CONTEMPORARY METHODS OF MORTALITY ANALYSIS Lecture 2 Leonid Gavrilov Natalia Gavrilova 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) 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. 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) 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 Trends in life expectancy for women in Russia, USA and Estonia Special methods based on life table approach Multiple decrement life tables Cause-elimination life tables Decomposition of life expectancy 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 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. Multiple decrement life table – steps of construction Construct an ordinary life table Calculate probabilities of death from cause k k x q = qx M k x Mx = qx D k x Dx Multiple decrement life table – steps of construction (continue) Calculate number of decrements from cause k in age interval (x, x+n): k x d =q k x lx Calculate numbers of survivors to age y for those who eventually die from cause k during his/her life: k x d l = x =y k x 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 Mean expected age at death by cause, women, Russia Васин С., доклад в Киеве 2006 Comparison of mortality structure for Russia and Western countries 1965 Vassin, 2006 Comparison of mortality structure for Russia and Western countries 2004 год Васин С., доклад в Киеве 2006 Decomposition of life expectancy Suggested by Andreev (1982), Pollard (1982) and Arriaga (1984) Decomposition by age 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 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 Decomposition by age (continue) = l 1 l 10 T 2 l2 T 1 l1 The last open age interval Decomposition by contribution of different causes of death i x = = R x m x i (2 ) x i (2 ) x m i (1 ) x m (x2 ) m (x1 ) m (2 ) x R i (1 ) x m (2 ) x m (1 ) x m (1 ) x where Rix designates a proportion of deaths from cause i in age group (x, x+n), which is Dix/Dx. In this case Dix corresponds to the observed number of deaths from cause i in age interval (x, x+n), and Dx is a corresponding number of deaths from all causes. 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 Δx corresponds to contribution of differences in mortality from all causes of death in =age interval (x, x+n) to the observed differences in life expectancy. It can be shown that i x x i 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. Additional reading Preston S. H., Heuveline P., Guillot M. Demography. Measuring and modeling population processes. Blackwell Publ., Oxford, 2001. Cause elimination life tables Cause elimination life table Uses an additive property of hazard rate m x = m + m + ... + m 1 x 2 x k x Chiang’s method (1978) – assumes proportionality of hazard rates from different causes k a =r k a , x a x+n Main formula for cause elimination life table k qx = 1 (1 1 qx ) r 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: rk = D kx Dx Mortality in Central Asia An example of practical use of demographic methods Background on Mortality in Russia Before the World War II Life expectancy (both sexes) 80 70 60 50 40 30 20 10 0 59 47 47 63 Russia 43 32 France USA 1900 1938 Catching up with the West Life expectancy in 1965 80 70 60 50 40 30 20 10 0 64.3 67.3 66.8 73.4 74.7 73.7 Russia France USA Men Women Stagnation after 1965 In 1992 and 1998 Russia experienced two serious economic crises accompanied by drop in personal income and rapid impoverishment Russia: Trends in life expectancy 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. Ethnic Differentials in Mortality 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 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) 2008 Workshop, Bishkek 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%) Recorded trends in adult mortality (20-60 years) Kyrgyzstan, 40q20 0.30 0.10 0.20 q2060 0.10 0.20 q2060 0.30 0.40 Females 0.40 Males 1960 1970 1980 y ear 1990 2000 1960 1970 1980 y ear 1990 2000 russian ky rgy z russian ky rgy z slv cas slv cas Mortality paradox? Soviet period: Russians/Slavs occupied dominant positions in the socio-economic structure of Central Asian societies (Kahn 1993) 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) Proportion of individuals with post-secondary education, by age and ethnicity, in 1989 census. Females SLAVIC (Russian, Ukrainian, Belorussian), 1989 CENTRAL ASIAN (Kyrgyz, Uzbek), 1989 0.300 Proportion higher education 0.250 0.200 0.150 0.100 0.050 0.000 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 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) Proportion of individuals with post-secondary education, by age and ethnicity, in 1989 census. Males. SLAVIC (Russian, Ukrainian, Belorussian), 1989 CENTRAL ASIAN (Kyrgyz, Uzbek), 1989 0.250 Proportion higher education 0.200 0.150 0.100 0.050 0.000 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 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) 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) IMR by ethnicity, 1958-2003, Kyrgyzstan 30 20 10 IMR 40 50 Urban areas 1960 1970 1980 year Central Asians 1990 Slavs 2000 Data Unpublished population and death tabulations since 1959 collected from local archives Individual census records – 1999 Individual death records – 19981999 obtained from national statistical office Possible explanations for mortality paradox Data artifacts Migration effects (esp. 1989-99) Cultural effects Data artifacts? Could the lower recorded mortality among Central Asian adults be due to lower data quality among them (coverage of deaths, age misreporting)? 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)? 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? 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+ Kyrgyzstan, 40q20, Urban areas 0.30 0.20 0.10 0.10 0.20 q2060 0.30 0.40 Females 0.40 Males 1960 1970 1980 y ear 1990 2000 1960 1970 1980 y ear 1990 2000 russian ky rgy z russian ky rgy z slv cas slv cas Health selection? Russians in KG vs. Russia, 40q20 0.40 0.50 Females 0.10 0.20 0.30 q2060 0.30 0.20 0.10 q2060 0.40 0.50 Males 1960 1970 1980 y ear Russians in KG 1990 2000 Russia 1960 1970 1980 y ear Russians in KG 1990 2000 Russia Cohort-specific changes in educational attainment, Males, 1989-99 SLAVIC, 1989 SLAVIC, 1999 0.300 Proportion higher education 0.250 0.200 0.150 0.100 0.050 0.000 Age in 1989: 20-24 Age in 1999: 30-34 25-29 35-39 30-34 40-44 35-39 45-49 40-44 50-54 45-49 55-59 50-54 60-64 55-59 65-69 60-64 70-74 65-69 75-79 70-74 80-84 75-79 85-89 80-84 90-94 Cohort-specific changes in educational attainment, Females, 1989-99 SLAVIC, 1989 SLAVIC, 1999 0.300 Proportion higher education 0.250 0.200 0.150 0.100 0.050 0.000 Age in 1989: Age in 1999: 20-24 30-34 25-29 35-39 30-34 40-44 35-39 45-49 40-44 50-54 45-49 55-59 50-54 60-64 55-59 65-69 60-64 70-74 65-69 75-79 70-74 80-84 75-79 85-89 80-84 90-94 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 Age-standardized Death Rates at working ages (per 100000), 1998-99, by cause and ethnicity, Males Infectious/par. diseases - incl. TB Neoplasms CVD CA Slavs - incl. IHD Respiratory diseases Digestive diseases Injuries/poisoning Other causes 0 50 100 150 200 250 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) 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 ri es In C V R D es pi ra to ry D is . D ig es t iv e D is . pl as m s N eo In fe ct io ns 0.0 ho m un de te rm in ed su ic id e . ic id ac e cid .p oi al so lo ni th ng er ac ci d. tra ca ns us po . rt ac ci ac de ci nt de s nt al dr ow ac c. ni ca ng us ./e ac le ct c. r.c m ec ur ha n. su ffo ca t. ot he r in ju ry ac ci d. po is on ./a lco h Age-standardized Death Rates at working ages (per 100,000). Detailed Injuries, Males 50 45 40 35 Slavs CA 30 25 20 15 10 5 0 Age-standardized Death Rates at working ages (per 100,000), 1998-99, by cause and ethnicity, Females Infectious/par. diseases - incl. TB Neoplasms CVD - incl. IHD Respiratory diseases Digestive diseases CA Slavs Injuries/poisoning Other causes 0 10 20 30 40 50 60 70 80 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) 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 Age-standardized Death Rates at working ages (per 100,000) Detailed Injuries, Females 9 Slavs CA 8 7 6 5 4 3 2 1 0 c ac ./a n o is o .p id h lco . m ho e id ic g in n iso e et po . d d ci un c y a r o. ju n i rm ed n i s. u a t.c ts ur re ng i i n c f . n e y tr w id c b o c e n l dr se ac /e l de . u i t a or us ca cc nt . p a a e d . d .c ns ci c lo ci c a l c c a a tr a a de ci i su 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) 50 45 CA Slavs 40 35 30 25 20 15 10 5 0 Males Females 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 Males, all causes of death In e s. ie s di s. di ju r es t iv Di g y Re sp ir a to r CV D pl as m s ns ca us es fe ct io Ne o In Al l Risk Ratio Slavs/CA Males 3.5 3.0 2.5 2.0 Model 1 1.5 Model 2 1.0 0.5 0.0 Risk Ratio Slavs/CA Females 3.5 3.0 2.5 2.0 Model 1 Model 2 1.5 NS NS 1.0 NS NS NS NS NS NS 0.5 au se s ie s O th e rc ju r In CV Re D sp ir a to ry Di s. Di ge st iv e Di s. pl as m s Ne o ns fe ct io In Al l C au se s 0.0 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 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? Further developments Divergent paths for adult mortality in Russia and Central Asia: Evidence from Kyrgyzstan By M.Guillot, N.S.Gavrilova and L.Torgashova Presented at the annual meeting of the European Association for Population Studies (2011) Age-standardized mortality rate, 40M20 Kyrgyzstan and Russia, 1981-2006 Age-standardized mortality rate, 40M20 Kyrgyzstan and Russia, 1981-2006 Study of autopsies in Barnaul during 1990-2004 (Zaridze et al., 2009) Among 5732 autopsied men aged 3569 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 Codes used for the calculation of cause-specific mortality in Russia And Kyrgyzstan Age-standardized mortality rate, 40M20 Kyrgyzstan, 1981-2006, all causes and broad causes Age-standardized mortality rate, 40M20 Kyrgyzstan, 1981-2006, all causes and broad causes 40M20 (Russia) – 40M20 (Kyrgyzstan), 1989-1999, all causes and strongly alcohol related causes 40M20 (Russia) – 40M20 (Kyrgyzstan), 1989-1999, all causes and strongly alcohol related causes 40M20 (Russia) – 40M20 (Kyrgyzstan), 1979-2009, all causes and strongly alcohol related causes 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 Greater importance of of detrimental adult health care health behaviors deterioration Trends in Life Expectancy: Men Russia Kyrgyzstan 65.00 63.00 61.00 59.00 57.00 55.00 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 Life expectancy 67.00 Calendar year Trends in Life Expectancy: Women Russia Kyrgyzstan 76.00 74.00 73.00 72.00 71.00 70.00 Calendar year 2010 2008 2006 2004 2002 2000 1998 1996 1994 1992 1990 1988 1986 1984 1982 69.00 1980 Life expectancy 75.00 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 Almaty is surrounded by mountains Workshop in Almaty ‘Montmartre’ in Almaty 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 Additional reading Guillot M, Gavrilova N, Pudrovska T. Understanding the "Russian mortality paradox" in Central Asia: Evidence from Kyrgyzstan. Demography, 2011, 48(3): 10811104.