CONTEMPORARY METHODS OF MORTALITY ANALYSIS

1
CONTEMPORARY METHODS OF MORTALITY ANALYSIS

• Lecture 2
• Leonid Gavrilov
• Natalia Gavrilova

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Measures of Mortality

• Crude Death Rate
• Age-Specific Death Rates (Age-Specific Mortality
  Rates)
• Age-Adjusted Mortality Rates (Standardized
  Mortality Rates)
• Life Expectancy (at birth or other age)
• Measures of Infant Mortality

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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

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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)

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Trends in crude death rates (per 1,000) for
Russia, USA and Estonia
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Distribution of crude death rates (per 1,000) in
Russia, 2003
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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.

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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)

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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)

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Age-Adjusted Death Rate or Age-Standardized
Death Rate

• Direct method of age standardization

• 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.

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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.

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Typical standard populations

• European standard population and World standard
  population suggested by the World Health
  Organization
• In the United States 1940 U.S. standard
  population and 2000 U.S. standard population
  (applied around 2003)

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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.

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Life Table

• Cohort life table as a simple example
• Consider survival in the cohort of fruit flies
  born in the same time

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Number of dying, d(x)
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Number of survivors, l(x)
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Number of survivors at the beginning of the next
age interval

• l(x1) l(x) d(x)

Probability of death in the age interval
q(x) d(x)/l(x)
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Probability of death, q(x)
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Person-years lived in the interval, L(x)
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)
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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
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Life expectancy, e(x)

• T(x) L(x) L?
• where L? 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, ,?

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Life Tables for Human Populations

• In the majority of cases life tables for humans
  are constructed for hypothetic birth cohort using
  cross-sectional 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

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Formula for q(x) using age-specific mortality
rates
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.
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Life table probabilities of death, q(x), for men
in Russia and USA. 2005
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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

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Life table number of survivors, l(x), for men in
Russia and USA. 2005.
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Life table number of dying, d(x), for men in
Russia and USA. 2005
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Life expectancy, e(x), for men in Russia and USA.
2005
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Trends in life expectancy for men in Russia, USA
and Estonia
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Trends in life expectancy for women in Russia,
USA and Estonia
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Special methods based on life table approach

• Multiple decrement life tables
• Cause-elimination life tables
• Decomposition of life expectancy

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Multiple decrement life tables

• Multiple decrement life tables
• Often used to construct life tables by cause of
  death
• In this case decrements are different causes of
  death

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Multiple decrement life tables vs ordinary life
tables

• In an ordinary life table, membership in a
  well-defined cohort can be terminated by a single
  attrition factor.
• In a multiple-decrement life table, there are
  multiple reasons for attrition (death).
• Ordinary life tables can be used to answer
  questions about longevity.
• A multiple-decrement life table will be used to
  answer the question, "What is the probability
  that a newborn will die due to a specific cause
  before reaching age 65?
• In an ordinary life table of mortality it is
  assumed that everyone eventually dies.
• The multiple-decrement life table will provide
  the probability that a person will eventually die
  due to a specific cause.

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Multiple decrement life table steps of
construction

• Construct an ordinary life table
• Calculate probabilities of death from cause k

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Multiple decrement life table steps of
construction (continue)

• Calculate number of decrements from cause k in
  age interval (x, xn)
• Calculate numbers of survivors to age y for those
  who eventually die from cause k during his/her
  life

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Multiple decrement life table steps of
construction (continue)

• Calculate life-time probability of dying from
  cause k
• lk/l0
• Calculate mean expected age at death from cause k
  by calculating Lkx and Tkx
• Calculated as life expectancy in the ordinary
  life table

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Mean expected age at death by cause,women, Russia
????? ?., ?????? ? ????? 2006
38
Comparison of mortality structure for Russia and
Western countries 1965
Vassin, 2006
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Comparison of mortality structure for Russia and
Western countries 2004 ???
????? ?., ?????? ? ????? 2006
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Decomposition of life expectancy

• Suggested by Andreev (1982), Pollard (1982) and
  Arriaga (1984)

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Decomposition by age
Where values lx, Lx, Tx represent standard
functions from ordinary life table, and notations
1 and 2 correspond to populations 1 and 2
respectively (comparing populations).
Thus, we need first to calculate ordinary life
tables for populations 1 and 2
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Decomposition by age (continue)
The last open age interval
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Decomposition by contribution of different causes
of death
where Rix designates a proportion of deaths from
cause i in age group (x, xn), which is Dix/Dx.
In this case Dix corresponds to the observed
number of deaths from cause i in age interval (x,
xn), and Dx is a corresponding number of deaths
from all causes.
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Decomposition by causes of death (continue)
Notations (1) and (2) correspond to comparing
populations. Values mx correspond to life table
mortality rates derived from ordinary life
tables, because mx dx/Lx. In this formula
value ?x corresponds to contribution of
differences in mortality from all causes of death
in age interval (x, xn) to the observed
differences in life expectancy. It can be shown
that
45
Decomposition of the U.S.-Russia gap in life
expectancy by cause
USA 1999 Russia 2001. Source Shkolnikov et
a. Mortality reversal in Russia.
46
Decomposition of the U.S.-Russia gap in life
expectancy by cause
USA 1999 Russia 2001. Source Shkolnikov et
a. Mortality reversal in Russia.
47
Additional reading

• Preston S. H., Heuveline P., Guillot M.
  Demography. Measuring and modeling population
  processes. Blackwell Publ., Oxford, 2001.
•  

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Cause elimination life tables
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Cause elimination life table

• Uses an additive property of hazard rate
• Chiangs method (1978) assumes proportionality
  of hazard rates from different causes

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Main formula for cause elimination life table
In this formula notation k means that
probability of death is related to cause
elimination (not a power).
Proportionality ratio rk can be obtained from the
observed number of deaths in a particular age
interval
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Mortality in Central Asia

• An example of practical use of demographic methods

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Background on Mortality in Russia
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Before the World War IILife expectancy (both
sexes)
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Catching up with the WestLife expectancy in 1965
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Stagnation after 1965
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In 1992 and 1998 Russia experienced two serious
economic crises accompanied by drop in personal
income and rapid impoverishment
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Russia Trends in life expectancy
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Mortality reversal

• Situation when the usual time trend of declining
  mortality is reversed (mortality is increasing
  over time).
• Observed in sub-Saharan Africa (AIDS epidemic), 
  Eastern Europe, and FSU countries including
  Russia.
• Mortality Reversal in FSU countries and Russia is
  particularly strong among male population, with
  excess mortality at ages about 35-55 years.
• Particularly high increase in mortality from
  violence and accidents among manual workers and
  low education groups.

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Ethnic Differentials in Mortality
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Based on the Study of Ethnic Differentials in
Adult Mortality in Kyrgyzstan

• Michel Guillot (PI), University of
  Wisconsin-Madison
• Natalia Gavrilova, University of Chicago
• Tetyana Pudrovska, University of Wisconsin-Madison

Demography, 2011, 48(3) 1081-1104
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Background on Kyrgyzstan

• Former Soviet republic became independent in
  1991
• Population 5.2 million (2006)
• Experienced a severe economic depression after
  break-up of Soviet Union
• GNI per capita 440 USD 28th poorest country
  in the world (2005)
• 48 of population below national poverty line
  (2001)

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2008 Workshop, Bishkek
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Ethnic Groups in Kyrgyzstan

• Native Central Asian groups Kazakh, Kyrgyz,
  Tajik, Turkmen, Uzbek (Sunni Muslims)
• Slavs Russian, Ukrainian, Bielorussian
• Kyrgyzstan, 1999 census
• Central Asians 79 of pop. (Kyrgyz 65)
• Slavs 14 of pop. (Russian 12)

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Recorded trends in adult mortality (20-60 years)
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Mortality paradox?

• Soviet period Russians/Slavs occupied dominant
  positions in the socio-economic structure of
  Central Asian societies (Kahn 1993)

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Mortality paradox?

• Slavic females more educated than Central Asian
  females (1989 and 1999 censuses)
• Slavic males educational advantage not so clear
  varies by age (1989 and 1999 censuses)
• Slavic households less poor than Central Asians
  (1993 World Bank poverty survey)
• Infant mortality lower among Slavs (Soviet and
  post-Soviet period)

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Proportion of individuals with post-secondary
education, by age and ethnicity, in 1989 census.
Females
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Mortality paradox?

• Slavic females more educated than Central Asian
  females (1989 and 1999 censuses)
• Slavic males educational advantage not so clear
  varies by age (1989 and 1999 censuses)
• Slavic households less poor than Central Asians
  (1993 World Bank poverty survey)
• Infant mortality lower among Slavs (Soviet and
  post-Soviet period)

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Proportion of individuals with post-secondary
education, by age and ethnicity, in 1989 census.
Males.
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Mortality paradox?

• Slavic females more educated than Central Asian
  females (1989 and 1999 censuses)
• Slavic males educational advantage not so clear
  varies by age (1989 and 1999 censuses)
• Slavic households less poor than Central Asians
  (1993 World Bank poverty survey)
• Infant mortality lower among Slavs (Soviet and
  post-Soviet period)

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Mortality paradox?

• Slavic females more educated than Central Asian
  females (1989 and 1999 censuses)
• Slavic males educational advantage not so clear
  varies by age (1989 and 1999 censuses)
• Slavic households less poor than Central Asians
  (1993 World Bank poverty survey)
• Infant mortality lower among Slavs (Soviet and
  post-Soviet period)

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IMR by ethnicity, 1958-2003, Kyrgyzstan
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Data

• Unpublished population and death tabulations
  since 1959
• collected from local archives
• Individual census records 1999
• Individual death records 1998-1999
• obtained from national statistical office

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Possible explanations for mortality paradox

• Data artifacts
• Migration effects (esp. 1989-99)
• Cultural effects

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Data artifacts?

• Could the lower recorded mortality among Central
  Asian adults be due to lower data quality among
  them (coverage of deaths, age misreporting)?

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Migration effects?

• 1/3 of Russian population has left Kyrgyzstan
  since 1991
• Could the increased disparity between Russian and
  Kyrgyz adult mortality be due to selective
  migration (healthy migrant effect)?

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Cultural effects?

• Culture may affect mortality in various ways
• individual health and lifestyle behaviors (e.g.,
  diet, smoking, alcohol, use of preventive care)
• family structure and social networks (denser
  social networks may produce lower stress levels
  and better health)
• Could different cultural practices among Slavs
  and Central Asians explain the observed mortality
  differentials?

82
Data artifacts?

• Intercensal estimates of death registration
  coverage above age 60 (Guillot, 2004)
• 90 as early as 1959 in urban areas
• coverage in rural areas was low initially (50)
  but caught up with urban areas in 1980s
• Total population 92 for 1989-99 period
• Adult deaths (20-59) usually better reported than
  deaths 60

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Health selection?
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Cohort-specific changes in educational
attainment, Males, 1989-99
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Cohort-specific changes in educational
attainment, Females, 1989-99
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Cultural effects?

• Analysis of causes of death by ethnicity, 1998-99
• Calculations based on micro-data
• Deaths vital registration (1998-99)
• Exposure census (March 1999)
• Ages 20-59
• Ethnicity Central Asians vs. Slavs
• 20,000 death records 2.2 million census
  records

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Age-standardized Death Rates at working ages (per
100000), 1998-99, by cause and ethnicity, Males
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Contribution of causes of death to the difference
in life expectancy at working ages (40e20)
between Slavs and Central Asians Males (total
difference 2.90 years)
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Age-standardized Death Rates at working ages (per
100,000). Detailed Injuries, Males
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Age-standardized Death Rates at working ages (per
100,000), 1998-99, by cause and ethnicity, Females
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Contribution of causes of death to the difference
in life expectancy at working ages (40e20)
between Slavs and Central Asians Females (total
difference .28 years)
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Age-standardized Death Rates at working ages (per
100,000) Detailed Injuries, Females
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Alcohol-related Causes of Death(Chronic
alcoholism, Alcohol psychoses, Alcohol cirrhosis
of the liver, Accidental poisoning by alcohol)
Age-standardized Death Rates at working ages
(per 100,000)
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Multivariate analysis

• Do ethnic mortality differentials at adult ages
  remain once we account for differences in
  education and urban/rural residence?
• Negative binomial regression
• Dependent variable deaths from all causes
  deaths by major cause (7)
• Explanatory variables exposure, dummy variables
  for age, ethnicity, urban/rural residence,
  education (3 cat.)
• Males and Females analyzed separately
• Model 1 age, ethnicity
• Model 2 age, ethnicity, education, residence

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Males, all causes of death
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Risk Ratio Slavs/CAMales
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Risk Ratio Slavs/CAFemales
NS
NS
NS
NS
NS
NS
NS
NS
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Conclusions

• Excess mortality among adult Slavs (Soviet and
  post-Soviet period) is not likely due to data
  artifacts or migration effects
• Excess mortality due to important ethnic
  differences in cause-specific mortality alcohol
  and suicide in particular
• Differences remain unexplained by education or
  residence

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Conclusions

• Role of cultural characteristics?
• Alcohol tied to cultural practices (culture of
  alcohol among Russians Impact of Islam for
  Central Asians)
• Denser social networks and stronger social
  support among Central Asian ethnic groups?

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Divergent paths for adult mortality in Russia and
Central AsiaEvidence from Kyrgyzstan
Further developments

• By M.Guillot, N.S.Gavrilova and L.Torgashova
• Presented at the annual meeting of the European
  Association for Population Studies (2011)

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Age-standardized mortality rate, 40M20Kyrgyzstan
and Russia, 1981-2006
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Age-standardized mortality rate, 40M20Kyrgyzstan
and Russia, 1981-2006
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Study of autopsies in Barnaul during 1990-2004
(Zaridze et al., 2009)

• Among 5732 autopsied men aged 35-69 years who
  were reported to have died from circulatory
  diseases 49 had alcohol detected in their blood
  and in 21 concentration of ethanol was 4g/l and
  higher (lethal dose)
• Of 5880 autopsied men aged 35-69 years who were
  reported to have died from injuries 76 had
  alcohol in their blood and in 38 concentration
  of ethanol was 4g/l and higher

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Codes used for the calculation of cause-specific
mortality in Russia
And Kyrgyzstan
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Age-standardized mortality rate,
40M20Kyrgyzstan, 1981-2006, all causes and
broad causes
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Age-standardized mortality rate,
40M20Kyrgyzstan, 1981-2006, all causes and
broad causes
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40M20 (Russia) 40M20 (Kyrgyzstan), 1989-1999,
all causes and strongly alcohol related causes
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40M20 (Russia) 40M20 (Kyrgyzstan), 1989-1999,
all causes and strongly alcohol related causes
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40M20 (Russia) 40M20 (Kyrgyzstan), 1979-2009,
all causes and strongly alcohol related causes
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Framework for Understanding Health Crisis in
Russia vs. Central Asia
Russia Kyrgyzstan (Central Asia?)
Infant mortality Declined Stalled
Adult mortality Large increase Moderate increase
Explanatory framework Greater importance of detrimental adult health behaviors Greater importance of health care deterioration
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Trends in Life Expectancy Men
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Trends in Life Expectancy Women
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Workshop in Almaty, Kazakhstan, July 2011

• Organized by the United Nations Population Fund
  (UNFPA)
• Results of applying new methods to demographic
  estimation of mortality in Central Asian countries

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Almaty is surrounded by mountains
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Workshop in Almaty
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Montmartre in Almaty
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Acknowledgements

• National Statistical Committee of the Kyrgyz
  Republic
• Zarylbek Kudabaev, Orozmat Abdykalykov, Liudmila
  Torgashova, Larissa Mimbaeva, Elena Komandirova
  and Mikhail Denisenko
• NICHD R03 HD38752, R01 HD045531

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Additional reading

• Guillot M, Gavrilova N, Pudrovska T.
  Understanding the "Russian mortality paradox" in
  Central Asia Evidence from Kyrgyzstan.
  Demography, 2011, 48(3) 1081-1104.