Causes of death and methods of their analysis.

Причины смерти и методы
их анализа
Н.С. Гаврилова
Causes of death and their
classification


Established by the World Health
Organization as International
Classification of Diseases (ICD)
Has several revisions. The most
recent revision is the 10th revision.
Adopted by most countries in the mid
1990s
Classification of causes of
death in Russia



Classification of causes of death used
in the Soviet statistical forms was
different from WHO classification.
Form #5 (later called form C51) had
185 causes of death.
Main differences between WHO and
Soviet classification are found in the
groups of CVD and injuries
New classification of causes of
death in Russia



After dissolution of the Soviet Union
most FSU countries continued to use
the old classification of causes of
death
In 1999 Russia adopted a new
classification of causes of death
corresponding to the 10th ICD
revision
Still incompatible with the WHO
classification
Selected Causes of Death
Total
Cancer
CardioVD
IHeartD
CerebrVD
Accident
USA
(1994)
Germany
(1995)
Russia
(1995)
776.1
195.0
307.2
157.6
48.0
55.5
764.1
196.7
343.8
151.2
78.3
41.2
1513.8
200.8
795.8
378.9
288.8
234.3
Major causes of death within the
group of injuries. Men
Иванова и др., Demoscope Weekly, N181-182, 2004
Major causes of death within the
group of injuries. Women
Иванова и др., Demoscope Weekly, N181-182, 2004
Degradation of mortality statistics
in Russia
Pace of Growth of Age-Adjusted Mortality in
1989-2000 for Classes of Causes of Death
9
8
7
6
5
Males
Females
4
3
2
1
0
All causes
Injuries
Ill-Def.C.
Infections
Proportion of deaths from illdefined conditions is a measure of
quality of mortality statistics
Proportion higher than 5%
indicates poor quality
In developed countries most
deaths from ill-defined conditions
are diagnosed at older ages
Is this increase in mortality from
ill-defined conditions related to
more cases of deaths from
senility?
Age Profile of Mortality from
Ill-Defined Conditions in Russia
Males
Females
160
140
2001
1991
Age-Specific Mortality per 100,000
Age-Specific Mortality Rate per 100,000
200
150
100
50
120
2001
1991
100
80
60
40
20
0
0
0
20
40
Age
60
80
0
20
40
Age
60
80
Top Five Causes of Death for
Young Adult Males (20-24)
1990
2001
Injuries
Injuries
Neoplasms
Symptoms, Signs and IllDefined Conditions
Diseases of Circulatory
System
Infectious Diseases
Symptoms, Signs and IllDefined Conditions
Neoplasms
Diseases of Nervous System
and Sens.Organs
Diseases of Respiratory
System
Top Five Causes of Death for
Young Adult Females (20-24)
1990
2001
Injuries
Injuries
Neoplasms
Neoplasms
Diseases of Circulatory
System
Diseases of Circulatory
System
Complications of Pregnancy
and Childbearing
Symptoms, Signs and IllDefined Conditions
Diseases of Nervous System
and Sens.Organs
Infectious Diseases
Which Causes of Death Are
Hidden Behind the Ill-Defined
Conditions?
We Used Individual Death Certificates With
More Detailed Description of Circumstances
of Death Collected by Kirov Department of
Health
Kirov is a Typical Russian Region with Lower
than Average Mortality from
Ill-Defined Conditions
Age-Adjusted Mortality from Injuries in 1996
for Russian Males Aged 0-64 years
Data from the WebAtlas Project (http://sci.aha.ru/ATL)
Deaths from Ill-Defined Conditions in
Kirov Region of Russia in 2003












Sudden infant death (R95)
3.3%
Decomposition in water (river, well, pond) (R99)
13.0%
Decomposition at home (R99)
53.5%
Decomposition in garden, summer house (R99)
1.7%
Decomposition in forest or field (R99)
6.0%
Decomposition in nonresidential building, on the street (R99)
12.3%
Decomposition in water pipe (R99)
0.7%
Decomposition on the cemetery (R99)
0.3%
Decomposition in bath, lavatory or barn (R99)
1.0%
Decomposition in other place (R99)
5.5%
unknown (R99)
2.3%
senility (R54)
0.3%
Ill-defined conditions and external
deaths of undetermined intent
are two sides of the same coin
It appears that both causes of death
may be used for concealing criminal
cases of violent death
Mortality in Moscow city
80
Ill-defined conditions
injuries of undetermined intent
Age-adjusted death rate per 100,000
70
60
50
40
30
20
10
0
1996
1998
2000
2002
Year
2004
2006
Top Five Causes of External Mortality in Russia
and Moscow in 2001
Russia
Moscow
Suicide
Accidental Falls
Undetermined Injury
Undetermined Injury
Homicide
All Other Accidental Causes
Accidental Poisoning by
Alcohol
Homicide
All Other Accidental Causes
Suicide
Autopsies in Russia


Autopsies are used to verify cause of
death
Autopsy is mandatory for violent
death, death of woman during
pregnancy, labor or postpartum
period, death of infant below 1 year,
death from cancer not supported
morphologically, death from any
infectious disease
Situation with medical examiner
services



Only 34-48% of jobs are filled by
physicians
38-54% of jobs are filled by
histologists
35% of workers reached retirement
age
Additional reading
Gavrilova N.S., Semyonova V.G.,
Dubrovina E., Evdokushkina G.N.,
Ivanova A.E., Gavrilov L.A. Russian
Mortality Crisis and the Quality of
Vital Statistics. Population Research
and Policy Review, 2008, 27: 551574.
Measures of Mortality





Crude Death Rate
Age-Specific Death Rates (AgeSpecific Mortality Rates)
Age-Adjusted Mortality Rates
(Standardized Mortality Rates)
Life Expectancy (at birth or other
age)
Measures of Infant Mortality
Crude Death Rate


Number of deaths in a population during a
specified time period, divided by the population
size "at risk" of dying during that study period.
For one-year period, Crude Death Rate,
CDR = Deaths in that year /mid-year population size
x 1,000 to adjust for standard-sized population of 1,000 persons
mid-year population = total population for July 1
Crude Death Rate Pros and Cons


Pros:
- Easy to calculate, and require less
detailed data than other mortality
measures
- Useful for calculation of the rate of
natural increase (crude birth rate minus
crude death rate)
Cons:
- Depends on population age structure
(proportions of younger and older people)
Trends in crude death rates (per
1,000) for Russia, USA and Estonia
Distribution of crude death rates
(per 1,000) in Russia, 2003
Age-Specific Death Rates (ASDR) or
Age-Specific Mortality Rates (ASMR)

Number of deaths in a specific age group during a
specified time period, divided by the size of this
specific age group during that study period.
Example:
For one-year study period, Age-Specific Death
Rates, ASDR for males at age 45-49 years =
= Deaths to males aged 45-49 in that year /
Number of males aged 45-49 at mid-year
x 1,000 to adjust for standard-sized population
of 1,000 persons of that age.
Age-Specific Death Rates
Pros and Cons


Pros:
- Allows to study mortality by age
(and sex)
Cons:
- Requires detailed data on deaths by
age (not always available for
developing countries, war and crisis
periods, historical studies)
Infant Mortality Rate, IMR

Proportion of infants who die in their first year
Number of deaths under age one during a specified time
period, divided by the number of live births
For one-year period, Infant Mortality Rate
Deaths under age one in that year
IMR 
Number of live births in that year
x 1,000 to standardize per 1,000 live births
Infant Mortality Rate Pros and Cons
Pros:
- Sensitive indicator of overall health conditions in a
country, particularly child health
- Useful for indirect estimates of mortality in other
age groups through imputation, using the socalled "model life tables"

Cons:
- Requires accurate data on births and infant deaths
(not always available for developing countries,
war and crisis periods, historical studies)

Changes in infant mortality in
Russia, USA and Estonia
Definition of live birth in the USSR was
not consistent with WHO definition




WHO definition of live birth: "the complete expulsion or
extraction from its mother of a product of conception,
irrespective of the duration of pregnancy which, after such
separation, breathes or shows any other evidence of life, such
as beating of the heart, pulsation of the umbilical cord or
definitive movement of voluntary muscles, whether or not the
umbilical cord has been cut or the placenta is attached.“
The Soviet Union adopted a less inclusive definition,
excluding infants born before 28 weeks and those weighing
less than 1000 grams, regardless of signs of life.
Soviet definition resulted in underestimation of infant
mortality
After getting independence, many FSU countries adopted
WHO definition of live birth
Distribution of infant mortality in
Russian regions, 2003
Стандартизованные
показатели



Стандартизованный коэффициент
(прямой метод)
Стандартизованное отношение
смертности
Потенциальные годы потерянной
жизни
Age-adjusted death rate (ADR),
standardized death rate (SDR) or
age-standardized death rate (ASDR)

Death rate expected if the studied
population had the age distribution of
another "standard" population (arbitrary
chosen for the purpose of comparison).
Calculated as weighted average (with
weights being proportions of the
"standard" population at each age)
Age-Adjusted Death Rate or
Age-Standardized Death Rate

Direct method of age standardization:
P si M ui
ADR =
i


Ps
Mui is mortality rate in the studied population
at age i
Psi – number of persons at age i in the standard
population. Ps – total standard population.
Age-Adjusted Death Rate or
Age-Standardized Death Rate


Pros:
- Allows comparison of death rates of
populations despite differences in their age
distribution
Cons:
- Requires data on death rates by age (not
always available for developing countries, war
and crisis periods, historical studies)
- Results of comparison may depend on the
arbitrary choice of standard.
Стандартизованное
отношение смертности или
Standardized mortality ratio
Du
SMR =
P ui M si
i
где Du - суммарное число умерших в изучаемой популяции, Msi - коэффициент
смертности в стандартной популяции в возрастной группе i, Pui - численность
населения в возрастной группе i для изучаемой популяции
Стандартизованное
отношение смертности


Полезно использовать для
маленьких регионов и редких
причин смерти
За стандартное распределение
обычно выбирается распределение
смертей по всей стране
Потенциальные годы
потерянной жизни Potential
Years of Life Lost (PYLL)
ai = T
xi
PYLL =
Di ai
где T - верхний предельный возраст, до которого рассчитывается недожитие (обычно 70 или 65 лет), x - середина
соответствующего возрастного интервала.
i
Потерянные годы потенциальной жизни рассчитываются как сумма произведений числа умерших на недожитые годы в каждой
возрастной группе
Коэффициент потерянных лет потенциальной жизни рассчитывается соответственно:
RatePYLL
= PYLL/Pu
где Pu - численность изучаемого населения в возрасте от 1 до T.
The Concept of Life Table

Life table is a classic demographic format of
describing a population's mortality experience
with age.
Life Table is built of a number of standard
numerical columns representing various
indicators of mortality and survival.
The concept of life table was first suggested in
1662 by John Graunt.
Before the 17th century, death was believed to be
a magical or sacred phenomenon that could not
and should not be quantified. The invention of
life table was a scientific breakthrough in
mortality studies.
Life Table


Cohort life table as a simple
example
Consider survival in the cohort of
fruit flies born in the same time
Number of dying, d(x)
Number of survivors, l(x)
Number of survivors at the
beginning of the next age interval:
l(x+1) = l(x) – d(x)
Probability of death in the age
interval:
q(x) = d(x)/l(x)
Probability of death, q(x)
Person-years lived in the interval, L(x)
Lx = x
lx + lx +
x
2
L(x) are needed to calculate life
expectancy. Life expectancy, e(x),
is defined as an average number of
years lived after certain age.
L(x) are also used in calculation of net
reproduction rate (NRR)
Calculation of life expectancy, e(x)
Life expectancy
at birth is
estimated as an
area below the
survival curve
divided by the
number of
individuals at
birth
Life expectancy, e(x)


T(x) = L(x) + … + Lω
where Lω is L(x) for the last age
interval.
Summation starts from the last age
interval and goes back to the age at
which life expectancy is calculated.
e(x) = T(x)/l(x)
where x = 0, 1, …,ω
Life Tables for Human Populations



In the majority of cases life tables for
humans are constructed for
hypothetic birth cohort using crosssectional data
Such life tables are called period life
tables
Construction of period life tables
starts from q(x) values rather than
l(x) or d(x) as in the case of
experimental animals
Formula for q(x) using
age-specific mortality rates
qx =
Mx
1 + (1
ax ) Mx
a(x) called the fraction of the last interval of life is
usually equal to 0.5 for all ages except for the first age
(from 0 to 1)
Having q(x) calculated, data for all other life table
columns are estimated using standard formulas.
Life table probabilities of death, q(x), for
men in Russia and USA. 2005
1
0
10
20
30
40
50
60
log(q(x))
0.1
0.01
0.001
0.0001
Age
Russia
USA
70
80
90
100
Period life table for hypothetical
population


Number of survivors, l(x), at the
beginning is equal to 100,000
This initial number of l(x) is called
the radix of life table
Life table number of survivors, l(x), for men
in Russia and USA. 2005.
120000
100000
80000
Russia
60000
USA
40000
20000
0
0
10
20
30
40
50
60
70
80
90
100
Life table number of dying, d(x), for men in
Russia and USA. 2005
Russia
USA
3500
3000
d(x)
2500
2000
1500
1000
500
0
0
10
20
30
40
50
Age
60
70
80
90
100
e(x)
Life expectancy, e(x), for men in Russia and
USA. 2005
80
70
60
50
40
30
20
10
0
Russia
USA
0
10
20
30
40
50
Age
60
70
80
90 100
Trends in life expectancy for men
in Russia, USA and Estonia
Distribution of life expectancy,
Men, 1999
Special methods based on life
table approach



Таблицы смертности
множественного выбытия
Таблицы смертности при
устранении причины смерти
Декомпозиция ожидаемой
продолжительности жизни
Таблицы смертности
множественного выбытия



Multiple decrement life tables
Часто используется для построения
таблиц смертности по причинам
Декременты – смерти от различных
причин
Таблицы смертности
множественного выбытия –
этапы построения


Построить обычную таблицу
смертности от всех причин
Рассчитать вероятность смерти от
причины k
q kx = q x
M kx
Mx
= qx
D kx
Dx
Таблицы смертности
множественного выбытия – этапы
построения (продолжение)

Рассчитать
число
декрементов
причины k в интервале (x, x+n):
от
d kx = q kx l x

Рассчитать числа доживших до возраста y
для тех, кто в течение последующей жизни
умрет от причины k:
k
x
d
l =
x =y
k
x
Таблицы смертности
множественного выбытия – этапы
построения (продолжение)



Рассчитать
вероятность
умереть
данной причины в течение жизни:
lk/l0
от
Рассчитать средний ожидаемый возраст
умерших, рассчитав соответственно Lkx
и Tkx
Рассчитывается так же как ожидаемая
продолжительность жизни в обычной
таблице
Средний
ожидаемый
возраст смерти
по причинам,
женщины России
Васин С., доклад в Киеве
2006
Вероятность для
новорожденного
умереть на
протяжении
жизни от семи
групп причин
смерти (на 100
родившихся),
мужчины России
БСК и новообр. – правая
ось Васин С., доклад в
Киеве 2006
Сравнение
структуры
смертности
мужчин
России и
Западных
стран.
1965 год
Васин С., доклад в Киеве
2006
Сравнение
структуры
смертности
мужчин
России и
Западных
стран.
2004 год
Васин С., доклад в Киеве
2006
Декомпозиция
продолжительности жизни
по возрасту и причинам
смерти
Метод декомпозиции

Предложен Андреевым (1982),
Поллардом (1982) и Арриагой
(1984)
Декомпозиция по возрасту
x
=
l
1
x
l
1
0
L
l
2
x
2
x
L
l
1
x
1
x
+
T
2
x +n
l
1
0
l
1
x
l
2
x
l
1
x +n
l
2
x +n
где величины lx, Lx, Tx представляют собой стандартные величины из обычной
таблицы смертности, а индексы 1 и 2 соответствуют не возведению в степень, а
популяции 1 и популяции 2 соответственно (то есть двум сравниваемым популяциям).
Необходимо рассчитать обычные таблицы смертности для
двух сравниваемых популяций
Декомпозиция по возрасту
=
l
1
l 10
T
2
l2
T
1
l1
Последний открытый возрастной интервал
Декомпозиция вклада отдельных
причин в различия по
продолжительности жизни
i
x
=
=
m
x
i (2 )
x
m
(2 )
x
R ix(2 ) m (x2 )
x
m (x2 )
m
i (1 )
x
m
(1 )
x
R ix(1 ) m (x1 )
m (x1 )
где Rix обозначает пропорцию смертей от причины i в возрастной группе (x, x+n), то есть
Dix/Dx. В данном случае Dix соответствует наблюдаемому чилу умерших от причины i в
возрастном интервале (x, x+n), а Dx - соответсвующее число умерших от всех причин.
Декомпозиция по причинам смерти
Индексы (1) и (2) соответсвуют сравниваемым популяциям.
Значения mx соответсвуют табличным коэффициентам смертности
от всех причин, которые можно получить из обычной таблицы
смертности, поскольку mx = dx/Lx. В данной формуле величина Δx
соответствует вкладу различий в смертности от всех причин в
возрастном интервале (x, x+n) в наблюдаемые различия в
i
ожидаемой продолжительности жизни. Можно показать, что
x =
x
i
а также что
e
(1 )
0
(2 )
x
e =
x
x
i
x
=
x
i
Decomposition of the U.S.-Russia
gap in life expectancy by cause
USA – 1999; Russia – 2001. Source: Shkolnikov et a. Mortality reversal in Russia.
Decomposition of the U.S.-Russia
gap in life expectancy by cause
USA – 1999; Russia – 2001. Source: Shkolnikov et a. Mortality reversal in Russia.
Contribution of different causes of
death to changes in LE, men
Contribution of different causes of
death to changes in LE, women
Age and cause components of LE
increase due to anti-alcohol campaign:
Men
Age and cause components of LE
increase due to anti-alcohol campaign:
Women
Contribution of causes of death to
40e20(CA) - 40e20(Slav)
Males (total difference = 2.90 years)
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
au
se
s
O
th
e
rc
ju
rie
s
In
CV
Re
D
sp
ir a
to
ry
Di
s.
Di
ge
st
iv
e
Di
s.
pl
as
m
s
Ne
o
In
fe
ct
io
ns
0.0
Contribution of causes of death to
40e20(CA) - 40e20(Slav)
Females (total difference = .28 years)
0.35
0.30
0.25
0.20
0.15
0.10
0.05
au
se
s
O
th
e
rc
ju
rie
s
In
Di
s.
e
es
t iv
CV
D
pl
as
m
s
Di
s.
Di
g
-0.10
Re
sp
ir a
to
ry
In
-0.05
Ne
o
fe
ct
io
ns
0.00
Additional reading
Preston S. H., Heuveline P., Guillot M.
Demography. Measuring and
modeling population processes.
Blackwell Publ., Oxford, 2001.
Таблицы смертности при
устранении причины
смерти
Таблица смертности при
устранении причины смерти

Использует свойство аддитивности
интенсиности смертности
m x = m + m + ... + m
1
x

2
x
k
x
Метод Чанга (1978) – допущение
пропорциональности смертности от
отдельных причин
k
a
=r
k
a
, x a x+n
Основная формула для расчета
таблицы смертности при устранении
причины смерти
k
qx = 1
(1
1
qx )
r
В данной
формуле индекс –k означает не возведение в степень, а тот факт, что показатель
относится к случаю, когда причина смерти k устранена.
Коэффициент пропорциональности rk можно получить из отношения наблюдаемых чисел
умерших в данном возрастном интервале:
rk =
D kx
Dx