2. Life expectancy at birth in India-65
Life expectancy at birth in Japan-83
Life expectancy at birth in United states-79
Life expectancy at birth in China-76
Life expectancy at birth in Sri lanka-75
Life expectancy at birth in Bangladesh -70
Life expectacy at birth in Iran-69
Life expectancy at birth in Nepal-68
Life expectancy at birth in Pakistan-67
Figures rounded of to nearest whole numbers.
WHO report -2011
Latest report of life
expectancy in India
MALES-67.3
FEMALES-69.6

3. How long will I live ????????
Many babies born today will live past 100.
Joseph Brownstein
ABC news medical unit
(OCT 1,2009)
If you leave to be one hundred, you have got it made.
Very few people die past that age.
George Burns
American Comedian
(January 20,1896-March 9,1996)

4. How long do we live?
Can not answer for an individual , but can make a
statement about a group.

5.  Brief overview
 Life table : A historical perspective
 Types of Life table
 Construction of a Life table
 Applications of Life table
 Conclusion

6. Edmond Halley was the first person to show us how to properly
calculate and construct the life table.
Halley was a british astronomer
, geophysicist, mathematician, meteorologist who is best known for
computing the orbit of Halley’s comet.
He calculated the first ever life table sometime 300 years back . Till
date the same methodology is followed with only slight variation.

7. Life table tells us how long people live on an average.
It converts a cross sectional information into a longitudinal
cohort information.

8. Average life span : or how long do we live
Suppose we have a population of 10 people and we follow the till
they all die. Here are their life spans.
1,2,10,20,35,45,50,60,70,80
So the average life span is
1+2+10+20+35+45+50+60+70+80=37.3
10

9. 0 20 40 60 80 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

10. 0 20 40 60 80 100
10
20
30
40
50
60
70
80
90
100
Percentagesurvived
U5
AREA=average survival
Adult mortality=70-30/70=57%
Age

11. 0 20 40 60 80 100
Age
PercentageSurvived

13. The first life table had been published in London in 1662 in a book
entitled Natural and Political Observations Made upon the Bills of
Mortality.
People still wonder nowadays if it was written by John Graunt, a
London merchant and author indicated on the book cover, or by his
friend William Petty, one of the founders of the Royal Society.
Their life table was subject to large errors.

14. At about the same time, Caspar Neumann, a theologian living in
Breslau, was collecting data about the number of birth, deaths and other
vital statistics in his city.
Breslau belonged to the Habsburg empire. (it is now in Poland and called
Wrocław)
Neumann sent to Henry Justel, the secretary of the Royal Society, his
demographic data from the city of Breslau for the years 1687–1691.
Justel died shortly after, and Halley got hold of the data, analyzed them and
in 1693 published his conclusions in the Philosophical Transactions of the
Royal Society.

15. Edmond Halley

16. HALLEY’S LIFE TABLE OF BRESLAU CITY

19. We do not know what will happen to the 65 year
olds in say 2050;
BUT we do know what happened to the 65 year old
in past year, and the 66year old in past year etc.

20. The life table methodology constructs a life
experience for a fictional cohort subjected to
current mortality rates as it progresses through
life, as if the current rates do not change.

21. 1. Current/Period vs Generation/Cohort.
2. Complete vs Abridged.
3. Multiple decremental tables.
4. Incremental –Decremental life tables

22. COHORT LIFE TABLE PERIOD LIFE TABLE
• The cohort life table
presents the mortality
experience of a particular
birth cohort.
• All persons born in a
year, from the moment of
birth through consecutive
ages in successive calendar
years.
• The cohort life table
reflects the mortality
experience of an actual
cohort from birth until no
The period life table presents
what would happen to a
hypothetical (or synthetic)
cohort if it experienced
throughout its entire life the
mortality conditions of a
particular time period.

23. COMPLETE ABRIDGED
A complete life table contains
data for every year of age.
An abridged life table
typically contains data by 5-
or 10-year age intervals .
A separate group is made for
age group 0-1 years .
In India a 5 year interval is
selected.

24. SINGLE DECREMENTAL MULTIPLE DECREMENTAL

26. To construct a life table, two things are required:
1.Population living at all individual ages in a
selected year.
2.Number of deaths that occurred in these ages
during the selected year.

27. Age
interval(x
tox+n)
Probability
dying(n q x)
Number
surviving(
(lx)
Number
Dying
(nd x)
Person-
years
lived
between
exact
agesx and
x+n
Person –
years
lived
above age
x (Tx)
Life
expectanc
y at age x
(ex)
This coloumn shows the age interval
between two exact ages indicated
Probability of dying in the age group(x-x+n)given
survival upto age xx
This column shows the number of persons, starting with a
cohort of 100,000 live births, who survive to the exact age
marking the beginning of each age interval
This column shows the number dying in
each successive age interval out of 100,000
live births.
Person-years lived between exact ages x and x+n
This takes into consideration the years that would have been
lived by the people that are dying
during this time interval
. It is number of years lived by group from age x until all of
them die
It is done by calculating the sum of the previous coloumn
data staring from particular age group till all cohort dies.
Average remaining lifetime for a person who survives to age
x
Calculated by the formula Tx/lx

28. 5+536 2.5

30. Calculation of probability of dying in a
particular age group

31. A Age expectancy at age 60=
355234+310042+250443+180901+113743+95820/74611=
1306183/74611= 17.50

32. Preston
Newton
Boston
Boston
Catholic

33. RA

35. Q) From the abridged SRS based life table, India,1976-77 for males and
females, find:
a. What proportion of men entering services at 20 will be eligible for
pension at age 55.
b. Calculate life expectation at age 55 for men.
c. If 20% of deaths occuring in men between the ages of 60 and 70
inclusive are due to cancer ,what proportion of men aged 60 yrs are
likely to die of cancer before reaching their 70th birthday.

37. l20=78368
L55=64886
Proportion eligible for
pension=
64,886/78,368*100=82.79
l20=77433
L55=58985
Proportion
58985/77433*100=76.17%

38. Life expectancy at 55=
Sum of lx coloumn from lx 55
onwards/number who started at lx
55 onwards + 2.5=
(58,985+51,345+41,150+30,952)*5/64886+
2.5=16.55
Now calculating by the method
discussed by us
276812+232232+180976+282667/58985=
16.49
Calculating life expectancy at age 40 by
adopting authors method
(71,977+68856+64886+58985+51345+4115
0+30092)*5/73801+(2.5)=28.73
Now adopting the method discussed by us
352655+335021+310579+276812+232232+180976
+282667/71977=
27.38

39. No of deaths in age group (60-70 yrs)= 51345-30952=20393
Cancer deaths=20*20393= 4078
Therefore proportion of men aged 60 likely to die of cancer
by 70 yrs=4078/51345 *100= 7.942
100

40. This method is modification of usual life table for calculating the
survival rates after specific treatment or operation or at any point
of time after that, It can be explained by an example of
tuberculosis.
A total of 23 patients of tuberculosis started treatment in a T.B.
clinic. Their number becomes less due to defaulters.
Out of 23 who started treatment in January, only 22 reported in
February,79 in March & so on till there were only 9 left in the
month of November.

41. Month Pt. Feb Mar Apr May Jun Jul Aug Sep Oct No
v
Jan 23 22 13 12 12 10 9 9 9 9 9
Feb 9 7 4 4 4 4 3 2 2 2
Mar 20 12 12 9 9 8 8 8 7
Apr 17 15 10 10 10 9 7 6
May 23 20 17 12 11 11 9
Jun 17 12 12 11 9 8
Jul 20 12 11 9 9
Aug 22 20 14 13
Sep 18 16 15
Oct 16 12

42. Month Pt. 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Jan 23 22 13 12 12 10 9 9 9 9 9
Feb 9 7 4 4 4 4 3 2 2 2
Mar 20 12 12 9 9 8 8 8 7
Apr 17 15 10 10 10 9 7 6
May 23 20 17 12 11 11 9
Jun 17 12 12 11 9 8
Jul 20 12 11 9 9
Aug 22 20 14 13
Sep 18 16 15
Oct 16 12
Total
no.
185 148 108 80 64 50 36 25 18 11 9
Next
month
185 136 93 67 55 42 27 19 11 9

43. No. of patients in 0th (xeroth) month/starting month =
185
Reported for treatment in next/1st month = 148
So, probability of coming in next/1st month
px = 148/185 = 0.80
Out of 148, history of 12 patients was not available, so
no. of patients left = 136
Reported for follow up in 2nd month =108
So, probability of coming in next month
p = 108/136 = 0.79
Probability of defaulting
qx = 1 - dx

44. How to calculate dx?
dx = lx × qx
e.g. dx at 1 month follow up = 1000×0.20 = 200
So, lx at 1 month follow up
1000 – 200 = 800
Similarly dx at 2 month follow up = 800×0.21 =168
So, lx at 2 month follow up = 800-168 = 632, so on…
How to fill up Lx (no. of months attended by starters)
column?
Lx=lx + 1/2dx
e.g. at the end of 1st month 800+100=900
at the end of 2nd month 632 + 84 =716, so on…

45. Mont
h of
Rx
x
Probabilit
y of
Reporting
px
Probabilit
y of
Defaulting
qx
No.
available
in every
month
lx
No. of
defaulters
in every
month
dx
No. of
months
attended by
starters
Lx
Total
months
attended
at all ages
Tx
Expected
to attend
at any
month
ex
0 0.8 0.20 1000 200 900 5,162 5.16
1 0.79 0.21 800 168 716 4,262 5.33
2 0.86 0.14 632 68 588 3,546 5.61
3 0.96 0.04 544 22 533 2,958 5.43
4 0.91 0.09 522 47 499 2,425 4.64
5 0.86 0.14 475 67 442 1,926 4.05
6 0.93 0.07 408 29 394 1,484 3.63
7 0.95 0.05 379 19 370 1,090 2.87
8 1.00 0.00 360 0 360 720 2.00
9 1.00 0.00 360 0 360 360 1.00
10 - - 360 - -

46.  How to calculate ex (expected no. of months for
which a person is likely to attend at any month)?
ex = Tx/lx
e.g.
at xeroth month ex = 5162/1000 = 5.16 months
at the end of 6th month ex = 1484/408 = 3.63

53. To find the number of survivors out of 1,000 or
10,000 or over birth or at any age thereafter say,
 At the age of 5, to find number of children likely to
enter primary school.
 At the age of 15, to find number of women entering
fertile period.
 At age of 18, to find number of persons become
eligible for voting.

54. • To estimate the number likely to die after joining service till
retirement, helping in budgeting for payment towards risk or
pension.
• To find expectation of life or longevity of life at birth or any other
age.
• Increase in longevity of life means reduction in mortality, thus life
table is another method applied to compare mortality of two
places, periods, professions or groups.

55. • To find survival rate after treatment in chronic disease
like tuberculosis, cancer or after cardiac surgery by
modified life table.
• Helps to project population estimates by age & sex.
• Calculate failure rate of contraceptive.

57. The Life table methodology was first adopted some 300 years back.
Credit must be given to Edmond Halley who used his innovative
mind to create this statistical tool.
In an era of sophisticated and advanced statistical applications, Life
tables have survived the test of time.
Life table is an old method and probably in this era may not be gold
but definitely it has not lost its shine and is still being used to
calculate some vital parameters(life expectancy, contraceptive
failure).

58. Who knows one day with certain modifications this old
methodology may ascertain its value as the gold
methodology.

59. HAPPY HOLI