Todays Topics

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Todays Topics

• Comparing death rates across populations
• Chapter 3 exercises
• Data sources
• Mortality types and mortality trends
• Life Table

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Excel Exercises
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Comparing Populations

• Whats the Problem?
• Apples and Oranges
• Why Bother?
• If the differences are real, helps to identify
  population and public health trends and problems

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Age Standardization

• Eliminate age-distribution differences
• Amx Pop A m-type death rate for age group x
• SPx Population exposed to risk of death in some
  standard population for age group x
• ASDR for Pop A

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What is the ASDR?

• What does this do?
• The expected deaths for population A if you
  assume you have the age-specific death rates of
  population A but the age-structure of a standard
  population

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What is the ASDR?

• Another way to state this
• ASDR is
• Crude Death Rate of Standard Population times the
  Comparative Mortality Factor

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Another Perspective The CMF
Exp Deaths in Std Pop if it had Pop A
Age-specific DR Actual Deaths in Std Population
(Crude Death Rate in the Standard Population)
ASDR
x
This is the Comparative Mortality Factor (CMF) or
Ratio of Death Rates Between Pop A and Std Pop
Deaths at age x in Std Pop
Total Deaths in Std Pop
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Move to Indirect Standardization
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Standardized Mortality Ratio (SMR)

• Why do we need this?
• The ASDR and CMF require that we know the
  age-specific death rates in Population A
• Often this is not available, is known with error,
  or is based on small samples
• The SMR handles this by asking
• What is the ratio of deaths in Pop A (which is
  usually known) to the the number of deaths we
  would have expected in Pop A if it experienced
  Age-specific death rates of the standard
  population?
• This requires we know the age distribution of
  Pop A and the age-specific death rates of a
  standard population. We will not know the
  age-specific death rates of Pop A

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Standardized Mortality Ratio (SMR)
Numerator Total Deaths in Population
A Denominator Total Deaths in Population A if
experienced age-specific
death rates of the
standard population
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What Standardization Relies Upon
If this ratio is similar across all age
groups, standardization works pretty well. If
not, standardization will not be ideal but at
least acceptable
This is theoretical because you wont know Amx in
SMR case
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What Do You Have?

• Direct Standardization
• Age-specific mortality rates of Pop A and Age
  Distribution of Standard Population
• Gives you actual rates
• Indirect Standardization
• Total deaths and age distribution of Pop A,
  Age-specific mortality rates of Standard
  Population
• Gives you SMR, a ratio

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Sources of Data

• Vital Records
• Births, deaths, fetal deaths, marriages
• U.S. Census Records
• Genealogies
• Surveys

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Vital Records Data Source

• www.demography.utah.edu
• National Center for Health Statistics
• http//www.cdc.gov/nchs/

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Census Data Source

• www.demography.utah.edu
• US Maps and how Utah stacks up
• Utah
• http//www.census.gov/census2000/states/ut.html

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Sources of Data

• Vital Records
• Births, deaths, fetal deaths, marriages
• U.S. Census Records
• Genealogies
• http//www.huntsmancancer.org/groups/ppr/
• Family Group Sheets
• Surveys

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Sources of Data

• Vital Records
• Births, deaths, fetal deaths, marriages
• U.S. Census Records
• Genealogies
• Surveys

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Surveys (1of 2)

• http//www.lib.utah.edu/icpsr/index.html
• Sampling
• Sampling frames and generalizability
• Coverage - RDD
• Nonresponse -Total Item
• Prospective/longitudinal
• Retrospective/cross sectional
• World Fertility Surveys - often with illiterate
  respondents
• Demographic and Health Surveys

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Surveys (2 of 2)

• Who and How You Get It
• Self vs Proxy
• Identifiers to link to other data (SSN)
• National Death Index
• Mode of administration
• Questionnaire construction
• Length of survey
• Types of questions
• Factual or subjective

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Mortality and the Life Table

• Definitions and trends in mortality
• Use of the life table to summarize a populations
  mortality experience

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Types of Mortality

• Infant Mortality
• Definitions
• Levels
• Global Trends
• The Rate of Progress
• Measurement
• Causes of Death

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Infant Mortality

• Stillbirth
• Death after 24 weeks gestation.
• Fetus shows no sign of life at birth
• http//www.cdc.gov/nchs/data/dvs/FDEATH11-03finalA
  CC.pdf
• Perinatal Mortality
• Stillbirths and deaths within first week
• Neonatal mortality
• Deaths under 28 days (excluding stillbirths)
• Postneonatal mortality
• Deaths from 28 days to 1 year
• Infant mortality
• Deaths under one year (excluding stillbirths)

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1997 Regional Under 5/ Infant Mortality Rates
(per 1000 live births)
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Rates of Progress
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Where Infant Mortality Has Increased?
4 out of 193 countries show an increase in
mortality 1960-1997 for children under age 5
(rates per 1000 live births) Country 1960 1990
1997 Bulgaria 70 18 19 Iraq
171 48 122 Rwanda 210 161
170 Zambia 213 192 202
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Causes of Infant Death

• 2 main types of infant death
• Endogenous
• Exogenous
• Endogenous Deaths
• Congenital malformations, hereditary diseases,
  perinatal conditions.
• Exogenous Deaths
• infectious diseases, malnutrition
• Prevention
• Improvements in living environment and basic
  health care

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What are the Leading Reasons for Childhood
Mortality in the World in 1998?
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Causes of Death in the World Agelt5 yrs
of Deaths
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Estimated impact of AIDS on under-5 child
mortality rates
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Why the Life Table?

• Describe the patterns of mortality experience
  by age for an entire population
• Involves basic concepts and calculations used
  for other demographic measures
• Precursor to more advanced techniques of
  survival analysis

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Force of Mortality

• At any moment, there is a probability that death
  can occur. This is the force of mortality
• Changes with age
• For any mortal species, there is an age where the
  probability of death is 100.
• Useful way to describe and compare populations

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Example Life TableHandout US Life Table
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Available Inputs for a Life Table

• Deaths between age x and xn (nDx)
• Mid-point Population size between age x and xn
  (nPx)
• M-type death rates
• nmx (nDx) /(nPx)
• nPx this notation will change when we discuss
  life tables

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Going From mx to qx (if necessary)

• If we had our choice we would use qx
• Often we end up calculating mx because this is
  calculable from vital records
• Use mx to get qx
• q (2m)/(2m) (unabridged) for single age groups
• nqx (n . nmx)/(1 (n/2)(nmx)) for grouped age
  categories

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Slope of Lines Plot of lx by age A vs B Same
number of deaths but force is greater in case B
because of smaller population at risk C vs B
Same number of deaths but force is greater in
case C because they occur faster Force of
mortality (qx) is a function of speed at which
deaths occur and number at risk of death
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Calculating q-type mortality rates

• assume a cohort of people born at the same time
  l0 (radix)
• lx is the number of people out of lo who are
  alive at exact age x

• where dx is the number of deaths between ages x
  and x1

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Calculating m-type mortality rates and Stationary
Populations

• If there is a constant number of people born
  into a population (radix of lo) and the
  age-specific death rates remain the same, then
  the Lx describe the number of people alive at age
  x in a stationary population (the age composition
  of a population).

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Calculating Person Years

• How many years are lived by people in a given
  population between ages x and x1?
• As a practical matter assume that people deaths
  are evenly distributed throughout the age
  interval

• Except at very young and old ages

• where ax is the average number of person years
  lived between ages x and x1 among those who die
  in that interval. Book often assumes ax is 0.1
  or 0.2.
• ax is usually .5 for most other age intervals

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Total Person Years of Life Left to Live

• At a given age x, how many total person years of
  life do we have left to live?

• where x is a given age and ? is the limiting
  age (e.g. 122)

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What is Life Expectancy?

• A child born today can expect to live to age 77
• Life expectancy can be evaluated at any age
  (e.g., how many years you can expect to live as
  evaluated at age 50)
• To actually calculate this number, you can use
  the quantities we have developed

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Median Survival and eo

• eo is the average number of years lived by each
  person at birth
• Median survival is the age at which half the
  population has died
• In general, median survival will be higher than
  eo because eo is more susceptible to extreme
  values (death at young ages mostly) which
  suppresses its value
• In future populations (low infant and child
  mortality, increases in exceptional longevity),
  this pattern will be reversed.

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Working With Life Tables

• 5q60 prob of dying between 60 and 65
• 5p10 prob of surviving between 10 and 15
• l50 no. of people in the life table pop at 50
• 5d10 no. of deaths to life table pop between 10
  15
• 5L30 no. of person-years lived by life table
  pop between 30 35
• T40 no. of person-years lived above exact age
  40
• e20 life expectancy at 20

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Common Calculations
Prob of survival from x to y ly/lx probability
of surviving between 40 55 or This can also
be calculated by multiplying npx between the
exact ages(5p40 x 5p45 x 5p50) Probability of
dying between exact ages by calculating nqx if we
already know ndx and lx nqx ndx / lx
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Some Practical Matters

• If you know mx (based on the raw data), then you
  can get qx
• If you know qx, then you can map out lx
• If you know lx, you can generate Lx and then Tx
• If you know Tx and lx, you can get ex

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Quantities Used in the Life Table
Survival probability
Abridged
Unabridged
In common
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Quantities Used in the Abridged Life Table

• Problem of dealing with extreme age groups
  (under age 5 and over age 90) when using grouped
  data.
• Closing out the abridged life table
• To get the L estimate for the last category,
  assume an e figure to generate L
• e.g. nL80 l80e80
• Use the fact that for the last category, nqx1
  which means that

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Mapping the lx is the same as the survival curve
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1990
Period Life Tables
1900
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1990 Female
1990 Male
1900 Male
1900 Female
Gender Comparison
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Whites
Blacks
1900
Whites
1990
Blacks
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Projected life expectancy at birthSelected
sub-Saharan countries
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WHO LIFE TABLE FOR 1999 RUSSIAN
FEDERATION Males x nMx nqx lx ex 0
0.0201 0.0198 100,000 62.67 1 0.0011 0.0042
98,024 62.93 5 0.0005 0.0027 97,612 59.19 10
0.0006 0.0028 97,347 54.34 15 0.0018 0.0089
97,077 49.48 20 0.0036 0.0178 96,211 44.91 25
0.0042 0.0205 94,500 40.68 30 0.0053 0.0261
92,559 36.48 35 0.0068 0.0336 90,145 32.39 40
0.0093 0.0454 87,120 28.42 45 0.0128 0.0620
83,163 24.66 50 0.0176 0.0841 78,011 21.12 55
0.0253 0.1190 71,453 17.83 60 0.0345 0.1588
62,953 14.90 65 0.0495 0.2204 52,953 12.24 70
0.0652 0.2805 41,283 9.99 75 0.0930 0.3774
29,704 7.92 80 0.1345 0.5033 18,494 6.20 85
0.2021 1 9,186 4.95
WHO LIFE TABLE FOR 1999 UNITED STATES OF
AMERICA Males x nMx nqx lx ex 0
0.0069 0.0068 100,000 73.80 1 0.0004 0.0014
99,318 73.31 5 0.0002 0.0009 99,175 69.41 10
0.0002 0.0012 99,081 64.48 15 0.0010 0.0048
98,958 59.55 20 0.0013 0.0066 98,482 54.83 25
0.0014 0.0069 97,829 50.18 30 0.0018 0.0089
97,158 45.51 35 0.0023 0.0115 96,295 40.89 40
0.0031 0.0155 95,191 36.34 45 0.0044 0.0216
93,712 31.87 50 0.0066 0.0322 91,688 27.52 55
0.0102 0.0496 88,732 23.35 60 0.0167 0.0800
84,332 19.44 65 0.0251 0.1182 77,589 15.92 70
0.0394 0.1795 68,419 12.71 75 0.0595 0.2590
56,139 9.95 80 0.0963 0.3881 41,597 7.55 85
0.1738 1 25,455 5.75
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Russian lx
Age
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Russian qx
Age
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Russian ex
Age
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Russian and US qx
Russia
US
Age
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Ratio of Russian to US qx
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Russian and US lx
Russia
US
Age
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Example Life Table
In the first interval, assume average yrs lived
among the dead is a0.1 In the last interval,
assume e80 is 8 years (see slide 24)