Life tables

Life tablesProf. MuchungaLife tablesGoal Define the life tables, outline types, hx, assumptions, anatomy and application of life tablesDefinition of Life tablesStatistical model used to derive some measures of mortality. Core function is the measurement of mortality; applied in different ways to study Longevity, fertility, migration, population growth. The entire life table is generated from age-specific mortality rates and the resulting values measure mortalityLife tables are one form of combining mortality rates of a population at different ages into a single statistical model. Consequently, the life table is not influenced by the age distribution of an actual population and do not require the adoption of a standard population Types of life tableDifferences occur due to 1. Reference year of the table 2. the age details 3. no. of factors in the table

The Current or Period Life TablesIs based on the experience over a short period of time one, two or three years during which mortality has remained unchangedThe table represents the combined experience by age of the population in a particular short period of time treated synthetically. Can be viewed as a snapshot of current mortality studied cross-sectionally. The cohort is however, artificial or synthetic that is subject to the Age-Specific Death Rate (ASDR) observed in that time period2. The Generation life tablesBased on the mortality experience by a particular birth cohort. For example, all persons born in 1940. This means observing the mortality experience of the cohort longitudinally from birth till all of them dieDue to challenges in constructing such a table, the table is used in projecting mortality, studying mortality trends and for measurement of fertility and reproductivityComplete Life tables (Unabridged)According to the length of the age interval in which data are presented. In this context, data are presented for every single year of age from 0 to the last applicable age (85 years or so)

The Abridged Life TablesContains data by intervals of 5-10 years of age. In most cases, the simpler abridged life tables is prepared rather than the elaborate complete life table

Standard Life Table- Is concerned with the general mortality experience of a single cohort by ageMultiple Decrement Life tableDescribes the separate and combined effects of more than one factor e.g. marriage and mortality; occupation and mortality etc.

History of life tablesOriginated in Europe around 1662; by Graunt.Earliest life tables based on mortality and birth registration for a single cityIn Kenya; AKI (Association of Kenya Insurers)Assumptions of life table5 major assumptions -> Period life tableAs noted earlier, the life table is a life history of a synthetic group or cohort, as it is diminished gradually by deaths

1. Cohort is closed from in and out migration. Therefore, there are no changes in membership except through losses occasioned by deaths

2. People in the Cohort die at each age according to a schedule (arrangement) that is fixed in advance, and does not change

3. The Cohort originates from some standard no. of births (set at 100, 1000, etc) called the radix of the life table. This standardized aspect facilitates comparison between different life tables. E.g. 5420 reach 35 years in a 10000 population; 54.2% are survivors.

4. At each age except first year of life, deaths are evenly distributed between one birthday and the next. That is, half of the deaths expected between age 9 and 10 will occur by the time everyone reached 9.5 years and son on

5. Cohort normally contains members of only one sex. It is however possible to construct a life table for both sexes, but the differences between male and female mortality at all ages are sufficient to justify treating them separately

Just like in an actual situation, a life tables looses a great many of original members at a very early age when deaths are relatively frequent. Anatomy of the Life TableEvery value in the table refers to some particular age. Every notation has specific meaningThe basic life functions nqx (mortality rate propability of dying), lx, ndx, nlx, Tx, e0xUN publishes 3: nqx, lx, e0x without siginificant loss of information since they are interrelated

X to x+n is simply the exact period between 2 ages e.g. 20-25 means the 5 year interval between 20th and 25th birthdaysN stands for the width of a time interval. Exact age 0 and exact age 1 equals 1 year. Nqx the probability of dying between x and x+nThe opposite the probability of surviving is nplx the number of persons living at the beginning of age interval x out of a total number of births assumed as the radix of the LT.Ndx number of persons who would die within x to x+n out of a total number of births assumed in the life table. E.g. 825 persons would die between age 0 and 1 (infant mortality)Nlx the number of person-years that would be lived out of 100,000 births as the radix within the indicated age interval x to x+n Calculate person yearsAt age 20 - 96111 25 95517 Multiply 951517 x 5+ (2.5 x (96111 95517)

Tx total no. of person years that would be lived after the beginning of the indicated age interval by the Cohort of 100000 births assumed. Technique of computing is bottom up using nlx

e0x the best known function is simply the average remaining life time in years for a person who survives to the beginning of the indicated age interval complete expectation of life/life expectancyE.g. someone who has reached 20th birthday has 58.542 yeasr to live on the average