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**Basic Life Table Computations - I**

(Session 12)

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Learning Objectives At the end of this and the next session, you will be able to construct a Life Table or abridged Life Table from a given set of mortality data express in words and in symbolic form the connections between the standard columns of the LT interpret the LT entries and begin to utilise LT thinking in more complex demographic calculations

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An Example Repeated from session 11, below is part of an abridged Life Table (LT) for South African males, published by WHO The highlighted portion is then pulled out to illustrate some further Life Table calculations. See your handout for the complete age range.

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Age range lx nqx <1 100000 50-54 50543 1-4 94535 55-59 43422 5-9 92734 60-64 36706 10-14 91921 65-69 29943 15-19 91366 70-74 22871 20-24 90173 75-79 15704 25-29 87322 80-84 9032 30-34 83271 85-89 3894 35-39 76446 90-94 1057 40-44 66143 95-99 191 45-49 57495 100+ 25

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Computations, not data Added columns discussed below represent additional calculations built solely on the same original nqx data. They are further derived values. Below see graph of nqx vs. x, approximate because rates reflect different age-groups and we have to “scale up” the first two values so their values are comparable with later age groups.

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Notes: 1 Graph shows a local peak in age-group This is not historically typical; might arise because in the population from which data are sourced there was a high effect of AIDS in this cohort. As we go through this session, note how this simple-seeming list of probabilities is manipulated in many ways to generate useful means of expressing information.

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**Two further Life Table columns**

Ages nqx lx ndx nLx <1 100000 5465 96175 1-4 94535 1801 373818 5-9 92734 813 461637 10-14 91921 555 458216 15-19 91366 1193 453845 20-24 90173 2851 443736

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What is ndx? ndx is simply the number expected to die in each age range, so can be expressed in several ways e.g. ndx = nqx . lx i.e. the probability of dying in an age-range times the number of people “available to die” at the start of the range ndx = lx - lx+n i.e. the number of people alive and “available to die” at the start of the range minus the number of survivors at the end of the age range

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Note that 5d0 was calculated as sum of deaths in ranges 0-1 and to put figures on a common scale herein

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Why compute ndx?: 1 By looking explicitly at this column we can see how many people are expected to die in each age range which depends on the mortality rate, & on the number left in the LT population. The largest single number in the ndx column (see handout) is 9232 for the age range 35 to 39 inclusive: death rates increase thereafter, but less people are “available to die”

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Why compute ndx?: 2 Note that in the age-range 35 to 39, an average of less than 1850 per year are expected to die BUT in the age-range 0-1 year 5077 babies expected to die: nearly 3 times as many on a 1-year basis; AND the babies potentially had their whole life ahead of them: this illustrates the importance of attention to infant health, morbidity and mortality.

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What is nLx?: 1 nLx is defined as the number of years lived between exact ages x and x+n by members of the Life Table population. Of course the starting number is lx at age x. All those lx+n who survive to age x+n each live n years in the period. A simple assumption is that the (lx- lx+n) who die have each lived n/2 years N.B. not very good assumption e.g. more baby deaths cluster nearer to age 0

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**What is nLx?: 2 On the simple assumption:-**

nLx = n.lx+n + ½n.[lx- lx+n], which is algebraically equivalent to:- nLx = n[½(lx+ lx+n)]. The expression [½(lx+ lx+n)] can be put into words as the “average population alive in the age range x to x+n”, so another way to express it is:- “over the n-year period, the average population each lived n years”

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What is L0? We noted that of those who die aged 0, the average age at death is usually much less than 6 months.) A rather better approximation to reality, but still simple, for the first year of life, is:- L0 = .3l l1 i.e. L0 = l1 + .3(l0 - l1) Note that this counts 0.3 of a year for each child that dies aged 0.

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**Practical work follows to ensure learning objectives are achieved…**

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SADC Course in Statistics Using Probability Ideas in Life Tables (Session 11)

SADC Course in Statistics Using Probability Ideas in Life Tables (Session 11)

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