A
life table presents a set of tabulation that describes the probability of
dying, the death rate, and the number of survivals for each age or age group. Accordingly,
life expectancy is at word is an outward of a life table.

In actuarial
science a life table (also called the mortality table or actuarial table) is a
table which shows for a person at each age, what is the probability is that
they die before their next birthday. From this starting point, a no of
statistics can be derived and also included in the table.

i) The probability
of serving any particular year of age.

ii)
Reaming life
expectancy for people at different ages.

iii) The proportion of the original work COHORT is
also still alive.

Life tables are usually constructed separately
for men and for women because of their ubstantially

different mortality rate.
Other characteristics can also be used to distinguish different risk, such as

smoking status, occupation, soco-economic class and other class.

__KINDS OF LIFE TABLE:__
There are two classic forms of life table,

i) Cohort (or
generation)

ii) Current (or
period table)

a) Complete life table and

b) A bridged life table.

*COHORT LIFE TABLE:*
Cohort
life tables consist of monitoring a population longitudinally from a determine
event. (For example: a birth cohort or a treatment cohort in a clinical trial)
until all the individuals die or until the observation period is discontinued.
The cohort table is usually used in the survival analysis of clinical trials,
which are carried out on a smaller population sample and over a short period of
time.

*CURRENT LIFE TABLE:*
Current life tables
provide a transversal view of mortality and survival expectancies at all ages
of a population during a short period of time, usually a year. They depend
directly on age specific mortality rates for the year for which they are
constructed.

a)

__COMPLETE LIFE TABLE OR UNABRIDGED LIFE TABLE:__
The complete life
table is constructed using single year of age from birth to the applicable age.

b)

However, the
abbreviated (abridge) life table are more often used. In which each age is
presented in groups, usually of children under one year, children one to four
years and five year age groups for the remainder of the ages until the final
age interval which remains open.__ABRIDGE LIFE TABLE:__

__COMPARISION BETWEEN COMPLETE AND ABRIDGE LIFE TABLE:__
There are small
differences in life tables measures derived from averaged and complete life
table. Abridge life table used group data or group age data and open ended
upper age group. By comparison, complete life tables use single year of age
data.

__ASSUMPTIONS OF LIFE TABLE:__
i)
The cohort is
closed.

ii)
A person dies
according to fix schedule.

iii)
Cohort starts
from some standards number. Known as Radix (like suppose no of hundred
thousand).

iv)
At each age
(generally deaths are evenly spare over time).

__COLUMNS OF LIFE TABLE:__

*COLUMN#1:*
Column 1
of ages is representing by x. Ages are either taken in a single year as 0, 1-4,
5-9 … Age zero signifies infants, those who have not reached first birthday of
their life.

*COLUMN#2:*
The Column 2 represents age specific
death rate signified by m

_{x. }They are calculated from population of the calendar year for which data has been collected, using classical definitions ratio of deaths in a year to mid-year population.
l
d

_{x}= P_{x}+_{x}
Or P
d

_{x}= l_{x}-_{x}
Where;

P

_{x}= mid year population.
l

_{x}= number of entering the age.
We
know m
and q
as per standard definition.

_{x}=_{x}=
Hence,

q
=
=

_{x }=_{}

*COLUMN#3:*
Column 3 is a probability of dying q

_{x}, is calculated as ASDR or m_{x}. ASDR is calculated as the ratio of no deaths to mid-year population, where as q_{x }is to be calculated as the ratio of no of deaths to the no persons and tends to the age group.
The assumption which we keep in consideration for construction of life
table is that the population is assumed to be closed. Hence;

NOTE: The last value of q

_{x }column must be less than or equal to 1, because probability can not be greater than 1 in any circumstances.

*COLUMN#4:*
The number of survival is designated
as l

_{x}and started with a fixed known value at the first age l_{0}is equals to 100,000 as radix of the life table. We can take any round number as a starting value. However commonly we take 100,000 as the radix of the life table.

*COLUMN#5:*
The number of deaths are then
estimated out of l

_{x}on the basis of probability of dying for an age for example d_{0}=l_{0}*q_{0}. As then the number of survival for second age l_{1}is determine by subtracting d_{0}from l_{0}. Similarly d_{1}=l_{1}*q_{1}and l_{2}= l_{1}-d_{1}and so on. In these calculations all values to be taken as whole numbers, because they are number of death or survival (discrete value).

*COLUMN#6:*
Column
6 gives the number of years lived by all individuals between the age x to x+1( x to x+1) and designated by l

_{x}. Keeping the assumption of evenly distribution of number of deaths we get “L_{X}=1/2 [lx+lx+1]”. For the last age group an approximation for L_{X}is given by:
L

_{99}= l_{99}* log_{10}l_{99}_{}

*COLUMN # 7:*
Column 7 gives number of years lived by all
individuals beyond age x and designated by T

_{x}. it is actually a cumulative value of L_{x}values from bottom of the live table.

*COLUMN # 8:*^{0}

_{x}is obtained by dividing T

_{x}coulumn#7 by the number of survivals l

_{x}given in column 4. This figure indicates on an average the number of years to be lived by an individual beyond his present age. First value of e

^{0}

_{x}indicates the overall or an average of an individual of the population for which the life table has been constructed.

## No comments:

## Post a Comment