sadc course in statistics basic life table computations - i (session 12)

SADC Course in Statistics

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

Age range lx nqx

<1 100000 0.05465 50-54 50543 0.14089

1-4 94535 0.01906 55-59 43422 0.15467

5-9 92734 0.00877 60-64 36706 0.18425

10-14 91921 0.00604 65-69 29943 0.23618

15-19 91366 0.01306 70-74 22871 0.31338

20-24 90173 0.03161 75-79 15704 0.42484

25-29 87322 0.04639 80-84 9032 0.56888

30-34 83271 0.08196 85-89 3894 0.72866

35-39 76446 0.13478 90-94 1057 0.81936

40-44 66143 0.13074 95-99 191 0.86743

45-49 57495 0.12092 100+ 25 1.00000

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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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Age-Specific Mortality Rate

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120

Age

Series1

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Notes: 1

• Graph shows a local peak in age-group 35-39. 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 0.05465 100000 5465 96175

1-4 0.01906 94535 1801 373818

5-9 0.00877 92734 813 461637

10-14 0.00604 91921 555 458216

15-19 0.01306 91366 1193 453845

20-24 0.03161 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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5dx

0

2000

4000

6000

8000

10000

12000

0 20 40 60 80 100 120

Age

Note that 5d0 was calculated as sum of deaths in ranges 0-1 and 1-4 - 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 = .3l0 + 0.7l1 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…