LIFE TABLES The life table is one of the most important devices used in demography. In its classical form, it is a table that displays various pieces of information about the dying out of a birth cohort. One column of a classical life table is invariably ‘age’.

LIFE TABLES Cont’d The remaining columns tabulate age-related functions pertaining to mortality such as the number of survivors to various age, deaths in particular age intervals, age specific death rates, probabilities of death in various age intervals etc. In summary, the life table is only one way of summarizing a cohort’s mortality experiences.

Life Tables ›Describes the death and survival pattern of a population ›Very important device in demography ›Describes the death and survival pattern of a population ›Gives information on the extent to which death diminishes population numbers as ages increase ›It measures, among others, the life expectancy

Different Life Tables Cohort life table: -pertaining to a real birth cohort, to real lifelines -records information about the survival of the cohort ›Period life table: -Model of what would happen to a hypothetical cohort if a certain set of mortality conditions pertained through-out its life.

Types of Life Tables Complete life table: Single year of age ›Abridged life table: Age grpoups

Abridged Life Tables Abridged life tables contain information for every fifth or tenth year of age, such as for five year steps to 85+. A row for age 1 is almost invariably included, however, because of the importance of infant mortality.  Sometimes the ages are labeled 5-9, 10-14 etc. This can be misleading because some life table functions refer to exact ages, not to an age interval. Therefore, it is preferable to list only the first age of the interval: 0, 1,5,10… and so forth.

Abridged Life Tables Cont’d In spreadsheet work, it is useful to include an extra column showing the size of the age interval (n), to save having to change the value of (n) in different formulae.  

Uses of Abridged Life Tables 1. Where summary data are wanted for 5 year age groups, e.g for projections or estimates. 2. For comparisons – comparing mortality through time or between countries. 3. Where mortality data are unreliable and are best used in an aggregated form. 4. Where the mid-year population is derived from estimates rather than from a census.

Life Table Processes (1) Single Decrement Assumptions: -Only two states: Alive (1) => Death (2) -All individuals transit from state 1 to state 2 ›Destination state is “absorbing”: no backflow Alive Death

Columns of a Life Table Age group – cohort age x to x+n Exact age (x) Interval (n) number of years between x and x+n ax – average number of person - years lived in the interval x to x+n for those dying in the interval

Columns of a Life Table nNx – Mid Year population of those aged x to x+n nDx- Number of deaths for those aged x to x+n nMx- Age-specific death rates between ages x to x+n nqx – Probability of dying between ages x and x+n

Columns of a Life Table npx – probability of surviving from age x to age x+n lx – Number of people left alive at age x ndx Number of people dying between ages x and x+n

Columns of a Life Table nLx – Person-years lived between ages x and x+n Tx - Person-years lived above age x eox- expectation of life at birth or age x

Construction of Abridged Life Tables   When constructing an abridged Life Table take note of the following steps: i) list the ages, (age groups and exact ages) ii) the age intervals (n)

Construction of Abridged Life Tables Cont’d iii) ax iv) Mid-Year population per age group v) Number of deaths per age group

Calculations of a Life Table 1. Age-specific death rates (nMx). nMx = nDx/nNx where: nNx = mid-year population aged x to x+n nDx = number of deaths during the year to persons aged x to x+n (or a yearly average)

Calculations of a Life Table Cont’d Use k = 1 to express the figure as a rate per person, or k = 1000 to express it as a rate per thousand. E.g the death rate at ages 10-14 = (deaths in year at ages 10-14)/(mid year pop aged 10-14)*k  

2. Calculate nqx nqx = the probability of dying between two exact ages  To calculate the probability of dying from the age-specific death rate use:  nqx = n*nMx 1+(n-ax)*nMx For open-ended intervals, such as 85+, the probability of dying is always 1.0: everyone will still be in the same age interval at death.

Calculate npx   npx = the probability of surviving between two exact ages. npx = 1 - n qx

lx+n = lx*npx lx+n = lx -ndx Calculate lx  lx = the number of survivors at exact age x.  The radix is set at 100 000; other lx values are calculated either from npx or ndx: lx+n = lx*npx lx+n = lx -ndx

Calculate ndx ndx = the number of deaths between two exact age, x + n   It may be calculated from the probability of dying:  ndx = Ix * n qx ndx = lx – lx+n

Calculate nLx n∞Lx = lx ∞Mx nLx = n*lx+n + ax*ndx   nLx = average person years lived between ages x and x + n.  nLx = n*lx+n + ax*ndx n = number of years in the age interval. For open-ended categories, e.g 85 +, the formula is: n∞Lx = lx ∞Mx The infinity symbol denotes an open-ended age interval x

Calculate Tx Tx = Σ Lx+n i=0   The total life table population is To, while for instance, the total population aged 65 and over is T65. ∞ Tx = Σ Lx+n i=0 The application of the Tx values is of measuring how many persons years of life are lived for each age. Tx is calculated as the sum of all the Lx values from age x to the highest age in the Life Table. Thus T65 is the sum of the Lx values from L65 to the Last Lx value in the life table.    ∞ 

Calculate Tx The Tx function has applications in calculating life expectancy, one of the main summary measures of mortality, as well as other estimates based on total population numbers.

Calculate ex   The life table function ex refers to life expectancy from exact age x or put differently, the average number of years lived by people aged x.  e0 x = T x__ Ix 

Additional Information for Life Table Calculations The probability of surviving from age x to age y = (ly)/lx Probability of dying between ages x and y lx-(ly)/lx Number of people dying between ages x and y lx-ly

Additional Information for Life Table Calculations Cont’d Person years lived between ages x and y Tx – Ty Probability that a newborn will die between ages x and x+n (ndx)/l0 Probability that a newborn will experience his death between ages x and y (lx-ly) / l0

Additional Information for Life Table Calculations Cont’d Number of years a newborn can expect to live between ages x and y (Tx-Ty) / l0