1. Basic Life Table Computations - I
(Session 12)

2. 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

3. 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.

4. 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

5. 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.

7. 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.

8. 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

9. 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

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

11. 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”

12. 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.

13. 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

14. 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”

15. 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.

16. Practical work follows to ensure learning objectives are achieved…