Unobserved population heterogeneity: A review of formal relationships

Demographic Research

Volumn 31, Issue 1, 2014, Pages 659-686

  Vaupel, James W ^a,b,c   Missov, Trifon I ^a,d  

^a MAX PLANCK INSTITUTE FOR DEMOGRAPHIC RESEARCH   (Germany)

^b UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^c DUKE UNIVERSITY   (United States)

^d UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84920280839     PISSN: None     EISSN: 14359871     Source Type: Journal    
DOI: 10.4054/DemRes.2014.31.22     Document Type: Article

References (47)

1. Aalen, O. (1987). Two examples of modelling heterogeneity in survival analysis. Scandinavian Journal of Statistics 14(1): 19-25.
2. Abbring, J.H. and van den Berg, G.J. (2007). The unobserved heterogeneity distribution in duration analysis. Biometrika 94(1): 87-99. doi:10.1093/biomet/asm013.
3. Bailey, W.N. (1935). Generalised Hypergeometric Series. Cambridge, England: University Press.
4. Bolstad, W. and Manga, S. (2001). Investigating child mortality in malawi using family and community random effects: A bayesian analysis. Journal of the American Statistical Association 96(453): 12-19. doi:10.1198/016214501750332659.
5. Clayton, D. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65(1): 141-151. doi:10.1093/biomet/65.1.141.
6. Doetsch, G. (1937). Theorie und Anwendung der Laplace-Transformation. Berlin: Springer.
7. Doetsch, G. (1950, 1955, 1956). Handbuch der Laplace-Transformation, Band 3. Basel: Birkhäuser.
8. Duchateau, L. and Janssen, P. (2008). The Frailty Model. New York: Springer.
9. Elbers, C. and Ridder, G. (1982). True and spurious duration dependence: The identifiability of proportitional hazard model. Review of Economic Studies 49(3): 403-409. doi:10.2307/2297364.
10. Gerdes, L.U., Jeune, B., Andersen-Ranberg, K., Nybo, H., and Vaupel, J.W. (2000). Estimation of apolipoprotein e genotype-specific relative mortality risks from the distribution of genotypes in centenarians and middle-aged men: Apolipoprotein e gene is a "frailty gene", not a "longevity gene". Genetic Epidemiology 19(3): 202-210. doi:10.1002/1098-2272(200010)19:3<202::AID-GEPI2>3.0.CO;2-Q.
11. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115: 513-583. doi:10.1098/rstl.1825.0026.
12. Gumbel, E.J. (1958). Statistics of Extremes. New York: Columbia University Press.
13. Heckman, J.J. and Singer, B. (1982). Population heterogeneity in demographic models. In: Land, K. and Rogers, A. (eds.). Multidimensional Mathematical Demography. New York: Academic Press: 567-599. doi:10.1016/B978-0-12-435640-5.50018-3.
14. Horiuchi, S. and Coale, A.J. (1990). Age patterns of mortality for older women: An analysis using the age-specific rate of mortality change with age. Mathematical Population Studies 2(4): 245-267. doi:10.1080/08898489009525312.
15. Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York: Springer.
16. Laplace, P.S. (1782, 1785). Mémoire sur les approximations des formules qui sont fonctions de tr`es grands nombres. Mem. Acad. roy. Sci. (Paris) 1-88.
17. Lenart, A. and Missov, T. (2014). Goodness-of-fit tests for the gompertz distribution. Communications in Statistics: Theory and Methods doi:10.1080/03610926.2014.892323.
18. Makeham, W.M. (1860). On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries 8(6): 301-310.
19. Manga, S.O.M. (2001). A comparison of methods for analyzing a nested frailty model to child survival in malawi. Australian and New Zealand Journal of Statistics 43(1): 7-16. doi:10.1111/1467-842X.00150.
20. Manton, K.G. and Stallard, E. (1981). Methods for evaluating the heterogeneity of aging processes in human populations using vital statistics data: Explaining the black/white mortality crossover by a model of mortality selection. Human Biology 53(1): 47-67.
21. Manton, K.G., Stallard, E., and Vaupel, J.W. (1981). Methods for comparing the mortality experience of heterogeneous populations. Demography 18(3): 389-410. doi:10.2307/20610058.
22. Marshall, A.W. and Olkin, I. (1988). Families of multivariate distributions. Journal of the American Statistical Association 83(403): 834-841. doi:10.1080/01621459. 1988.10478671.
23. Mellin, H. (1900). Eine formel für den logarithmus transcendenter funktionen von endlichem geschlecht. Acta Soc. Sci. Fennicae 29.
24. Missov, T.I. (2012). What Properties Should a Frailty Distribution Possess? Presented at the Population Association of America 2012 Annual Meeting, San Francisco, CA, May 3-5.
25. Missov, T.I. (2013). Gamma-gompertz life expectancy at birth. Demographic Research 28(9): 259-270. doi:10.4054/DemRes.2013.28.9.
26. Missov, T.I. and Finkelstein, M. (2011). Admissible mixing distributions for a general class of mixture survival models with known asymptotics. Theoretical Population Biology 80(1): 64-70. doi:10.1016/j.tpb.2011.05.001.
27. Missov, T.I. and Lenart, A. (2013). Gompertz-makeham life expectancies: Expressions and applications. Theoretical Population Biology 90: 29-35. doi:10.1016/j.tpb.2013.09.013.
28. Missov, T.I., Lenart, A., Canudas-Romo, V., Nemeth, L., and Vaupel, J.W. (2014). The gompertz force of mortality in terms of the modal age at death. Demographic Research (under review).
29. Missov, T.I. and Vaupel, J.W. (2014). Mortality implications of mortality plateaus. SIAM Review (in press).
30. Price, G.R. (1970). Selection and covariance. Nature 227: 520-521. doi:10.1038/227520a0.
31. Rebke, M., Coulson, T., Becker, P.H., and Vaupel, J. (2010). Reproductive improvement and senescence in a long-lived bird. PNAS 107(17): 7841-7846. doi:10.1073/pnas.1002645107.
32. Sastry, N. (1997). A nested frailty model for survival data, with an application to study of child survival in northeast brazil. Journal of the American Statistical Association 92(438): 426-435. doi:10.1080/01621459.1997.10473994.
33. Vaupel, J. (1992). Analysis of Population Changes and Differences: Methods for Demographers, Statisticians, Biologists, Epidemiologists and Reliability Engineers. Paper presented at Annual Meeting of the PAA, Denver, Colorado, April 30-May 2.
34. Vaupel, J., Manton, K.G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3): 439-454. doi:10.2307/2061224.
35. Vaupel, J. and Yashin, A.I. (1985). Heterogeneity's ruses: Some surprising effects of selection on population dynamics. The American Statistician 39(3): 176-185.
36. Vaupel, J. and Yashin, A.I. (2001a). L'hétérogénéité cachée des populations. In: Caselli, G., Vallin, J., and Wunsch, G. (eds.). Démographie: analyse et synthése, Volume I.: la dynamique des populations. Paris: Institut National d'' Etudes Démographiques (INED): 463-478.
37. Vaupel, J. and Yashin, A.I. (2006). Unobserved population heterogeneity. In: Caselli, G., Vallin, J., and Wunsch, G. (eds.). Demography: analysis and synthesis; a treatise in population studies, volume 1. London: Academic Press: 271-278.
38. Vaupel, J.W. (1988). Inherited frailty and longevity. Demography 25(2): 277-287. doi:10.2307/2061294.
39. Vaupel, J.W. and Canudas-Romo, V. (2003). Decomposing change in life expectancy: A bouquet of formulas in honor of nathan keyfitz's 90th birthday. Demography 40(2): 201-216. doi:10.1353/dem.2003.0018.
40. Vaupel, J.W. and Yashin, A.I. (2001b). L'eterogeneità non osservata delle popolazioni. In: Caselli, G., Vallin, J., and Wunsch, G. (eds.). Analisi demografica: nuovi approcci; dall'omogeneità all'eterogeneità delle popolazioni. Rome: Carocci editore: 85-103.
41. Vaupel, J.W. and Zhang, Z. (2010). Attrition in heterogeneous cohorts. Demographic Research 23(26): 737-748. doi:10.4054/DemRes.2010.23.26.
42. Vaupel, J. (2002). Life expectancy at current rates vs current conditions: A reflexion stimulated by bongaarts and feeney's "how long do we live?". Demographic Research 7: 365-378. doi:10.4054/DemRes.2002.7.8.
43. Wienke, A. (2010). Frailty Models in Survival Analysis. Boca Raton, FL: Chapman & Hall/CRC Press.
44. Yashin, A.I., Iachine, I.A., and Begun, A.W. (2000). Mortality modeling: A review. Mathematical Population Studies 8(4): 305-332. doi:10.1080/08898480009525489.
45. Yashin, A.I., Vaupel, J.W., and Iachine, I.A. (1995). Correlated individual frailty: An advantageous approach to survival analysis of bivariate data. Mathematical Population Studies 5(2): 145-159. doi:10.1080/08898489509525394.
46. Yau, K.K.W. (2001). Multilevel models for survival analysis with random effects. Biometrics 57(1): 96-102. doi:10.1111/j.0006-341X.2001.00096.x.
47. Zeng, Y. and Vaupel, J.W. (2004). Association of late childbearing with healthy longevity among the oldest-old in china. Population Studies 58(1): 37-53. doi:10.1080/0032472032000175437.