13_AS_9_lec_a

3 045 1 town b population 10000 20000 70000 deaths 15

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Unformatted text preview: hs 210 90 100 Death rate 0.3% 0.45% 1% Town B Population 10000 20000 70000 Deaths 15 60 525 Death rate 0.15% 0.3% 0.75% For each age, the death rates are higher in Town A than Town B. BUT, the crude death rate is higher for Town B. This is an apparent paradox. Why? The crude death rate takes no account of the fact that the age profiles of the two populations are very different This problem can be dealt with by applying weighting factors of a standard population to each age group to compensate for the different population structures (standardization). 8/15 Actuarial Statistics – Module 9: Standardization and new developments Directly standardized mortality rate 1 Introduction: Single Index Approach 2 Crude Mortality rate 3 Directly standardized mortality rate 4 Indirectly Standardized Mortality Rate 5 The standardized mortality ratio 6 More advanced mortality models 9/15 Actuarial Statistics – Module 9: Standardization and new developments Directly standardized mortality rate Directly standardized mortality rate The Directly Standardized Mortality Rate is defined as x sEc m x ,t x ,t x sEc x ,t , c which is a weighted average of age specific rates using s Ex ,t as weights. Removes differences in the crude rate for the population that result from differences in age structure Requires age specific rates for each population 9/15 Actuarial Statistics – Module 9: Standardization and new developments Directly standardized mortality rate Example Given a standard population with the following characteristics Age 20 40 60 Total Population 40,000 35,000 25,000 100,000 for the previous example with Age 20 40 60 Town A Population 70000 20000...
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