Demographic Analysis and Evaluation Workshop on Demographic Analysis and Evaluation 1

Mortality: The Life Table (continued)

Life Table Construction (continued) In this part of the workshop we will cover: Calculation of separation factors Closing the life table Smoothing the life table m(x) values 3

Separation Factors A frequently accepted approximation of the values of the separation factors is half of the age interval for which the separation factors are being calculated. For instance, for constructing abridged life tables, separation factors for the 5-year age groups over age 5 are accepted to be 2.5. 4

Separation Factors Although it is accepted that separation factors for ages 5 and over are half of the age interval (when the age interval is not greater than 5 years), this assumption is not accepted for ages under 5. Separation factors for ages under 1 year and from 1 to 4 years are smaller than half the age interval. This is due to the fact that mortality is very high during the first day of life and declines rapidly during the first year and up to the fifth year. p. 130 Smaller b/c they live less time, on ave. 5

Calculating Separation Factors The estimation of separation factors for ages under 1 year and 1 to 4 years can be calculated by using detailed information about the age of deceased persons; and using established relationships between the level of infant mortality and the separation factors. 6

Separation Factors Calculated from Statistics Separation factors for age under 1 year are a weighted average of the fraction of a year lived by those dying, weighted by the number of infants dying at each age. Σ Di * ti D Where: k0 is the separation factor for age under 1 year; Di is the number of infants dying within certain ages during the first year of life; ti is the time lived from birth to the day the infant dies, expressed as a fraction of a year; and D is the total number of infant deaths during the first year of life. K0= 7

Separation Factors Calculated from Statistics Calculation of the separation factor for age under 1: Example from Chapter 3 of the Census Bureau’s Population Analysis with Microcomputers 8

Separation Factors Calculated from Statistics Separation factors for ages 1 to 4 years use a similar calculation. Those dying at age 1 during their second year of life, lived only half a year during the age interval 1 to 4 Those dying at ages 2,3 and 4 years lived on average 1.5, 2.5 and 3.5 years during the interval 9

Separation Factors Calculated from Statistics Calculation of the separation factor for age group 1-4: Example from Chapter 3 of the Census Bureau’s Population Analysis with Microcomputers 10

Separation Factors from Calculated from Observed Relationships From observed relationships in existing life tables From observed relationships in model life tables and correlations 11

Separation Factors from Calculated from Observed Relationships From observed relationships in existing life tables: To calculate the separation factor for any age group x to x+n years, the formula is: nLx - n * lx+n nkx = ndx Impose existing empirical LT on your LT; just take K? 12

Separation Factors from Calculated from Observed Relationships From observed relationships in model life tables and correlations: 13

Separation Factors from Calculated from Observed Relationships From observed relationships in model life tables and correlations: Determined by IMR also!! 14

Mortality at the Youngest Ages There are several possibilities for estimating infant mortality rates, and the selection of a procedure depends on the availability and quality of information on births and deaths. Population Analysis with Microcomputers describes Infant mortality calculated from reliable statistics, where infant deaths are not only complete but classified by year of birth. Infant mortality calculated using separation factors. The “conventional” infant mortality rate, equal to the ratio of registered infant deaths to registered number of births during the same year. 15

Mortality at the Youngest Ages Infant mortality calculated using a 3-year average of registered infant deaths and births Dt-1 + Dt + Dt+1 q0 = Bt-1 + Bt + Bt+1 Where: D and B represent registered infant deaths and births, respectively; and t refers to the year of registration. Infant mortality calculated from survey birth history data Indirect estimation of infant (and child) mortality using child survivorship data 16

Mortality at the Oldest Ages A possible problem remains: how to close the open-ended age group. If a life table is not closed properly – the estimation of the Lx+ at the open-ended age group – the level of life expectancy at all ages will be affected. One option, based on the assumption that the death rate for the open-ended age group calculated from vital statistics is the same as the one in the life table, gives acceptable results for life tables with open-ended age groups 90+ ... mx+ = lx / Lx+ and Lx+ = lx / mx+ 17

Mortality at the Oldest Ages Coale and Demeny (1968) proposed the following relationships: L85+ = l85 . log10 l85 L80+ = (3.725 + 0.0000625 x l80)l80 18

Mortality at the Oldest Ages Finally, for populations with acceptable data, the closing of the life table is sometimes performed by extrapolating the force of mortality using Gompertz-type functions. These functions are fitted to the life table functions at younger ages and are used to extrapolate the survivors of the life table up to ages where most of them have died. In their UN model life tables (1982), the United Nations closes life tables assuming that the force of mortality at the older ages follows a Makeham function. 19

Smoothing the Life Table Death rates may be smoothed in various ways, but simple techniques are usually the best. As smoothing will be applied in instances where overall death registration is judged to be complete, the result should retain the original registered total number of deaths pertaining to the span of age groups being smoothed. A moving average works well. 20

Smoothing the Life Table After the young adult ages (15 or 20 years), the pattern of death rates by age follows an approximately exponential shape (see figures III-1-A and III-1-B). Because of this exponential shape, a simple arithmetic average for smoothing would produce rates that overestimate the level of mortality. Therefore it is recommended to take logarithms of the death rates before calculating the average. The PASEX spreadsheet uses a moving average of the logs of the m(x) estimates to smooth in spreadsheet LTPOPDTH.xls (Population Analysis with Microcomputers, volume I, p.84) Spreadsheet: LTPOPDTH.xls 21

Adjustment of Estimated m(x) Values, Figure III-1-A

Adjustment of Estimated m(x) Values, Figure III-1-B

Adjustment of Estimated m(x) Values, Figure III-4-A

Adjustment of Estimated m(x) Values, Figure III-4-B