Admissible mixing distributions for a general class of mixture survival models with known asymptotics

Theoretical Population Biology

Volumn 80, Issue 1, 2011, Pages 64-70

  Missov, Trifon I ^a,b   Finkelstein, Maxim ^a,c  

^a MAX PLANCK INSTITUTE FOR DEMOGRAPHIC RESEARCH   (Germany)

^b UNIVERSITY OF ROSTOCK   (Germany)

^c UNIVERSITY OF THE FREE STATE   (South Africa)

Author keywords

Frailty distribution; Function of regular variation; Mixture survival model; Mortality asymptotics; Tauberian theorem

Indexed keywords

AGE CLASS; HAZARD ASSESSMENT; HETEROGENEITY; MORTALITY; NUMERICAL MODEL; POPULATION DISTRIBUTION; STATISTICAL ANALYSIS; SURVIVAL; THEORETICAL STUDY; UNCERTAINTY ANALYSIS;

AGED; ARTICLE; BIOLOGICAL MODEL; FEMALE; FRAIL ELDERLY; HUMAN; LIFE EXPECTANCY; MALE; MORTALITY; STATISTICS; SURVIVAL;

AGED, 80 AND OVER; FEMALE; FRAIL ELDERLY; HUMANS; LIFE EXPECTANCY; MALE; MODELS, BIOLOGICAL; MORTALITY; SURVIVAL ANALYSIS;

ABELIA; LEVINSENIA;

EID: 79959376882     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2011.05.001     Document Type: Article

References (22)

1. Aalen O. Heterogeneity in survival analysis. Statistics in Medicine 1988, 7:1121-1137.
2. Aalen O. Modelling heterogeneity in survival analysis by the compound poisson distribution. Annals of Applied Probability 1992, 4(2):951-972.
3. Abbring J., van den Berg G. The unobserved heterogeneity distribution in duration analysis. Biometrika 2007, 94(1):87-99.
4. Beard R. Note on Some Mathematical Mortality Models 1959, 302-311. Little, Brown and Company, Boston. G.E.W. Woolstenholme, M. O'Connor (Eds.).
5. Bingham N., Goldie C., Teugels J. Regular Variation 1989, Cambridge University Press.
6. Block H., Joe H. Tail behavior of the failure rate functions of mixtures. Lifetime Data Analysis 1997, 3(3):269-288.
7. Elbers C., Ridder G. True and spurious duration dependence: The identifiability of proportitional hazard model. Review of Economic Studies (XLIX) 1982, 403-409.
8. Feller W. Probability Theory and its Applications. Vol. I 1971, John Wiley & Sons.
9. Finkelstein M. Failure Rate Modelling for Reliability and Risk. Springer Series in Reliability Engineering 2008, Springer, London.
10. Finkelstein M., Esaulova V. Asymptotic behavior of a general class of mixture failure rates. Advances in Applied Probability 2006, 38:242-262.
11. Gampe J. Human mortality beyond age 110. Demographic Research Monographs 2010, No. 7:219-230. Springer, Heidelberg (et al.), Ch. III. H. Maier, J. Gampe, B. Jeune, J.-M. Robine, J. Vaupel (Eds.).
12. Heckmann J., Singer B. The identifiability of the proportional hazard model. Review of Economic Studies 1984, 231-241.
13. Hoem J. Identifiability of hazard models with unobserved heterogeneity: the compatibility of two apparently contradictory results. Theoretical Population Biology 1990, 37:124-128.
14. Hougaard P. Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika 1984, 71:75-83.
15. Hougaard P. Survival models for heterogeneous populations derived from stable distributions. Biometrika 1986, 73(2):387-396.
16. IDL. 2010. The international database on longevity. http://www.supercentenarians.org/.
17. McGilchrist C., Aisbett C. Regression with frailty in survival analysis. Biometrics 1991, 47:461-466.
18. Robine, J.-M., Cournil, A., Gampe, J., Vaupel, J., 2005. Idl, the international database on longevity. In: Living to 100 and beyond. Living to 100 and Beyond Symposium, Orlando, FL. Society of Actuaries.
19. Steinsaltz D., Wachter K. Understanding mortality rate deceleration and heterogeneity. Mathematical Population Studies 2006, 13:19-37.
20. Tuljapurkar S., Li N., Boe C. A universal pattern of mortality decline in the g7 countries. Nature 2000, 405(6788):789-792.
21. Vaupel J., Manton K., Stallard E. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 1979, 16:439-454.
22. Yashin A., Vaupel J., Iachine I. A duality in aging: the equivalence of mortality models based on radically different concepts. Mechanisms of Ageing and Development 1994, 74:1-14.