Where Are We So Far

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Where Are We So Far?

• Vital m-type vs. q-type rates
• Lexis diagram
• Confounding
• Standardization
• Direct (ASDR)
• Indirect (SMR)
• Types of mortality
• Age-period-cohort issues
• Life Table (more today)
• Cause-specific mortality and cause elimination

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Age-Period-Cohort Problem

• 3 possible explanations
• Age
• Period (time, calendar year)
• Cohort (Birth year)
• Perfect confound

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PERIODS AND COHORTS

• Periods
• Time point or interval
• Period perspective looks at populations or
  subpopulations for a given year or for a series
  of years
• e.g. deaths to aged 90 in the US for 1900, 1910,
  etc.
• Cohort
• a group of people sharing a common characteristic
  followed over time
• e.g. the birth cohort of 1983, the 2001 marriage
  cohort
• Cohort perspective follows a cohort over time as
  they age

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A-P-C
Age
Cohorts
A
B
C
100
75
50
25
0
1950
1975
1925
2000
2025
Calendar Year (Period)
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Period vs Cohort Life Tables
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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/Utah Life Tables

• http//www3.who.int/whosis/life_tables/life_tables
  .cfm?pathevidence,life_tableslanguageenglish
• http//governor.utah.gov/dea/demographics/liftab/l
  ifetable.html
• http//www.demography.utah.edu
• http//www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14
  .pdf (for 2003)
• http//www.cdc.gov/nchs/products/pubs/pubd/lftbls/
  lftbls.htm (for all years)

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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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Utah Vs. U.S. (2002)
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Life Table Summary

• qx, px, Px, Dx, mx, lx, dx, Lx, ex
• Synthetic (m-type) versus real (q-type) cohorts
• Median vs mean survival
• Exceptions at extreme ages
• Reading survival (lx) curves

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Examples

• Limits of longevity
• Marriage life table

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Risk Factor Simulation
Alameda Healthy II
Alameda Healthy I
Blair
Mormon High Priests
Mormon Insured
7th Day Adventists
1986 US Life Table
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Marriage Life Table
A life table for an actual cohort of 655
Bangladeshi women aged 45-49 in 1993-94 who all
married before the age of 30. No need to deal
with mx here because it is a real cohort, not a
synthetic cohort. (radix is not 100000) Age n
lx ndx nqx nLx Tx ex 0 5 655 0 0.00000
3275 9202.5 14.05 5 5 655 0 0.00000 3275
5927.5 9.05 10 2 655 119 0.18168 1191
2652.5 4.05 12 3 536 388 0.72388 1026
1461.5 2.73 15 3 148 106 0.71622 285
435.5 2.94 18 2 42 16 0.38095 68 150.5
3.58 20 2 26 13 0.50000 39 82.5 3.17 22
3 13 7 0.53846 28.5 43.5 3.35 25 5 6 6
1.00000 15 15.0 2.50
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Leading Causes of Death?
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Causes of Death 2004
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What would happen to the life table estimates if
we could hypothetically eliminate a cause of
death?
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Dependent and Independent Death Rates

• The independent death rates are the death rates
  from decrement (cause of death) a if we could
  eliminate decrement (cause of death) ß.
• Often called cause-deleted or cause-elimination
  life tables
• The independent death rate for cause of death a
  will not be the same as the dependent death rate
  for cause of death a.
• Independent rates gt dependent rates, in general.

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Note this result and then ignore
In this simple example of multiple (two)
decrements, they happen in sequence usually
they happen randomly throughout the year with a
happening before ß sometimes and ß happening
before a sometimes.
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The Usual Circumstance Getting Independent Rates
from Dependent Rates (what you actually measure
from vital records)
The WHOPPER assumption Surviving one cause has
no effect on the remaining causes.
Approximation improves as qxs get smaller
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Excel Example of Dependent and Independent
RatesandPublished Estimates of Competing
Risks
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Table 5.2 in Hinde
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Exercises

• Questions 5.1