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Mortality measures-- crude, specific, & summary (the life table)

Mortality measures-- crude, specific, & summary (the life table). Recall lesson about rates: crude, age-specific, summary stats. Crude death rate: conceals a lot because mortality varies greatly by age

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Mortality measures-- crude, specific, & summary (the life table)

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  1. Mortality measures-- crude, specific, & summary (the life table)

  2. Recall lesson about rates:crude, age-specific, summary stats • Crude death rate: conceals a lot because mortality varies greatly by age • Age-specific death rates: asdr = deaths agex/pop. at risk agex (for specific period and place) • Summary statistic-->the life table: life expectancy: mean years expected to live from age x under current mortality conditions

  3. The Life Table: demographic fossil or “most useful tool” • Laid out by John Graunt in 1662, when data and ability to calculate were scarce commodities • The life table was designed to both “show the work”, how death rates by age are used to compute all stats of the table, and to “show the results”. • Notion can be extended beyond mortality

  4. Brief history of the Life TableGraunt’s Observations (1662) • Graunt “Observations on the London Bills of Mortality” Graunt speculated on the regularities of demographic events: more male births than female, higher male mortality than female, frequency of various causes of deaths, etc. • Graunt’s life table constructed without age or sex data birth 100 individuals6 64 (based on deaths attributed to children16 40 (total conjecture: arithmetical formula)26 2536 16…76 1

  5. Brief history of the Life TableEdmond Halley (1656-1742) • Halley (1693), “An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw” • Critique of Graunt’s shortcomings: lacked the number of people, ages at death, London had too much migration • Breslau (Poland) seemed to be a closed population with little migration and death data were available by age (individual years) • 1 (birth) 1000 individuals2 8553 7984 7605 732….33 507…84 20 1675 – published his first paper on astronomy… in the Philosophical Transactions of the Royal Society… followed by many others 1680s principal editor of the Philosophical Transactions 1691 – denied professorship of astronomy at Oxford: charged with not accepting literal truth of the Bible Identified the comet of 1682 as the same as 1531, 1607, … and 1305, 1380 and 1456 Predicted its return for Dec. 1758; he was proven correct when it appeared Dec. 25. 1704 – appointed professor of geometry at Oxford.

  6. Brief history of the Life TableEdmond Halley (1656-1742) • Uses of life table, according to Halley • Proportion of men to bear arms • Show differing degrees of mortality by age; the odds that a person shall live from one age to another • Years that a person is likely to die (used the median) • The price of insurance upon lives • The valuation of annuities • The valuation of joint annuities (husband+wife; wife+child, etc.) • Halley’s observation: “the Growth and Encrease of Mankind is not so much stinted by any thing in the Nature of the Species, as it is from the cautious difficulty most People make to adventure on the state of Marriage, from the prospect of the Trouble and Charge of providing for a Family. Nor are the poorer sort of People herein to be blamed, since their difficulty of subsisting is occasioned by the unequal Distribution of Possessions, all being necessarily fed from the Earth, of which yet so few are Masters.”

  7. The Life Table (see spreadsheet): 3 fundamental mysteries revealed • How to read a life table:from age specific death rates, derive life expectancy • How a table is constructed: with deaths at age x, derive the rest • What do life tables reveal about mortality transitions of the past quarter millennia (a few surprises)

  8. key: x = age x; n = interval. • qx = ndx/lx, the mortality quotient, the likelihood of dying at age x to age x+n. NOTE: every statistic in the entire life table is derived from nqx • lx = number of individuals alive at exact age x • ndx = number of deaths at exact age x to x+n • nLx = years lived by individuals from exact age x to age x+n • Tx = total years lived from exact age x to maximum age in life table: Tx+n + nLx • ex = life expectancy at exact age x: Tx/lx

  9. The Life Table: 3 fundamental mysteries revealed • How to read a life table:at age x, 2 stats: mortality rate, life expectancy • How a table is constructed: with death rates, derive... • What do life tables reveal about mortality transitions of the past quarter millennia (a few surprises)

  10. The Life Table: 3 fundamental mysteries revealed • How to read a life table:at age x, 2 stats: mortality rate, life expectancy • How a table is constructed: with deaths at age x, derive the rest • What do life tables reveal about mortality transitions of the past quarter millennia (a few surprises)

  11. Life table mortality probabilities and life expectancies in historical perspective: The case of Sweden, 1751-1999

  12. Changing demographic patterns of dying: Sweden, 1751-1996 • Indicator: nqx, or mortality quotient • graphics of nqx by: • age (0, 1, 5...85+), • sex and • time (1751, 1851, 1951, 1996-9)

  13. nqx Females: 1751 1q0 = 0.211 5q65 = 0.198 5q15 = 0.029

  14. nqx Females and Males: 1751 1q0 = 0.211 5q65 = 0.198 5q15 = 0.029

  15. nqx 1751- 1851: Sweden Females 1751-1851: gains for youth; losses for elders 1q0 = 0.211 5q65 = 0.198 5q15 = 0.029

  16. nqx 1751- 1951: Sweden Females 1851-1951: major gains to 65 small gains for 65+ 1q0 = 0.211 5q65 = 0.198 5q15 = 0.029

  17. nqx 1751- 1996: Sweden Females 1951-1999: major gains all agesincluding 65+ 1q0 = 0.211 5q65 = 0.198 5q15 = 0.029

  18. ex 1751, 1851, 1951 and 1996: Sweden Females age 081734438 age 1071654949 age 6520151012

  19. Life expectancy and the mortality transition • First improvements: infant mortality; 1751-1851: e0 increases 6 years; e65decreases 2 years • Second, 1851-1951: infant and child mortality, e0 increases 29 and e10 16 years; e65 increases 5 years • Last, 1951-: e0 increases 8 years; e10 increases 6; e65 increases 5 years.

  20. Life expectancy and the mortality transition Increase in additional years of life: Sweden, Females Period e0 e10 e65 1751-1851 +6 0 -2 1851-1951 +29 +16 +5 1951-1999 +8 +6 +5 • First improvements: infant mortality; 1751-1851: e0 increases 6 years; e65 decreases 2 years • Second, 1851-1951: infant and child mortality, e0 increases 29 and e15 16 years; e65 increases 5 years • Last, 1951-: e0 increases 8 years; e15 increases 6; e65 increases 5 years.

  21. Life expectancy and the mortality transition Net increases in additional years of life: Sweden, Females Period e0 e10 e65 1751-1851 +6 0 -2 +6 +2 -2 1851-1951 +29 +16 +5 +13 +11 +5 1951-1999 +8 +6 +5 +2 +1 +5 • First improvements: infant mortality; 1751-1851: e0 increases 6 years; e65 decreases 2 years • Second, 1851-1951: infant and child mortality, e0 increases 29 and e15 16 years; e65 increases 5 years • Last, 1951-: e0 increases 8 years; e15 increases 6; e65 increases 5 years.

  22. e0 in the Americas, 1900-2005unequal in 1900; converging since 1960 2005 79 78 1980 76 75 71 1960 1940 1920 1900

  23. e0: 2005source: www.prb.org

  24. End

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