adoption of health risk behaviours and access to medical services.

Full text

Vol.:(0123456789)
Journal of Population Research (2020) 37:323–344
https://doi.org/10.1007/s12546-020-09247-9
1 3
ORIGINAL RESEARCH
Modal lifespan anddisparity atolder ages byleading
causes ofdeath: aCanada‑U.S. comparison
ViorelaDiaconu1 · NadineOuellette2· RobertBourbeau2
Published online: 5 November 2020
© The Author(s) 2020
Abstract
The U.S. elderly experience shorter lifespans and greater variability in age at death
than their Canadian peers. In order to gain insight on the underlying factors respon-
sible for the Canada-U.S. old-age mortality disparities, we propose a cause-of-death
analysis. Accordingly, the objective of this paper is to compare levels and trends
in cause-specific modal age at death (M) and standard deviation above the mode
(SD(M +)) between Canada and the U.S. since the 1970s. We focus on six broad
leading causes of death, namely cerebrovascular diseases, heart diseases, and four
types of cancers. Country-specific M and SD(M +) estimates for each leading cause
of death are calculated from P-spline smooth age-at-death distributions obtained
from detailed population and cause-specific mortality data. Our results reveal simi-
lar levels and trends in M and SD(M +) for most causes in the two countries, except
for breast cancer (females) and lung cancer (males), where differences are the most
noticeable. In both of these instances, modal lifespans are shorter in the U.S. than
in Canada and U.S. old-age mortality inequalities are greater. These differences are
explained in part by the higher stratification along socioeconomic lines in the U.S.
than in Canada regarding the adoption of health risk behaviours and access to medi-
cal services.
Keywords Mortality at older ages· Causes of death· Modal age at death· Lifespan
inequalities· Canada· U.S.
* Viorela Diaconu
diaconu@demogr.mpg.de
1 Max Planck Institute forDemographic Research, Rostock, Germany
2 Department ofDemography, Université de Montréal, Montreal, QC, Canada
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V.Diaconu et al.
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Introduction
International comparisons of life expectancy at birth or at a later age, and of lifes-
pan variation—i.e., individual differences in the timing of death—revealed that
the U.S. lags behind most industrialised countries (Barbieri and Ouellette 2012;
Edwards and Tuljapurkar 2005; Engelman et al. 2010; Glei et al. 2010; White
2002; Wilmoth and Horiuchi 1999; Wilmoth etal. 2010; Wilson 2001). In com-
parison to Canada, the U.S. disadvantage in terms of survival time and inequality
has been observed since the early 1960s and has gradually become more pro-
nounced over time (Barbieri and Ouellette 2012; Edwards and Tuljapurkar 2005).
The Canada-U.S. mortality differentials have also been observed at older ages:
the U.S. elderly experience shorter lifespans and greater variability in age at
death than their Canadian peers (Barbieri and Ouellette 2012; Glei et al. 2010;
Ouellette and Bourbeau 2011).
A key question has been whether the U.S. disadvantage at older ages is observ-
able for all major causes of death, or are there specific causes for which the situ-
ation is reversed, i.e. the United States has an advantage over Canada? To answer
this question, we compare levels and trends in cause-specific modal age at death,
M, and standard deviation above the mode, SD(M +), between Canada and the
U.S. over the period 1974–2011. We selected this mode-based pair of indicators
because, as discussed later in the introduction, M is a lifespan measure that places
special focus on survival improvements at older ages and it captures age shifts
of old-age mortality more accurately than life expectancies at some selected old
age (Horiuchi etal. 2013). Canada-U.S. differences in all-cause M and SD(M +)
have already been reported by Ouellette and Bourbeau (2011). Figure1 displays
country-specific trends by sex from 1974 to 2011.
In the present article, we examine six leading causes of death among Cana-
dian and U.S. elderly: cerebrovascular diseases, heart diseases, and four types of
cancers, namely colorectal, lung, breast (females), and prostate (males) cancer.
The present study is the first to conduct a Canada-U.S. comparison of patterns
and trends in cause-specific modal age at death and standard deviation above the
mode. We also provide the first available estimates in M and SD(M +) by lead-
ing causes of death in the U.S. (those for Canada were published in an earlier
paper (Diaconu et al. 2016)). This comparative analysis aims to (1) determine
whether the U.S. disadvantage with respect to old-age survival and lifespan vari-
ation holds for all six leading causes for the entire study period or only for spe-
cific causes and/or time periods and (2) examine whether the between-country
difference with respect to cause-specific M and SD(M +) has narrowed or wid-
ened during the past four decades. Given that some causes are strongly related to
health-related behaviours, such as lung cancer, while others are mostly amenable
to medical care, such as prostate cancer, our results should provide insight on
the factors responsible for the Canada-U.S. disparities in old-age mortality and
uncover whether differences in health care systems stand out as the main culprit.
We focus on mortality changes at older ages because during the second half
of the twentieth century, the extension of human life in high-income countries
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325
1 3
Modal lifespan anddisparity atolder ages byleading causes…
has been chiefly due to survival improvements at older ages, with the significant
decline in mortality at ages 60 and above being its main contributor (Barbieri and
Ouellette 2012; Mazui etal. 2014; Payeur 2011). In the last decades, the elderly
have become a growing segment of the Canadian and U.S. population going from
a level of about 10% in the early 1970s to about 15% in 2017 and are expected to
reach 20–25% by 2030 (Statistics Canada 2012; US Census Bureau 2011; Vespa
2018). As increasingly more individuals survived to older ages the cause of death
structure shifted from infectious diseases to chronic degenerative diseases. Heart
disease, cancers, and stroke became the leading causes of death in developed
countries, including in Canada and the U.S., since the 1960s.
Two demographic indicators, the adult modal age at death, M, and the standard
deviation above the mode, SD(M +), have increasingly been used in the last decades
for monitoring changes in the distribution of deaths at older ages in low mortality
countries (Brown etal. 2008, 2012; Cheung and Robine 2007; Cheung etal. 2005,
2008, 2009; Diaconu et al. 2016; Kannisto 2007; Ouellette and Bourbeau 2011;
Ouellette etal. 2012a, b; Robine and Cheung 2008; Thatcher etal. 2010), where
the extension of the length of human life is primarily due to improvements in old-
age survival (Meslé and Vallin 2006; Vallin and Meslé 2001; Wilmoth etal. 2010).
Under a given mortality regime, M represents the most common (i.e., frequent) or
‘typical’ length of life among adults. Introduced in the nineteen century by Lexis
(1877, 1878) as the most central and natural characteristic of human longevity, the
adult modal age at death was rarely used by demographers until the early 2000s
when it was reintroduced and popularised by Kannisto (2001) in human longevity
studies.
M
^
75
80
85
90
Males, U.S.
Males, CAN
Females, CAN
Females, U.S.
SD(M+)
5
6
7
8
9
10
Males, CAN
Males, U.S.
Females, U.S.
Females, CAN
1980 1990 2000 2010
M
^CAN−M
^U.S.
−1
1
2
3
Males
Females
1980 1990 2000 2010
SD(M+)CAN−SD(M+)U.S.
−2
−1
Males
Females
Fig. 1 Estimated modal age at death,

M
, and standard deviation above the mode,

SD
(M +), for all causes
of death combined in Canada and the U.S., 1974–2011. Source: Authors’ calculations based on the Cana-
dian Vital Statistics Death database, U.S. National Vital Statistics System data files, and Human Mortal-
ity Database
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326
V.Diaconu et al.
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M’s importance as a major indicator of old-age survival arises from a series of
features, primarily as, unlike life expectancy at birth, M is solely influenced by old-
age mortality (Canudas-Romo 2010; Horiuchi etal. 2013; Kannisto 2001). In fact,
2010 analytically showed that when mortality changes occur at younger ages but not
at older ages, M remains unchanged. In the reversed situation, i.e. mortality reduc-
tions at older ages and no improvements at younger ages, M rises. For this reason,
in many high-income countries, M remained constant or increased slightly over
most of the first half of the twentieth century, when the increase in the length of
human life was mainly due to survival im-provements among infants, children and
young adults. However, throughout the second half of the twentieth century, mor-
tality at older ages declined more rapidly than at younger ages, and M followed a
steep upward trend (Canudas-Romo 2010; Cheung and Robine 2007; Cheung etal.
2009; Kannisto 2001; Office of National Statistics 2012). Another interesting fea-
ture of M was highlighted in a later study by Horiuchi and colleagues (2013), who
provide empirical evidence and a mathematical proof that when mortality shifts
to older ages, M increases at the exact pace as the old-age mortality shift while
conditional life expectancy at some early old age, i.e. 50, 65, 75, increases more
slowly. It should also be added that M has special mathematical properties, making
for instance widely-used mortality models (e.g., Gompertz, logistic, Weibull) more
clearly and straightforwardly understandable when M is used in replacement of the
original mortality level parameter (Bergeron-Boucher etal. 2015; Horiuchi et al.
2013; Janssen and de Beer 2019; Missov etal. 2015).
With the reintroduction of the late modal age at death in contemporary demog-
raphy, measures of variation relative to the modal age at death have also been
proposed, the most frequently used being the standard deviation above the mode,
SD(M +). The calculation of SD(M +) is based on deaths occurring beyond the
modal age, such that a decline in SD(M +) over time indicates that deaths became
increasingly concentrated into a shorter old-age interval beyond M, a phenomenon
known as old-age mortality compression. In some high-income countries, the com-
pression of mortality at older ages stalled in recent years, such as reflected by a con-
stant SD(M +), while M’s upward trend continued. This phenomenon is known as
the shifting mortality regime. Still, it should be noted that conceptually, according
to Lexis’ (1878) concept of normal (i.e. gaussian) lifespans, the SD(M +) indicator
is in- tended to measure the dispersion of senescent deaths around the modal age.
Also, similarly to other measures of variation, SD(M +) can be used to inform on the
degree of variability (inequality) in age at death across individuals.
Data andmethods
Sources ofdata
Cause-specific mortality data for Canada and the U.S. are taken respectively from
the Canadian Vital Statistics Death (CVSD) database of Statistics Canada and the
U.S. National Vital Statistics System (NVSS) data files of the National Center for
Health Statistics. In these two data sets, cause-specific death counts gathered from
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327
1 3
Modal lifespan anddisparity atolder ages byleading causes…
sub-national vital statistics registries are given by single years of age and sex since
1974 in Canada and since 1959 in the U.S. In the present paper, our analyses of
levels and trends in cause-specific M and SD(M +) start in 1974 and end in 2011,
covering three revisions of the ICD (i.e., the 8th, 9th and 10th revisions). Changes
resulting from successive revisions of the ICD may create major discontinuities in
cause-specific mortality trends over time, especially for highly detailed causes of
death. The use of broad disease categories is less problematic. We thus focus on the
following six broad leading underlying causes of death among males and females
aged 10years and above, in Canada and the U.S.: cerebrovascular diseases, heart
diseases, and the four most diagnosed types of cancers, namely colorectal, lung,
breast (females), and prostate (males) cancer. The concordance table used for bridg-
ing the three revisions of the ICD is provided in the “Appendix” (Table 1). We
excluded individuals for which the age at death is unknown, as well as Canadians
and non-U.S. residents deceased in the U.S. Their number accounts for less than 2%
in each calendar year and country.
Canada and the U.S. are two rare countries where detailed high-quality data on
deaths by underlying cause and single years of age over a long period of time are
available. Because information is gathered at the individual level, the Canadian
cause-specific mortality data are confidential, while the U.S. data still are freely
available online. We were granted access to the Canadian data set through the Data
Liberation Initiative, a program initiated by Statistics Canada to improve access to
data resources for Canadian postsecondary institutions. Analyses made with the
Canadian data are scrupulously verified before any analytic report is released or
published in order to prevent the disclosure of any information deemed confidential.
These cause-specific mortality series from the CVSD and the NVSS are supple-
mented by estimates of population exposure by single years of age (10 and above),
sex, and single calendar years (1974 to 2011) for Canada and the U.S., taken from
the Human Mortality Database (HMD).
The Poisson P‑spline method forcause‑specic mortality data
Within a cause-of-death framework, two functions characterise and describe the
joint distribution of survival time X and type (cause) of death K: the cause-specific
force of mortality and the cause-specific probability density function. Using sex-
specific observed deaths counts by single years of age and cause of death as well as
the population’s amount of exposure to the risk of dying at each age, these two mor-
tality functions are estimated using a nonparametric smoothing technique known as
P-splines (Eilers and Marx 1996). The Poisson P-spline method formerly introduced
by Ouellette and Bourbeau (2011) for obtaining smooth age distributions of deaths
(all causes combined) and for monitoring with great precision how these distribu-
tions have changed over time at older ages in low mortality countries was recently
adapted to the context of cause-of-death analysis (Diaconu etal. 2016). Compared to
mathematical mortality models for fitting age variations in adult mortality, namely
the Gompertz, the logistic and the Weibull models, the P-spline method does not
impose any assumptions related to the structure of the data. It has also been proven
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328
V.Diaconu et al.
1 3
highly effective for fitting age-specific mortality rates and hence for obtaining
smooth forces of mortality while remaining faithful to the specific characteristics of
the observed data (Camarda 2008, 2012; Currie etal. 2004).
The smooth density function for cause k, describing the distribution of deaths
across ages, is obtained from cause-specific smooth forces of mortality as follows:
where 
S
(x)=exp
[
−
x
∫
0
𝜇 (u)du
]
and
𝜇 (u)
represents the all force of mortality esti-
mated within a Poisson P-spline regression setting. For an illustration of cause-spe-
cific P-spline-smooth density curves see Fig.4 for the U.S. in the “Appendix” (and
Fig. A-2 in Diaconu etal. (2016) for Canada).
Under the assumption that causes of death are mutually exclusive and mutually
exhaustive (Preston etal. 2001), the all-cause smooth force of mortality is derived
from cause-specific smooth forces of mortality through summation.
The modal age at death for a given cause k,

Mk
, indicating the age at which the
highest proportion of deaths from this particular disease occurred, was obtained as
follows:
As for its associated measure of dispersion, the standard deviation above the
mode,

SD(
M
k
+
)
, it is given by:
where
𝜔
is the highest attained age at death.
Results
Canada‑U.S. dierentials in

Mk
Figure 2 depicts cause-specific trends and levels in the most frequent age at
death,

Mk
, among males (panel a) and females (panel b) in Canada and the U.S.
over the period 1974–2011. In terms of trends, the figure firstly reveals that

Mk
increased substantially for all leading causes of death across sexes in both coun-
tries since the mid-1970s. Secondly, the pace of increase was nearly the same
for most causes in the two countries, except for heart diseases (greater pace for
males), breast cancer (greater pace for females), and lung cancer (blip in the early
1990s and greater pace in the 1970s for U.S. males and females only, respec-
tively). In contrast, notable differences between the various causes of death stud-
ied are observable in terms of country-specific

Mk
levels. Males and females that
died from lung cancer in Canada and in the U.S. exhibited the lowest modal age

f
k
(x)=𝜇
k
(x)

S(x)
,

M
k=max
x

fk(x)
.
�
SD(
Mk+
)
=
√
∫𝜔

Mk
(
x−
Mk
)
2
fk(x)dx
/
∫𝜔

Mk

fk(x)
,
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329
1 3
Modal lifespan anddisparity atolder ages byleading causes…
M
^k
60
65
70
75
80
85
90
95
Heart diseases
Cerebrovascular diseases
a
Males
60
65
70
75
80
85
90
95
Prostate cancer
Colorectal cancer
Lung cancer
1980 1990 2000 2010
M
^kCAN− M
^kU.S.
−3
−1
1
3
Heart diseases
Cerebrovascular diseases
1980 1990 2000 2010
−3
−1
1
3
Prostate cancer
Colorectal cancer
Lung cancer
M
^k
60
65
70
75
80
85
90
95
Heart diseases
Cerebrovascular diseases
b Females
60
65
70
75
80
85
90
95
Breast cancer
Colorectal cancer
Lung cancer
1980 1990 2000 2010
M
^kCAN− M
^kU.S.
−2
−1
1
2
Heart diseases
Cerebrovascular diseases
1980 1990 2000 2010
−9
−6
−3
3
6
9
Breast cancer
Colorectal cancer
Lung cancer
1980 1990 2000 2010
84
86
88
90
92
Fig. 2 Estimated modal age at death,

Mk
, for leading causes of death among the elderly in Canada (dark
colors) and the U.S. (light colors) and corresponding country differences in

Mk
values, 1974–2011. Note:
For calendar years 1977 and 1978 (in Canada), and 1974–1976, 1978 (in the U.S.), the smooth density
function for breast cancer is bimodal. That is, we can distinguish two modal ages at death. In Fig. 2,
only the “dominant” mode is illustrated, i.e., the age with the highest proportion of deaths. Please refer
to Fig.4 in the "Appendix" and to Figure A-2 in Diaconu etal. (2016) for an illustration of a smooth
bimodal density function obtained with U.S. and Canadian data respectively. Source: Authors’ calcula-
tions based on the Canadian Vital Statistics Death database, U.S. National Vital Statistics System data
files, and Human Mortality Database
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330
V.Diaconu et al.
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at death values while those who succumbed from cerebrovascular diseases, and
from heart diseases in more recent years, had the highest values. Colorectal can-
cer’s modal ages at death ranked in between those for prostate and lung cancer
among males, and slightly above those for breast cancer among females.
Looking at males’ trends in

Mk
for heart diseases and lung cancer closely,
Fig.2 (panel a) shows that in 1974, modal age at death was 75.2 (heart) and 69.1
(lung) years among U.S. males, ranking them 2.5 and 1.3years behind their Cana-
dian counterparts. For heart diseases, however, a crossover occurred in the early
1980s, allowing U.S. males to take the lead, but the gap then narrowed gradually
and became barely noticeable by the end of the study period. In 2011, males died
from heart disease in the U.S. and in Canada most frequently at around 88years.
For lung cancer, the Canada-U.S. gap in modal age at death remained quite stable
in the beginning and in the end of the study period, with a clear dip for the U.S.
somewhere in the middle. Indeed, from 1974 to 1990,

Mk
increased steadily and
at a comparable pace in the two countries, but the level of the trend for Canadian
males remained about 1 year higher than that of U.S. males. Then,

M
k
estimates
for lung cancer among U.S. males declined slightly for about five consecutive
years (due to a moderate increase in death rates for males in their early 70 s),
while the upward trend of their Canadian peers continued uninterrupted. The gap
in modal age at death between the two countries peaked at 2.6years in 1995. In
the following years, the gap narrowed and the pre-1990 upward trend resumed
among U.S. males. In 2011 the most frequent age at death for lung cancer in
American males was 1.3years lower than their Canadian counterparts (77.3 vs.
78.6years).
For causes other than heart diseases and lung cancer among males, differences
in

Mk
levels between Canada and the U.S. are rather small. The modal age at
death values for cerebrovascular diseases went from about 81years in 1974 to
86years in 2004, increasing at a similar pace in both countries for most of the
study period. As of 2005, however, a small gap emerged between the two coun-
tries and became gradually more pronounced during the following years. In 2011,
Canadian males dying from cerebrovascular diseases ‘typically’ survived about
1.2 years more than their American peers (87.9 vs. 86.7 years). For colorectal
and prostate cancer, the U.S. modal age at death estimates show a subtle sinusoi-
dal variation around the Canadian ones. Since 1974, the increase in

Mk
for both
countries was about 7years for the two types of cancer, reaching almost 82 and
87years in 2011, respectively.
Among females the greatest disparities between Canada and the U.S. in

Mk
levels are recorded for lung cancer in the first years of the study period, and for
breast cancer since the mid-1980s (Fig.2, panel b). In 1974, the most frequent
age at which lung cancer deaths occurred among U.S. females was about 5 years
younger than for their Canadian counterparts (61.9 vs. 67.3years). This promi-
nent gap between the two countries was however observed for a short period of
time only. Indeed, lung cancer’s

Mk
in the U.S. increased very rapidly from 1974
to the mid-1980s, reaching the Canadian levels by the early 1980s. From this
point onwards, U.S. and Canadian females not only shared similar

M
k
levels but
also followed a similar upward trend that culminated at nearly 78years by 2011.
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331
1 3
Modal lifespan anddisparity atolder ages byleading causes…
In contrast, the modal age at death among Canadian and U.S. females dying from
breast cancer were almost identical in 1974 (about 72years) and no definite gap
could be discerned between these countries over the next 10

M
k
years. However,
since the mid-1980s and until the end of the study period, a substantial survival
advantage was observed for Canadian females. In 2011, the majority of deaths
from this disease occurred at 85years in Canada, or about 3 years later than in
the U.S.
Canadian and U.S. female modal age at death estimates for the remaining causes
displayed quite similar levels throughout the period 1974–2011. For the two main
subcategories of cardiovascular diseases,

Mk
in 1974 was close to 85years every-
where, but Canadian females started to record slightly higher levels for cerebro-
vascular diseases and, to a lesser extent, heart diseases in the mid-1990s and early-
2000s, respectively. In 2011, Canadian females dying from heart or circulatory
system condition survived until the year following their 90th anniversary, which
is about 1 year later than their American peers. For colorectal cancer, females in
Canada and the U.S. exhibited similar levels and patterns in

Mk
over the entire study
period; they gained a little more than five years of ‘typical’ length of life since 1974,
at an initial level of about 80years.
In short, our close examination of sex- and cause-specific modal age at death esti-
mates reveals that, with a few notable exceptions, Canada resembles greatly the U.S.
in terms of pace of increase and level of

Mk
throughout the period under study. This
resemblance applies to most causes of death, apart from lung cancer among males
and breast cancer for females.
Canada‑U.S. dierentials in

SD(
Mk+
)
Figure3 shows cause-specific trends and levels in

SD(
M
k
+
)
among Canadian and
U.S. males (panel a) and females (panel b) between 1974 and 2011. It reveals that

SD(
M
k
+
)
declined for all leading causes among Canadian and U.S. elderly since
1974. However, the causes of death differ greatly in terms of

SD(
M
k
+
)
levels. In
general, male and female deaths from heart diseases are more dispersed across the
old-age range than cerebrovascular diseases. The various types of cancers among
males rank, according to their

SD(
M
k
+
)
values (from lowest to highest), as follows:
prostate cancer, colorectal cancer, and lung cancer. Among females, colorectal can-
cer displayed the lowest

SD(
M
k
+
)
values in both countries with lung cancer, in Can-
ada, and breast cancer, in the U.S., the highest.
Figure 3 (panel a) reveals similar levels in cause-specific

SD(
M
k
+
)
among
males in both countries, except for heart diseases and lung cancer during specific
time periods. For heart diseases, the highest Canada-U.S. difference in

SD(
M
k
+
)
was observed during the first 6years of the study period. In 1974, variability of age
at death above M was about 1.3years higher in the U.S. than in Canada (10.3 vs
9years respectively). The gap between the two countries rapidly narrowed follow-
ing the accelerated decline in

SD(
M
k
+
)
in the U.S. By the early-1980s, variability
of age at death above M in Canada was slightly higher than in the U.S. and remained
this way throughout the rest of the study period. In 2011, variability in age at death
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V.Diaconu et al.
1 3
SD(Mk+)
5
6
7
8
9
10
11
Heart diseases
Cerebrovascular diseases
a
Males
5
6
7
8
9
10
11
Prostate cancer
Colorectal cancer
Lung cancer
1980 1990 2000 2010
SD(Mk+)CAN−SD(Mk+)U.S.
−2
−1
1
2
Heart diseases
Cerebrovascular diseases
1980 1990 2000 2010
−2
−1
1
2
Prostate cancer
Colorectal cancer
Lung cancer
SD(Mk+)
5
7
9
11
13
15
17
19
Heart diseases
Cerebrovascular diseases
b Females
5
7
9
11
13
15
17
19
Breast cancer
Colorectal cancer
Lung cancer
1980 1990 2000 2010
SD(Mk+)CAN−SD(Mk+)U.S.
−1
1
Heart diseases
Cerebrovascular diseases
1980 1990 2000 2010
−4
−2
2
4
Breast cancer Colorectal cancer
Lung cancer
1980 1990 2000 2010
5
6
7
8
Fig. 3 Estimated standard deviation of ages at death above the mode,

SD(
Mk+
)
, for leading causes of
death among the elderly in Canada (dark colours) and the U.S. (light colours) and corresponding country
differences in

SD(
Mk+
)
values, 1974–2011. Source: Authors’ calculations based on the Canadian Vital
Statistics Death database, U.S. National Vital Statistics System data files, and Human Mortality Database
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

333
1 3
Modal lifespan anddisparity atolder ages byleading causes…
among elderly Canadian males was a tad higher compared to their U.S. coun- ter-
parts (6.3 and 6.0years, respectively).
Substantial differences between Canadian and U.S. males were also noticed for
lung cancer, especially during the 1990–2002 period. Until the late 1980s, variabil-
ity of age at death among the elderly changed slightly in both countries (oscillated
around 9years). However, in the early 1990s a gap emerged between the two coun-
tries as

SD(
M
k
+
)
among U.S. males increased for about 4 years. During this period,

SD(
M
k
+
)
among Canadian males remained stable for about 2 years and declined
afterwards. Hence, the greatest gap between the two countries occurred in 1994
when

SD(
M
k
+
)
reached 9.9years in the U.S. and 8.7years in Canada. Since the
mid-1990s,

SD(
M
k
+
)
for lung cancer declined consistently in both countries attain-
ing a similar level of about 8.2years in 2011. Despite the identical level in

SD(
M
k
+
)
observed in both countries in more recent years, Canadian male deaths from lung
cancer were in general concentrated into a shorter old-age interval compared to
those of their U.S. counterparts for most of the study period.
For the remaining causes of death, the two countries exhibit small differences in
terms of

SD(
M
k
+
)
levels. In addition, these countries experienced similar reduc-
tions in variability of age at death above M, for cerebrovascular diseases, prostate
cancer, and to some extent colorectal cancer. In fact,

SD(
M
k
+
)
for cerebrovascular
diseases and prostate cancer declined for about 1.4years in both countries over the
1974–2011 period; going from a level of about 7.4 to 6years.

SD(
M
k
+
)
for colorec-
tal cancer, stagnated at a similar level of 9.0years in both countries until 1989 and
followed a downward trend in the years after. Since the early 1990s, U.S. elderly
males registered lower lifespan inequalities than their Canadian peers, however a
cross-over occurred in the early 2000s. Variability of age at death above M in 2011
was about 7months higher in the U.S. than Canada (8.1 vs 7.4years, respectively).
Canada-U.S. comparison of cause-specific

SD(
M
k
+
)
for females revealed small
differences between the two countries for most leading causes of death, except for
lung cancer, until late 1970s, and for breast cancer, since the 1980s (Fig.3). In 1974,
variability of deaths at ages above M for lung cancer in the U.S. was 14.7years, that
is about 2 years higher than in Canada. However, the

SD(
M
k
+
)
gap between the two
countries narrowed rapidly and attained a level of about 4months in 1981 as U.S.
old-age variability levels converged towards the Canadian ones. For the remaining
years of the study period,

SD(
M
k
+
)
exhibited similar trends and levels in both coun-
tries. In 2011, variability of age at death above M for lung cancer was slightly above
8.0years in both countries.

SD(
M
k
+
)
for breast cancer fluctuated in Canada and in
the U.S. for about 10years before starting to steadily decline in the 1980s. Indeed,

SD(
M
k
+
)
among Canadian and U.S. females went respectively from about 13.3 and
12.1years, in 1984, to 7.7 and 9.1years, in 2011. Throughout most of this period,
Canadian females exhibited lower levels of variability of age at death than their U.S.
peers.
For the remaining causes, the gap in

SD(
M
k
+
)
levels between the two countries
reached half a year at best throughout the 1974–2011 period. Unlike colorectal can-
cer for which almost identical

SD(
M
k
+
)
levels are observed in both countries, vari-
ability of age at death above M in Canada were slightly lower for cerebrovascular
diseases and slightly higher for heart diseases compared to those in the U.S. In 1974,
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334
V.Diaconu et al.
1 3

SD(
M
k
+
)
for these three specific causes of death varied between 7.9 (colorectal can-
cer) and 6.4years (cerebrovascular diseases) in Canada and between 6.8 (heart dis-
eases) and 7.5years (cerebrovascular diseases) in the U.S. The corresponding 2011
figures for these causes are respectively 6.4 and 5.7 years in Canada and 6.7 and
5.9years in the U.S.
In sum, our analysis shows minor differences between Canada and the U.S. in
terms of trends and levels in cause-specific

SD(
M
k
+
)
. Two causes of death, how-
ever, exhibited a clear distinct pattern in Canada compared to the U.S. in terms of

SD(
M
k
+
)
trends: heart diseases (males only) and lung cancer (males and females).
The differences were observed during specific time periods only, that is from 1974
to the early-1980s for heart diseases (males) and lung cancer (females) and from
1990 to 2002 for lung cancer (males).
Discussion
This study has compared levels and trends in sex and cause-specific modal lifes-
pan (Mk) and disparity (SD(Mk +)) between Canada and the U.S. during the period
1974–2011. For many years since the mid-1970s, the U.S. had a mortality disadvan-
tage relative to its northern neighbour with respect to these two lifespan indicators.
Our paper investigated whether this U.S. old-age survival and inequality disadvan-
tage was universal across the various leading causes of death examined, namely cer-
ebrovascular diseases, heart diseases, colorectal cancer, lung cancer, female breast
cancer, and male prostate cancer. The available evidence shows the contrary: the
disadvantage was in fact due to specific causes at specific times only. We discuss
this finding below, after offering our view on the otherwise similar trends and levels
recorded in both countries.
The overall trends in modal lifespan are positive for all leading causes among
males and females in Canada and the U.S. throughout the study period. The exten-
sion in the ‘typical’ length of human life was primarily due to improvements in old-
age survival initiated by the “cardiovascular revolution”, which began around 1970
in most industrialised countries (Ouellette etal. 2014; Vallin and Meslé 2004). Fol-
lowing major breakthroughs in curative and preventive medicine, as well as changes
in behavioural patterns and lifestyles brought upon by this revolution, cardiovascu-
lar mortality at adult and old ages started to decline steadily. The ongoing medical
progress in the years that followed the onset of the cardiovascular revolution paved
the way to a new wave of mortality reductions, but this time with respect to cancer.
Indeed, the decline in cancer mortality observed in Canada and in the U.S. since the
early 1990s (Cole and Rodu 1996; McLaughlin etal. 1997; Ouellette et al. 2014)
has been primarily associated with advanced screening procedures, earlier detection
of cancerous polyps, and effective therapeutic interventions (Cutler 2008; Edwards
etal. 2005; Hankey etal. 1999; Karim-Kos etal. 2008; Mandel etal. 2000; Mariotto
etal. 2002; Nam and Klotz 2009; NIH 1991; Schatzkin etal. 1994). Similar trends
have also been observed for smoking-related cancers, in particular lung cancer, but
the decline in mortality from this malignancy was mainly attributed to changes in
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335
1 3
Modal lifespan anddisparity atolder ages byleading causes…
patterns of smoking cessation (Devesa et al. 1989; Jemal et al. 2001) as well as
reduced smoking uptake. The successful fight against cardiovascular diseases and
the types of cancers studied here relied not only upon new biomedical knowledge
and identification of risk factors, but also on individuals’ understanding and use of
these preventive and curative developments. The ability of individuals to optimize
their potential for a longer life has been notably associated with gains in educational
attainment (Hayward etal. 2006; Hidajat et al. 2007). The changing educational
composition of the Canadian and American populations since the 1970s has there-
fore certainly played a key role in lowering death rates for these diseases. As the
educational attainment levels increased, individuals became more able to understand
the benefits of new medical technologies and of healthier lifestyles.
While progress against cardiovascular and cancer mortality was being made,
deaths that would have occurred at younger old ages were delayed to older old ages.
This resulted in an increasing concentration of deaths in the age range beyond M,
such as reflected by downward trends in cause-specific

SD(
M
k
+
)
since 1974 in the
two countries. The compression of deaths into a shorter age span suggests narrower
inequalities in the number of years lived by individuals dying within old age from
these particular causes. In other words, individuals became increasingly similar
in their capability of making informed decisions about their health and achieving
longer lives. In addition to the benefits of rising educational attainment and declin-
ing educational differences between individuals, this capacity also appears to have
been reinforced by health promotion campaigns, targeted to increase individuals’
knowledge regarding disease prevention. Indeed, in past decades, governments
in North America notably have used various media campaigns to raise awareness
within the population about the harmfulness of tobacco use, about heart disease
avoidance, and about the importance of cancer screening (Wakefield etal. 2010).
Another factor which likely played an important role in reducing lifespan variation
at older ages is the greater capability of the health care system to meet individuals’
needs, both in terms of medical care via technological advancements in treating par-
ticular diseases and in increased means of providing health services to a larger seg-
ment of the population (Cohen etal. 2009; Easterlin 1996; Weatherall etal. 2006).
Levels in

Mk
and

SD(
M
k
+
)
between Canada and the U.S. were also highly simi-
lar for most causes of death studied (i.e. heart diseases, cerebrovascular diseases,
colorectal cancer, male prostate cancer, and female lung cancer). This somewhat
surprising finding may be a result of the differential comparative advantages of
the Canadian and U.S. healthcare systems. While Canadians have a broader access
to preventive care at all ages, there seems to be more aggressive medical treat-
ment in the U.S., particularly at older ages when more Americans have access
to insurance coverage. A study comparing U.S. all-cause agespecific death rates
with those of 18 OECD countries, including Canada, indeed revealed that the U.S.
ranked poorly at ages below 70years but that its ranking improved dramatically
after age 70 (Ho and Preston 2010). This reversal in ranking has been associ-
ated with the U.S.’s more aggressive treatment and use of drugs for curing dis-
eases among the elderly. In particular for stroke and acute myocardial infarction,
the U.S. has higher survival rates among individuals aged 65+ than in Canada,
and the U.S. survival advantage grows with increasing age (Moise 2003; OECD
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336
V.Diaconu et al.
1 3
2003). Canadian patients diagnosed with acute myocardial infarction had a sig-
nificant survival advantage over their American peers before undergoing revas-
cularization. However, the survival gap between the two countries faded once a
revascularization was performed (Kaul etal. 2004). The authors concluded that
the U.S. survival advantage was due to the highly intrusive medical treatment pro-
vided to acute myocardial infarction patients. The U.S. is also more likely to resort
to carotid endarterectomy, a surgical procedure which removes plaque from the
carotid artery, for preventing death in individuals with high risk of stroke or recur-
rent stroke, than Canada (OECD 2003). Pharmacological treatments for reducing
risk factors, such as hypertension, are also more aggressively used in the U.S. than
in Canada. In fact, a higher percentage of older individuals (aged 50 and over) are
taking antihypertensive drugs in the U.S. than in Canada (Crimmins etal. 2010;
Wolf-Maier et al. 2014). Differences between the two countries have also been
observed in the aggressiveness of the treatment regime provided to individuals
diagnosed with prostate cancer. American urologists tended to use more intrusive
screening methods and were also more likely to perform radical prostatectomy on
older patients than their Canadian counterparts (Fleshner et al. 2000). In short,
without a more intrusive medical approach in treating chronic diseases in the U.S.
among the elderly, the U.S. would have ranked poorly with respect to old-age sur-
vival compared to Canada, as well as to other high income countries.
We found only two notable differences in modal age at death,

Mk
, and standard
deviation above the mode,

SD(
M
k
+
)
, between Canada and the U.S, namely for lung
cancer among males (throughout the period 1974–2011) and breast cancer among
females (since the mid-1980s). In both cases, the U.S. showed a disadvantage com-
pared with Canada by recording younger modal ages at death and greater variability
around that mode.
With respect to lung cancer, the literature has identified prevalence and intensity
of smoking as the primary sources of explanation for mortality differences across
nations (Mackay etal. 2006; Pampel 2010). In the U.S., the percentage of adults
who smoke and the cigarette consumption per smoker has been higher than in Can-
ada since the 1980s (Ritchie and Roser 2020). The long-lasting U.S. lung mortality
disadvantage with Canada among males in terms of modal age at death may also be
explained in part by differences in smoking uptake. Studies show that individuals
who never smoked have a much lower risk of dying from lung cancer than those who
have (Anthonisen 2005; Doll etal. 2004; Ockene etal. 1990). In the U.S., residents
aged 18 and over in 2002–2003 were interviewed and found to be more likely to be
current smokers that their Canadian peers, who in contrast were more likely to be
never smokers (Jones etal. 2010). The higher inequality in the age at death for lung
cancer faced by U.S. elderly males compared to their Canadian counterparts may
also stem from socioeconomic disparities in prevalence and intensity of tobacco use
between the two countries. Indeed, in spite of similar levels of economic develop-
ment and knowledge regarding the adverse health effects of cigarette consumption,
developed nations differ with respect to smoking prevalence and intensity (Pampel
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337
1 3
Modal lifespan anddisparity atolder ages byleading causes…
2010). We suspect that these differences are even more pronounced in countries dis-
playing a wider economic divide between individuals from different social strata,
given the strong association between smoking and socioeconomic status (Macken-
bach etal. 2015; Tjepkema etal. 2012, 2013). Therefore, the larger income inequali-
ties observed in the U.S. (Ross etal. 2000, 2005; Smeeding 2004) may be responsi-
ble for the higher levels of variability among U.S. males than Canadian ones.
The substantial gap in

M
and

SD(M+)
levels for breast cancer puts U.S. females
at a disadvantage. This result was somewhat unexpected because earlier stud-
ies have reported greater breast cancer survival rates in the U.S. than in Canada,
thanks to more aggressive screening and treatment (Hughes 2003; Ugnat et al.
2005). The most compelling explanation for the U.S. old-age survival and lifes-
pan inequality disadvantage for breast cancer may thus lie at the intersection of
behavioural differences and social distribution mechanisms, such as accessibil-
ity of the health care system. Postmenopausal breast cancer has been associated
with behavioural risk factors, including obesity and sedentary lifestyle (Levi etal.
2005; Menvielle etal. 2006; Yung and Ligibel 2016). While adult obesity preva-
lence increased in Canada and in the U.S. since the late 1970s, the gap between
the two countries gradually widened with the highest proportion of overweight
adult females being recorded in the U.S. (Alley etal. 2010). Also, because breast
cancer is highly amenable to medical intervention through screening and therapy,
it is possible that Canada and the U.S. differ with respect to access to these medi-
cal services. Studies comparing large metropolitan areas in Canada and the U.S.
showed that Canadian women diagnosed with breast cancer and living in low-
income areas have higher 5-year breast cancer survival rates than their U.S. coun-
terparts. However, no significant Canada-U.S. differences were observed in the
survival rates of women living in middle- and high- income areas (Gorey 2009;
Gorey et al. 1997, 2009a). The Canadian advantage was observed even when
women in the U.S. became eligible for Medicare (Gorey 2009). Therefore, dif-
ferences in

Mk
for breast cancer may in part reflect the higher survival of Cana-
dian women residing in less affluent areas compared to their American peers. This
Canadian survival advantage has been associated to the more inclusive health care
insurance coverage in Canada compared to the U.S., particularly among poorer
women. Moreover, these studies have also revealed that unlike in Canada, there is
a strong socioeconomic gradient in breast cancer survival in the U.S. (Gorey etal.
2000, 2009b). In the U.S. indeed, women diagnosed with breast cancer and living
in high-income areas exhibited a higher survival advantage than their counterparts
from middle-income areas, which in turn had higher survival chances compared
to those residing in low-income areas. The country-difference in the magnitude of
the socioeconomic gradient in breast cancer survival may in part be responsible
for the Canada-U.S. gap in

SD(M+)
levels.
In closing, while our study is the first to put forward the use of modal lifespan
and disparity indicators in a cause-of-death analysis, we have yet to show how the
cause-specific modal ages (
Mk
) contribute to changes in all-cause modal age (M), and
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338
V.Diaconu et al.
1 3
similarly for the standard deviations above the mode (SD(M +) and
SD(Mk+)
). There
are currently no methods which allow decomposing M or SD(M +) by cause of death.
Acknowledgements Open access funding provided by Projekt DEAL. We thank Carlo G. Camarda,
as well as participants at the 2016 Meeting of the Population Association of America and at the 2016
European Population Conference for valuable comments and suggestions. This project received finan-
cial support from the Fonds de recherche du Québéc - Société et culture (Grant No. 205739), the Social
Sciences and Humanities Research Council of Canada (Grant No. 435-2013-1893), the French National
Research Agency (ANR-12-FRAL-0003-01 DIMOCHA), and by the AXA project Mortality Divergence
and Causes of Death (MODICOD). Analyses based on the Canadian data were conducted at the Quebec
Interuniversity Centre for Social Statistics, part of the Canadian Research Data Centre Network, whose
services and activities are funded by Quebec universities and several Canadian governmental agencies.
Compliance with ethical standards
Conict of interest The authors declare that they have no conflict of interest.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Interna-
tional License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons license, and indicate if changes were made. The Crea-
tive Commons Public Domain Dedication waiver (http://creat iveco mmons .org/publi cdoma in/zero/1.0/)
applies to the data made available in this article, unless otherwise stated.
Appendix
See Table1 and Fig.4.
Table 1 Concordance table for bridging revisions 8, 9, and 10 of the ICD for leading causes of death in
Canada and the U.S
Items of ICD-8 for years 1969–1978, ICD-9 for 1979–1999, and ICD-10 since 2000 for Canada. Items of
ICD-8 for years 1968–1979, ICD-9 for 1979–1998, and ICD-10 since 1999 for the U.S.
Source: Diaconu etal. (2016)
Cause of death ICD-8 ICD-9 ICD-10
Circulatory diseases 390–458 390–459 I00–I99
Cerebrovascular diseases 430–434, 436–438 430–434, 436–438 I00–I69
Heart diseases 390–398, 402, 404, 410–429 390–398, 402, 404, 410–429 I00–I09,
I11,
I13,
I20–I51
Malignant neoplasms 140–208 140–208 C00–C97
Breast cancer 174 174 C50
Colorectal cancer 153–154 153–154 C18–C21
Prostate cancer 185 185 C61
Lung cancer 162 162 C33–C34
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339
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Modal lifespan anddisparity atolder ages byleading causes…
0
1
2
3
4
5
f
^k(x) per 100 deaths
20 40 60 80 100
Prostate cancer
0
1
2
3
4
f
^k(x) per 100 deaths
20 40 60 80 100
Colorectal cancer
0
1
2
3
4
f
^k(x) per 100 deaths
20 40 60 80 100
Lung cancer
0
1
2
3
4
Age x
f
^k(x) per 100 deaths
20 40 60 80 100
Heart diseases
0
1
2
3
4
Age x
f
^k(x) per 100 deaths
20 40 60 80 100
Cerebrovascular diseases
Males
20 40 60 80 100
0
1
2
3Breast cancer
0
1
2
3
4
20 40 60 80 100
Colorectal cancer
0
1
2
3
4
20 40 60 80 100
Lung cancer
0
1
2
3
4
5
Age x
20 40 60 80 100
Heart diseases
0
1
2
3
4
5
Age x
20 40 60 80 100
Cerebrovascular diseases
Females
Fig. 4 Smooth density functions describing the age-at-death distribution for leading causes of death
among elderly U.S. males and females aged 10 and above, for calendar years 1974 (thin line), 1993
(medium line), and 2011 (thick line). Source: Authors’ calculations based on the U.S. National Vital Sta-
tistics System data files, and Human Mortality Database
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

340
V.Diaconu et al.
1 3
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