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Life Table analysis
Dr Debjyoti MohapatraJunior resident
Dept. of Community MedicinePGIMS,Rohtak
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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-67.3FEMALES-69.6
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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)
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How long do we live?
Can not answer for an individual , but can make a statement about a group.
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Contents
Brief overview
Life table : A historical perspective
Types of Life table
Construction of a Life table
Applications of Life table
Conclusion
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Brief overview
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.
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Brief overview
Life table tells us how long people live on an average.
It converts a cross sectional information into a longitudinal cohort information.
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Brief overview
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
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0.10.20.30.40.50.60.70.80.9
1
0 10 20 30 40 50 60 70 80 90
1*0.1+2*0.1+10*0.1+20*0.1+35*0.1+45*0.1+50*0.1+60*0.1+70*0.1+80*0.1=37.3
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Survival curve or life table curve
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90
Per
cent
age
surv
ived
U5
AREA=average survival
Adult mortality=70-30/70=57%
Age
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0 10 20 30 40 50 60 70 80 90
Age
Perc
en
tag
e S
urv
ived
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Life table : A historical perspective
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.
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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.
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Edmond Halley
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HALLEY’S LIFE TABLE OF BRESLAU CITY
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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.
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Finally the definition
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.
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Types of Life Table
1. Current/Period vs Generation/Cohort.
2. Complete vs Abridged.
3. Multiple decremental tables.
4. Incremental –Decremental life tables
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Current/Period vs Generation/Cohort
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 lives remain in the group.
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.
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Complete vs Abridged
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.
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Single and Multiple Decremental Life Tables
SINGLE DECREMENTAL MULTIPLE DECREMENTAL
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Multistate or Incremental-decremental Life table
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Construction of Life table
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.
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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 expectancy at age x(ex)
This coloumn shows the age interval between two exact ages indicatedProbability 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+nThis 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
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5+536
2.5
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Calculation of probability of dying in a particular age group
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Application of life tables
A Age expectancy at age 60=355234+310042+250443+180901+113743+95820/74611=
1306183/74611=17.50
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Applications of life table
Preston
Newton
Boston
BostonCatholic
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Application of life table
RA
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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.
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l20=78368L55=64886Proportion eligible for pension=64,886/78,368*100=82.79
l20=77433L55=58985Proportion58985/77433*100=76.17%
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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 methoddiscussed 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+41150+30092)*5/73801+(2.5)=28.73
Now adopting the method discussed by us
352655+335021+310579+276812+232232+180976+282667/71977= 27.38
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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
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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.
Modified life table
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Follow-up results of tuberculosis patients
Month
Pt. Feb
Mar Apr May Jun Jul Aug Sep Oct
Nov
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
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Month
Pt. 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10t
h
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 12Total no.
185 148 108
80 64 50 36 25 18 11 9
Next mont
h
185 136 93 67 55 42 27 19 11 9
Follow-up results of tuberculosis patients
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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 monthpx = 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 =108So, probability of coming in next month p = 108/136 = 0.79
Probability of defaulting qx = 1 - dx
Contd…
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How to calculate dx?dx = lx × qxe.g. dx at 1 month follow up =
1000×0.20 = 200So, lx at 1 month follow up
1000 – 200 = 800 Similarly dx at 2 month follow up =
800×0.21 =168So, 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…
Contd…
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Month of Rx
x
Probability of
Reporting px
Probability of
Defaulting qx
No. available in every month
lx
No. of defaulte
rs 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 - -
Table 4 Follow-up results in life table form
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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
Contd…
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Uses & Applications
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.
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Contd…
• 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.
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Contd…
• 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.
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ConclusionThe 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).
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Conclusion
Who knows one day with certain modifications this old
methodology may ascertain its value as the gold
methodology.
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HAPPY HOLI