Life Table Approach (2)

8/12/2019 Life Table Approach (2)

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INTRODUCTION

Life tables are used by demographers,

public health workers, actuaries, and many

others in studies of mortality, longevity,

fertility, marriage, migration, and

population growth, as well as in making

projections of population, and in many

other areas


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HISTORYJohn GrauntsNatural and Political

Observations upon the Bills of

Mortality(1662)Implications ofinformation obtained from christening anddeath lists in London

Edmund Halleys presentation of theBreslau (Wroclaw, Poland) life table(1693)


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Antoine Deparcieuxsseries of life tablesfor annuitants and monastic orders (1746)

Lowell Reed and Margaret Merrells new

technique to estimate the life tableprobability of dying within an interval from

the age-specific death rates (1939)


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T.N.E. Grevillesdevelopment of another

technique to estimate the life table

probability of dying within an intervalfrom the age-specific death rate (1943)


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L ife table is also known as Mortali ty

table or Actuar ial table.

L ife table is a table which shows, for a

person at each age, what the probabil i ty

is that they die before their next bir thday

(PROBABI L I TY OF DEATH)


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Uses Of L ifeTable

Biology Epidemiology


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USESOFL I FETABLEAnalysis of mortality

Measurement of morbidity and health

Analysis of mortality by causes of death

Future projections of life expectancyLife table survival rates

Estimation of migration

Insurance sector

Evaluation of different public healthprogrammes

Resource allocations


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INFERENCESFROML I FETABLES

The Probabi l i ty of surviving any particular years of

age.

The Remaining l i fe expectancyfor people at

different ages.

The Proportion of the Original bi r th cohor t still

alive.


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TYPESOFL I FETABLE

1. Periodic or Static l i fe Tables:- Shows the

current probability of death (for people of different

ages, in current year.)

2. Coho rt L ife Tables :- Shows the probability of

death of people from a given cohort (especially

Birth year) over the course of their life time.


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OTHERTYPESOFL I FETABLEComplete Life Table:

It is made for every single year of age from birth

to the last applicable age.

Ex:0,1,2,3,4,,70+

o Abridged Life Table:

It is made for age intervals of 5 to 10 years up tolast applicable age.

Ex:0,1-4,5-9,10-1470+


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CONSTUCTION OF A L IFE 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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COLUMNS OF A COMPLETE LIFE

TABLE:

The basic columns of a complete life table are:

AGE Number

Started

Life

Number

Died

No. Of

Person

years

Lived

Total

Person-

years

Lived

Expectati

on of life

X lx dx Lx Tx ex


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COLUMN 1: AGE

Column X indicates the age at which cohorts start

life such as at birth indicated by 0 or at any age

after that such as at age 1, age 2, and so on.


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COLUMN 2: lx

Column lxgives the number that started life at any

particular age such as 1,00,000 at birth, 90,000

survivors at age 2 and so on.


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COLUMN 3: dx

Column dx is the number died in each year, such as

10,000 in the first year. This number is found at the

specific mortality rate of each year. For e.g., in the

first year from age 0 to age 1, 10,000 died at the

infant mortality rate of 100 per 1000.


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COLUMN 4: LX

This column gives the estimated total no. of person

- years lived by the cohort at each age. It will

always be more than the survivors at the end of any

particular year because all do not die in the

beginning of the year.


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COLUMN 5: TX

This column gives the total no. of years lived till any

age.


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COLUMN6: ex

The mean expectation or longevity of life i.e.,

average number of years a person is likely to live at

age 0 or at any age after is denoted by ex.

ex = L x

lx


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COLUMNSOFANABRIDGEDL I FETABLE

The basic columns of An abridged life table are:

Age

interv

al

(years

)

nmx nqx lx ndx nLx Tx ex

(x,

x+n)


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COLUMN1: XTOX+NThe period of life between two exact ages

x and x+n.

Ex:5-9,10-14etc.


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COLUMN2 nmx

This is the age specific mortality rate. This is

essential to construct a life table.


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COLUMN3 : nQxThe Probability of dying before reaching

age x+n for a person who is of exact age x.

Ex:10-14: 5q10, 15-19: 5q15

nQx = 2n*nmx

2+ n*nmx

where nmx is the Age specific Mortality rate


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COLUMN4: LXThe number of persons living at exact

age x.

Ex:10-14:l10, 15-19:l15

lx+n = lx- ndx


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COLUMN5: ndxThe number of deaths between age x to

x+n.

Ex: 10-14: 5d10, 15-19: 5d15

ndx = lx * nqx


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COLUMN6: nL xThe number of persons year lived during

the interval x and x+n.

Ex: 10-14: 5L10,15-19: 5L15

nL x = n / 2 * lx+ lx+n


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COLUMN7: TX

The total number of persons years lived by the

survivors lxin the future.

Or Total life time after age x

Ex: 15-19: T15

Tx= nL x+ nL x+n+ ............


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COLUMN8: e0xThe expectation of life at exact age x.

Ex: 10-14: e010

e0x = Tx

lx


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IMPORTANCE OF LI FE TABLE:

No. of survivors

At 5 years, the no, of children likely to enter

primary school

At 15 years, no. of women entering fertile period

At 21 years. no. eligible for voting

No. likely to die after life insurance or afterjoining service to budget for payment towards

risk or pension.


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IMPORTANCE OF LI FE TABLE:

Calculation of expectation of life and

comparison of mortality among

communities.

Population studies

Survival rate after treatment

Analysis by causes of death


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STRENGTH-

measure of mortality providing an overall

pict u r e of m or t a lit y, a llowin g coun t r iesa n d r egion s t o be com pa r ed.

o WEAKN ESS -

I t does n ot sa y m u ch a bou t wh o is s t ill

a live, a nd t heir qu alit y of life; for

exam ple, how m any year s ar e l ived w ith

disability before dying.


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Life Table Approach (2)