LIFE TABLE

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)    ABRIDGE LIFE TABLE:

      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.

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:

Life table is a compact from of showing mortality pattern of a cohort of population. Usually it contains 8 columns as shown below:

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_x = P_x +  d_x

Or                     P_x = l_x -   d_x

Where;

         P_x = mid year population.

         l_x = number of entering the age.

We know m_x =  and q_x =  as per standard definition.

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 l₀ 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 d₀=l₀*q₀. As then the number of survival for second age l₁ is determine by subtracting d₀ from l₀. Similarly d₁=l₁*q₁ and l₂= l₁-d₁and 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:

L₉₉ = l₉₉ * log₁₀ l₉₉

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:

Finally expectation of live e⁰_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 e⁰_x indicates the overall or an average of an individual of the population for which the life table has been constructed.