1. A Bayesian Method for Forecasting Mortality Rates by Health State:
LONGEVITY 13： International Longevity Risk and Capital Markets Solutions Conference 2017
A Bayesian Method for Forecasting
Mortality Rates by Health State:
with Rising Life Expectancy
Atsuyuki Kogure
Keio University, Japan
Shinichi Kamiya
Nanyang Technological University, Singapore
Takahiro Fushimi
Stanford University, USA
September 21-22, 2017 1

2. Aging and mortality forecasting
heavy burdens on
long-term care cost 2

3. Japan has been and will be aging　very fast !
Population Pyramid of Japan from 1920 to 2050

4. Subpopulation mortality forecasting4

5. Our objectives 5

6. Mortality forecasting for total population
Death numbers
for age x at time t
Exposures (population sizes)
for age x at time t
Dxt
Ext
Force of mortality

7. Subpopulations by health state
Death numbers
for age x at time t in state j
Exposures (subpopulation sizes)
for age x at time t in state j
Dxt0
Health state 0
(no problem)
Ext0
Health state 1
(least severe)
Ext1
Dxt1
．．．
．．．
．．．
Health state J
(most severe)
ExtJ
DxtJ

8. Lee-Carter structure by health state

9. Mortality forecasting for subpopulations

10. Force of mortality for total population

11. Mixture Lee-Carter model

12. Identifiability of the mixture LC model

13. Bayesian estimation: parameter uncertainty

14. Priors for observation equation14

15. Priors for health factors15

16. Priors for State Equation16

17. Hyperparameters

18. Application:
Public Long-term Care Insurance System in Japan

19. Japanese Public Long-term Care System

20. Source: Monthly Report on the Status of Long-term Care Insurance
Trends of Persons Certified As Requiring Long-term Care
Total number of certified persons in 2015 is 608 (in 10, 000’s)
increased by a factor of for the past 15 years.
total
In 10,000’s
Care levels
Transitional
Care levels
levels
Support
2000
2005
2010
2015
Source: Monthly Report on the Status of Long-term Care Insurance

21. Health states

22. Sizes of LTC subpopulations

23. Bayes Computation: MCMC

24. Posterior distributions for η，γ65，β65，κ2001: male

25. Summary statistics of posterior distributions: male

26. Changes in posterior means of γx，βx，κt over x or t
male

27. Posterior distributions for η，γ65，β65，κ2001: female

28. Summary statistics of posterior distributions: female

29. Chanes in posterior means of γx， βx ，κt over x or t
female

30. Gender difference in health effects
male ηj
ｈealth effect
femae
j=health state

31. Future mortality rates by health status

32. Future mortality rates by health status
ｊ=5
ｊ=4
ｊ=3
ｊ=2
ｊ=1
ｊ=0
Male
Female

33. Survival rates by health status

34. Future survival rates by health status
Male
Female

35. Conclusions (1)

36. Conclusions (2)

37. References

38. References