Modeling human mortality using mixtures of bathtub shaped failure distributions

Journal of Theoretical Biology

Volumn 245, Issue 3, 2007, Pages 528-538

  Bebbington, Mark ^a   Lai, Chin Diew ^a   Zitikis, Ričardas ^b  

^a MASSEY UNIVERSITY   (New Zealand)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Aging; Curvature; Gompertz Makeham distribution; Hazard rate; Survival function

Indexed keywords

AGING POPULATION; MORTALITY; NATURAL SELECTION; POPULATION MODELING; SURVIVAL; WEIBULL THEORY;

ACCURACY; AGING; ARTICLE; COMPARATIVE STUDY; HAZARD RATIO; INFANT MORTALITY; LIFESPAN; MORTALITY; POSTNATAL CARE; PRIORITY JOURNAL; QUALITATIVE ANALYSIS; RELIABILITY; SURVIVAL;

ADOLESCENT; ADULT; AGED; AGED, 80 AND OVER; AGING; CHILD; CHILD, PRESCHOOL; COMPUTER SIMULATION; HUMANS; INFANT; INFANT MORTALITY; INFANT, NEWBORN; LONGEVITY; MIDDLE AGED; MODELS, BIOLOGICAL; MORTALITY; PROPORTIONAL HAZARDS MODELS;

EID: 33847630878     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.11.011     Document Type: Article

References (40)

1. Abernethy J. Gompertzian mortality originates in the winding down of the Mitotic clock. J. Theor. Biol. 192 (1998) 419-435
2. Abrams P.A. The fitness costs of senescence: the evolutionary importance of events in early adult life. Evol. Ecol. 5 (1991) 343-360
3. Al-Hussaini E.K., and Sultan K.S. Reliability and hazard based on finite mixture models. In: Balakrishnan N., and Rao C.R. (Eds). Advances in Reliability, Handbook of Statistics vol. 20 (2001), North-Holland, Amsterdam 139-183
4. Anson J. The parameters of death: a consideration of the quantity of information in a life table using a polynomial representation of the survivorship curve. Stat. Med. 7 (1988) 895-912
5. Bains W. Statistical mechanic prediction of non-Gompertzian ageing in extremely aged populations. Mech. Ageing Dev. 112 (2000) 89-97
6. Barlow, R.E., Proschan, F., 1981. Statistical Theory of Reliability and Life Testing Models (second printing). To Begin With, Silver Spring, MD.
7. Bebbington M., Lai C.D., and Zitikis R. Estimating the turning points of failure rate and mean residual life functions. Commun. Dependability Qual. Management 8 (2005) 11-15
8. Bebbington M., Lai C.D., and Zitikis R. Useful periods for lifetime distributions with bathtub shaped hazard rate functions. IEEE Trans. Reliab. 55 (2006) 245-251
9. Bebbington, M., Lai, C.D., Zitikis, R., 2006b. Operating hazard of a bathtub shaped failure distribution. Submitted for publication. 〈http://www.stats.uwo.ca/faculty/zitikis/research/papers/oper.pdf〉.
10. Bebbington, M., Lai, C.D., Zitikis, R., 2006c. The mean residual life function of a bathtub shaped failure distribution. Submitted for publication. 〈http://www.stats.uwo.ca/faculty/zitikis/research/papers/mrl.pdf〉.
11. Bebbington, M., Lai, C.D., Zitikis, R., 2007. A flexible Weibull extension. Reliab. Eng. Syst. Saf., in press, doi:10.1016/j.ress.2006.03.004.
12. Charlesworth B. Optimization models, quantitative, genetics and mutation. Evolution 44 (1990) 520-538
13. Charlesworth B. Patterns of age-specific means and genetic variances of mortality rates predicted by the mutation-accumulation theory of aging. J. Theor. Biol. 210 (2001) 47-65
14. Charlesworth B., and Partridge L. Ageing: levelling of the grim reaper. Curr. Biol. 7 (1997) R440-R442
15. Dolejs J. The extension of Gompertz law's validity. Mech. Ageing Dev. 99 (1997) 233-244
16. Finkelstein M., and Esaulova V. Asymptotic behavior of a general class of mixture failure rates. Adv. Appl. Probab. 38 (2006) 244-262
17. Fukui H.H., Xiu L., and Curtsinger J.W. Slowing of age-specific mortality rates in Drosophila melanogaster. Exp. Gerontol. 28 (1993) 585-599
18. Gavrilov L.A., and Gavrilova N.S. The Biology of Life Span: A Quantitative Approach (1991), Harwood Academic Publisher, New York
19. Gavrilov L.A., and Gavrilova N.S. The reliability theory of aging and longevity. J. Theor. Biol. 213 (2001) 527-545
20. Golubev A. Does Makeham make sense?. Biogerontology 5 (2004) 159-167
21. Gompertz B. 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. Philos. Trans. R. Soc. London 115 (1825) 513-585
22. Hamilton W.D. The moulding of senescence by natural selection. J. Theor. Biol. 12 (1966) 12-45
23. Heligman L., and Pollard J.H. The age pattern of mortality. J. Inst. Actuaries 107 (1980) 49-80
24. Horiuchi S., and Wilmoth J.R. Deceleration in the age pattern of mortality at older ages. Demography 35 (1998) 391-412
25. Jaisingh L.R., Kolarik W.J., and Dey P.K. A flexible bathtub hazard model for non-repairable systems with uncensored data. Microelectronics Reliab. 27 (1987) 87-103
26. Juckett D.A., and Rosenberg B. Comparison of the Gompertz and Weibull functions as descriptors for human mortality distributions and their intersections. Mech. Aging Dev. 69 (1993) 1-31
27. Kirkwood T.B.L., and Rose M.R. Evolution of senescence: late survival sacrificed for reproduction. Philos. Trans. R. Soc. London B 332 (1991) 15-24
28. Lai C.D., and Xie M. Stochastic Ageing and Dependence for Reliability (2006), Springer, New York
29. Lai C.D., Zhang L.Y., and Xie M. Mean residual life and other properties of Weibull related bathtub shaped failure rate distributions. Int. J. Reliab. Quality Saf. Eng. 11 (2004) 113-132
30. Lawless J.F. Statistical Models and Methods for Lifetime Data. second ed. (2003), Wiley, New York
31. Luder H.U. Onset of human aging estimated from hazard functions associated with various causes of death. Mech. Ageing Dev. 67 (1993) 247-259
32. Lynch S.M., and Brown J.S. Reconsidering mortality compression and deceleration: an alternative model of mortality rates. Demography 38 (2001) 79-95
33. Makeham W.L. On the law of mortality. J. Inst. Actuaries 13 (1867) 325-367
34. Miller A.R. The distribution of wearout over evolved reliability structures. J. Theor. Biol. 136 (1989) 27-46
35. Mueller L.D., and Rose M.R. Evolutionary theory predicts late-life mortality plateaus. Proc. Nat. Acad. Sci. USA 93 (1996) 15249-15253
36. Pletcher S.D., and Neuhauser C. Biological aging-criteria for modeling and a new mechanistic model. Int. J. Mod. Phys. C 11 (2000) 525-546
37. Rose M.R., Rauser C.L., Mueller L.D., and Benford G. A revolution for aging research. Biogerontology 7 (2006) 269-277
38. Siler W. A competing risk model for animal mortality. Ecology 60 (1979) 750-757
39. Strehler B.L., and Mildvan A.S. General theory of mortality and aging. Science 132 (1960) 14-21
40. Xie M., and Lai C.D. Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliab. Eng. Syst. Saf. 52 (1995) 87-93