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Title: Mortality table construction
Description: This note is from the first hand of a student who attended the classes. Help you understand the course and build structures.
Description: This note is from the first hand of a student who attended the classes. Help you understand the course and build structures.
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Mortality Table Construction
Individual data based methods
1
...
Leaving the study may be by death, withdrawal, or termination of the study
...
Assume: the hazard rate is constant for each age
...
Actuarial exposure – the same as exact exposure except for those who die
...
Variance of estimators
Using the delta method,
̂ ( 𝑛 𝑞̂𝑗 ) = (1 −
𝑉𝑎𝑟
̂ (𝑞̂𝑗 ) =
𝑉𝑎𝑟
𝑞̂𝑗 (1 − 𝑞̂𝑗 )
,
𝑒𝑗
𝑛
2
𝑛
𝑞̂𝑗 ) 𝑛2 (
𝑑𝑗
)
𝑒𝑗2
𝑤ℎ𝑒𝑟𝑒 𝑞̂𝑗 = 𝑛
𝑑𝑗
𝑒𝑗
4
...
Multiple decrement
The estimators may be used to calculate decrement rates in multiple-decrement situations
...
If the forces of decrement are
constant between interval boundaries and all decrements are independent, then the maximum
likelihood estimate of the decrement rate equals the exact exposure estimate
...
Estimating transition intensities
Assume that the transition intensity 𝜇 𝑖𝑗 is constant in an interval
...
𝜇 𝑖𝑗 is
estimated as the number of transitions from i to j, divided by the amount of time spent by all
individuals in state i
Title: Mortality table construction
Description: This note is from the first hand of a student who attended the classes. Help you understand the course and build structures.
Description: This note is from the first hand of a student who attended the classes. Help you understand the course and build structures.