Cause-of-death contributions to declining mortality improvements and life expectancies using cause-specic scenarios Alexander M. T. L. Yiu Torsten Kleinow and George Streftaris

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Cause-of-death contributions to declining mortality improvements and life

expectancies using cause-speciﬁc scenarios

Alexander M. T. L. Yiu, Torsten Kleinow, and George Streftaris

School of Mathematical and Computer Sciences, Heriot-Watt University, and Maxwell

Institute for Mathematical Sciences, UK

Abstract

In recent years, improvements in all-cause mortality rates and life expectan-

cies for males and females in England and Wales have slowed down. In this

paper, cause-speciﬁc mortality data for England and Wales from 2001 to 2018

are used to investigate the cause-speciﬁc contributions to the slowdown in im-

provements. Cause-speciﬁc death counts in England and Wales are modelled

using negative binomial regression and a breakpoint in the linear temporal trend

in log mortality rates is investigated. Cause-speciﬁc scenarios are generated,

where the post-breakpoint temporal trends for certain causes are reverted to

pre-breakpoint rates and the eﬀect of these changes on age-standardised mortal-

ity rates and period life expectancies is explored. These scenarios are used to

quantify cause-speciﬁc contributions to the mortality improvement slowdown.

Reductions in improvements at older ages in circulatory system diseases, as well

as the worsening of mortality rates due to mental and behavioural disorders and

nervous system diseases, provide the greatest contributions to the reduction of

improvements in age-standardised mortality rates and period life expectancies.

Future period life expectancies scenarios are also generated, where cause-speciﬁc

mortality rate trends are assumed to either persist or be reverted. In the majority

of scenarios, the reversion of cause-speciﬁc mortality trends in a single cause of

death results in the worsening of period life expectancies at birth and age 65 for

both males and females. This work enhances the understanding of cause-speciﬁc

contributions to the slowdown in all-cause mortality rate improvements from

2001 to 2018, while also providing insights into causes of death that are drivers

of life expectancy improvements. The ﬁndings can be of beneﬁt to researchers,

policy-makers and insurance professionals.

Keywords:

Causes of death; Life expectancy; Mortality projections; Mor-

tality rates; Mortality trends; Negative binomial regression

arXiv:2210.12442v1 [stat.AP] 22 Oct 2022

1 Introduction

In recent years, England and Wales have been experiencing a reduction in the

annual improvements in all-cause mortality rates. This study uses cause-speciﬁc

mortality experience to investigate the observed slowdown in these annual im-

provements in all-cause mortality. The aim of the study is to quantify the

contributions of diﬀerent causes of death towards the reduction in mortality rate

improvements, and also to investigate life expectancies under various scenarios

for cause-speciﬁc mortality rate trends. Aiming at enhancing the understanding

of the slowdown in all-cause mortality improvements, cause-speciﬁc scenarios

are generated in order to explore the diﬀerences in mortality rate improvements

that are observed, compared to improvements in scenarios where cause-speciﬁc

trends are reverted to pre-slowdown levels. These cause-speciﬁc scenarios are

useful for the purpose of investigating what would have happened if the trends

for certain causes of death had remained the same throughout the observed

slowdown in mortality improvements. The use of scenarios is a novel approach

for quantifying cause-speciﬁc contributions. Investigating the impact of individ-

ual causes towards the slowdown in mortality improvements is important for

better understanding of the drivers of increasing human longevity.

Many countries in the world have experienced improvements in life expectancy

throughout the 20th century into the 21st century. A number of authors have

noted that reductions in infectious disease and infant mortality have led to

the greatest amount of improvements in life expectancy in the ﬁrst half of

the 20th century for Europe and North America (Wilmoth, 2000; Oeppen and

Vaupel, 2002; Cutler, Deaton, and Lleras-Muney, 2006; Leon, 2011; Mackenbach

and Looman, 2013). In the United States and Western European countries,

improvements in cardiovascular disease mortality at older ages led to the contin-

ued improvement in life expectancies after 1970 (Tuljapurkar and Boe, 1998;

Wilmoth, 2000; Levi, Lucchini, Negri, and La Vecchia, 2002; Oeppen and Vaupel,

2002; Cutler, Deaton, and Lleras-Muney, 2006; Leon, 2011; Mackenbach and

Looman, 2013). However, Eastern European countries experienced increasing

levels of cardiovascular disease mortality (Levi, Lucchini, Negri, and La Vecchia,

2002; Leon, 2011), which led to slower gains and even worsening of life expectan-

cies (Leon, 2011). The improvement in cardiovascular disease mortality was

linked to improvements in risk factors and in treatments (Levi, Lucchini, Negri,

and La Vecchia, 2002; O’Flaherty, Ford, Allender, Scarborough, and Capewell,

2008; Scholes, Bajekal, Love, Hawkins, Raine, O’Flaherty, and Capewell, 2012).

Mackenbach and Looman (2013) also suggested that the improvement in cardio-

vascular mortality at older ages might be related to the national income of a

country.

England and Wales have also experienced similar reductions in infectious

disease and cardiovascular disease mortality during the 20th century (Griﬃths

and Brock, 2003; O’Flaherty, Ford, Allender, Scarborough, and Capewell, 2008).

Along with improvements in cardiovascular disease mortality, England and

Wales have shown changing trends in associated risk factors. O’Flaherty et al.

(2008) and Scholes et al. (2012) noted reductions in smoking prevalence, but

also increases in the prevalence of obesity and diabetes. While improvements

in cardiovascular disease mortality continued to occur at older ages, the rate

of improvement appeared to be slowing for individuals aged 55 and younger

(O’Flaherty, Ford, Allender, Scarborough, and Capewell, 2008; Howse and

Harper, 2008).

The rate at which mortality is improving may have lowered in recent years.

The Oﬃce for National Statistics (ONS) identiﬁed a reduction in mortality

improvement in England and Wales. In particular, using the all-cause mortality

experience in England and Wales from 1990 to 2017, the ONS suggested that a

change in the temporal trend of mortality rate improvements in age-standardised

mortality rates occurred in the early 2010s, for both males and females (Oﬃce

for National Statistics, 2018c).

The Oﬃce for National Statistics (2018a) have also explored all-cause mortal-

ity and cause-speciﬁc rate trends in the United Kingdom and have indicated

that reductions in improvements in circulatory system diseases and increases

in cancer mortality and mortality due to mental and behavioural disorders,

to be the leading contributors to the observed increase in mortality rates at

older ages across the United Kingdom. At younger ages, increases in deaths

due to external causes of death, such as accidents and intentional self-harm,

provided the greatest contributions to increased mortality at these ages. Bennett

et al. (2018), Public Health England (2018), and Steel et al. (2018) investigated

the mortality rate trends in England and suggested that the most deprived

groups in terms of socio-economic status were associated with greatest lack of

improvements, in both all-cause and cause-speciﬁc mortality. This was also

addressed by Boumezoued et al. (2021), where they suggested that this pattern

was observable across all countries.

The recent reduction in mortality rate improvements is not limited to England

and Wales, or the rest of the United Kingdom. The Oﬃce for National Statistics

(2018b) performed a comparison of the changes in average annual life expectancy

improvements between 20 countries and the United Kingdom was identiﬁed to

have experienced one of the highest reductions in improvement amongst the

countries studied. The observed slowdown in improvements did not appear to

be a result of the life expectancy approaching a maximum, as countries with

higher life expectancy than the United Kingdom, such as Japan and Sweden,

did not experience slowdowns. Boumezoued et al. (2019) also noted a slowdown

in mortality rate improvements in the United States, with circulatory system

diseases being the major cause of this slowdown. Leon et al. (2019) discussed

the lower estimated life expectancies compared to other high-income countries

due to a worsening of observed mortality rates at ages 25 to 44. Raleigh (2019)

provided additional discussions on the potential risk factors which contributed to

the observed trends in the slowdown of mortality rate improvements. While the

comparison of cause-speciﬁc mortality trends between diﬀerent countries would

greatly aid the understanding of observed all-cause mortality trends, diﬀerences

in the recording and coding of causes of death prevent a reliable comparison

between countries.

Hiam et al. (2017 and 2018) noticed a sharp increase in mortality in England

and Wales in 2015 in contrast to the trends in previous years. While reductions

in mortality due to cancers and circulatory system diseases provided positive

contributions to male and female life expectancies, increases in mortality due to

diseases such as Alzheimer’s disease and dementia resulted in a net reduction in

estimated life expectancies. In addition, the oldest age group had the greatest

contribution to the reduction in the estimated life expectancy (Hiam et al., 2017).

Although a single year with higher than average mortality rates inﬂuences the

overall temporal trend in mortality rates, the eﬀects of the single year may be

oﬀset by the observed mortality rates in other years.

Modelling mortality by the cause of death introduces additional challenges

that are not necessarily present when modelling all-cause mortality. Despite

individuals facing a potential risk of dying due to a number of causes, normally

only one cause is recorded at the actual event of death. Cause-speciﬁc mortality

rates can be modelled by using competing risk methods, where an individual

is exposed to multiple risks of death arising from diﬀerent causes during his or

her lifetime, but death can only result from a single cause of death. However,

a problem arises in competing risk methods for cause-speciﬁc mortality, as

the dependency structure between the diﬀerent causes of death is not known

(Tsiatis, 1975). Dimitrova et al. (2013) explored copula methods with a known

dependency structure in order to model competing causes of death. Alai et al.

(2015) investigated the dependencies between diﬀerent causes of death using

multinomial logistic models.

In addition to competing risk models, relationships between cause-speciﬁc

mortality rates have also been examined. Arnold-Gaille and Sherris (2013)

investigated cause-speciﬁc mortality rates using time-series models. The models

included vector autoregressive models and vector error correction models in

order to model the dependence of cause-speciﬁc mortality rates through time.

Arnold-Gaille and Sherris (2015) also investigated cause-of-death mortality rates

using cointegration analysis.

In this paper, negative binomial regression is used in order to assess the

contributions of cause-speciﬁc mortality rate trends on the observed slowdown in

mortality rate improvements observed in England and Wales from 2001 to 2018.

The methodology being employed here diﬀers from existing methodologies by

quantifying additional rates of improvement of mortality rates and life expectan-

cies under the assumptions of continuing cause-speciﬁc mortality rate trends.

In addition to observed rates, future life expectancy scenarios are generated

under diﬀering assumptions of cause-speciﬁc mortality rate trends. These future

life expectancy scenarios reveal the causes of death with the greatest inﬂuence

towards life expectancy improvements in the future.

The paper begins with a brief outline of the dataset that is used in the

analyses. An initial investigation into the log age-standardised mortality rates is

performed for the purpose of determining a suitable single breakpoint location

for changes in temporal trends in all-cause and cause-speciﬁc mortality rates.

This breakpoint location is used with negative binomial regression in order to

model cause-speciﬁc death counts and to investigate cause-speciﬁc contributions

to the observed temporal trends in log age-standardised mortality rates and

period life expectancies. Lastly, future life expectancy scenarios are generated

for the purpose of investigating the potential eﬀects of cause-speciﬁc trends on

period life expectancies in the near future. While deaths from COVID-19 occur

during the projection period, this cause is not considered for the analyses in

this paper. The analyses performed in this paper and detailed discussions are

elaborated in greater detail in Yiu (2022).

2 Data

In this paper, we use data comprising cause-speciﬁc mortality and population in-

formation in England and Wales, obtained from the Oﬃce for National Statistics

(2019). The dataset is chosen for the purpose of investigating the cause-speciﬁc

mortality experience in England and Wales, and includes generalised mortality

data about the cause-speciﬁc mortality experience of individuals from birth to

age 85 and above, from 2001 to 2018. The data include death counts grouped

by 5-year age bands, cause of death, gender, and the year in which the deaths

are registered. Corresponding mid-year population estimates are also obtained

from the same source. The causes of death were classiﬁed according the Interna-

tional Classiﬁcation of Diseases (ICD) 10th revision (World Health Organization,

2016). The time period from 2001 to 2018 is chosen in order to avoid possible

problems arising from changes in cause-of-death classiﬁcations. However, the

ONS documented a change in the classiﬁcation from the classiﬁcation system

ICD-10 v2001.2 used in 2001 to ICD-10 v2010 in 2011 (Oﬃce for National

Statistics, 2011). Another update to the classiﬁcation was implemented in 2014

(Oﬃce for National Statistics, 2014). These changes in the classiﬁcations of

deaths present a problem to cause-speciﬁc mortality analyses, as the number of

deaths attributed to a speciﬁc cause may not be consistent under the diﬀerent

classiﬁcation schemes. Some of the eﬀects of the classiﬁcation changes were

discussed by the Oﬃce for National Statistics (2011, 2014, 2016).

Speciﬁc causes of death are grouped into larger groups according to the chap-

ters in the 10th revision of the International Classiﬁcation of Diseases (World

Health Organization, 2016). A full list of the deaths by ICD-10 code and their

assigned groups are provided in Table 1.

Following an initial exploration into cause-speciﬁc mortality rates by age

group, it appears that the patterns in the mortality rates range greatly across

age groups for diﬀerent causes of death. For the purpose of modelling age- and

cause-speciﬁc mortality, the age groups are treated as levels of a factor covariate

rather than values of a numerical variable. The age groups,

, are the 5-year

age bands ranging from

1, 1-4, 5-9, ..., 80-84, and the last group of individuals

aged 85 and above, giving a total of 19 age groups.

3 Cause-speciﬁc mortality rates

Let

dx,t

denote the observed death counts in age group

in calendar year

, where

the age groups

are deﬁned in Section 2, and the calendar years

range from

2001 to 2018.

Ex,t

represent the corresponding mid-year population estimates for

age group

in calendar year

. Death counts and mid-year population estimates

are considered here by gender separately, and for the remainder of the paper

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Cause-of-deathcontributionstodecliningmortalityimprovementsandlifeexpectanciesusingcause-specicscenariosAlexanderM.T.L.Yiu,TorstenKleinow,andGeorgeStreftarisSchoolofMathematicalandComputerSciences,Heriot-WattUniversity,andMaxwellInstituteforMathematicalSciences,UKAbstractInrecentyears,improvementsi...

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Cause-of-death contributions to declining mortality improvements and life expectancies using cause-specic scenarios Alexander M. T. L. Yiu Torsten Kleinow and George Streftaris

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