Analysis of oldest-old mortality: Lifetables revisited

Annals of Statistics

Volumn 26, Issue 1, 1998, Pages 126-163

  Wang, Jane Ling ^a   Müller, Hans Georg ^a   Capra, William B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Aging; Biodemography; Discretization bias; Hazard function; Hazard surface; Local polynomial fitting; Nematodes; Samples of lifetables; Smoothing; Transformation

Indexed keywords

EID: 0040579233     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1030563980     Document Type: Article

References (51)

1. ANDERSON, J. and SENTHILSELVAN, A. (1980). Smooth estimates for the hazard function. J. Roy. Statist. Soc. Ser. B 42 322-327.
2. BLOOMFIELD, D. and HABERMAN, S. (1987). Graduation: some experiments with kernel methods. J. Inst. Actuaries 114 339-369.
3. BORGAN, O. (1979). On the theory of moving average graduation. Scand. Actuar. J. 3 83-105.
4. BROOKS, A., LITHGOW, G. and JOHNSON, T. (1994). Rates of mortality in populations of Caenorhabditis Elegans. Science 263 668-670.
5. CAREY, J. R., LIEDO, P., OROZCO, D. and VAUPEL, J. W. (1992). Slowing of mortality rates at older ages in large medfly cohorts. Science 258 457-461.
6. CLEVELAND, W. (1979). Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74 829-836.
7. CONGDON, P. (1993). Statistical graduation in local demographic analysis and projection. J. Roy. Statist. Soc. Ser. A 156 237-270.
8. COPAS, J. and HABERMAN, S. (1983). Nonparametric graduation using kernel methods. J. Inst. Actuaries 110 135-156.
9. CURTSINGER, J. W., FUKUI, H. H., TOWNSEND, D. R. and VAUPEL, J. W. (1992). Demography of genotypes - failure of the limited life-span paradigm in Drosophila Melanogaster. Science 258 461-463.
10. EUBANK, R. (1988). Spline Smoothing and Nonparametric Regression. Dekker, New York.
11. FAN, J. (1992). Design-adaptive nonparametric regression. J. Amer. Statist. Assoc. 87 998-1004.
12. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modeling and Its Applications. Chapman and Hall, London.
13. GASSER, T. and MÜLLER, H. G. (1979). Kernel estimation of regression functions. Smoothing Techniques in Curve Estimation. Lecture Notes in Math. 757 23-68. Springer, New York.
14. GOMPERTZ, B. (1825). On the nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society 2.
15. GRAM, J. P. (1879). Om Raekkeuviklinger, bestemte ved Hjaelp af de mindste Kradraters Methode. A. F. Høst & Son, Copenhagen.
16. GRAM, J. P. (1883). Ueber Entwickelung reeller Functionen in Reihen mittelst der Methode der Kleinsten Quadrate. J. Math. 94 41-73.
17. GRAY, R. (1990). Some diagnostic methods for Cox regression models through hazard smoothing. Biometrics 46 93-102.
18. GREEN, P. J. and SILVERMAN, B. W. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman and Hall, London.
19. HALL, P., KAY, J. and TITTERINGTON, D. (1990). Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika 77 521-528.
20. HOEM, J. (1972). On the statistical theory of analytic graduation. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 569-600. Univ. California Press, Berkeley.
21. HOEM, J. (1976a). The statistical theory of demographic rates. Scand. J. Statist. 3 169-185.
22. HOEM, J. (1976b). On the optimality of modified minimum chi-square analytic graduation. Scand. J. Statist. 3 89-92.
23. HOEM, J. (1983). The reticent trio: some little-known discoveries in life insurance mathematics by L. H. F. Opperman, T. N. Thiele, and J. P. Gram. Internat. Statist. Rev. 51 213-221.
24. HOEM, J. (1984). A contribution to the statistical theory of linear graduation. Insurance Math. and Econ. 3 1-17.
25. HOEM, J. and LENNEMANN, P. (1988). The tails in moving average graduation. Scand. Actuarial J. 11 193-229.
26. JAZWINSKI, S. M. (1996). Longevity, genes, and aging. Science 273 54-59.
27. JUCKETT, D. and ROSENBERG, B. (1993). Comparison of the Gompertz and Weibull functions as descriptors for human mortality distributions and their intersections. Mechanisms of Ageing and Development 69 1-31.
28. KELNER, K. L. and MARX, J. (1996). Patterns of aging. Science 273 41-41.
29. LEJEUNE, M. (1985). Estimation non-paramétrique par noyaux: régression polynomiale mobile. Rev. Statist. Appl. 33 43-67.
30. MANTON, K. G., STALLARD, E. and VAUPEL, J. W. (1986). Alternative models for the heterogeneity of mortality risks among the ages. J. Amer. Statist. Assoc. 81 635-644.
31. MÜLLER, H. G. (1987). Weighted local regression and kernel methods for nonparametric curve fitting, J. Amer. Statist. Assoc. 82 231-238.
32. MÜLLER, H. G. (1988). Nonparametric Regression Analysis of Longitudial Data. Springer, New York.
33. MÜLLER, H. G. and STADTMÜLLER, U. (1993). On variance function estimation with quadratic forms. J. Statist. Plann. Inference 35 213-231.
34. MÜLLER, H. G. and WANG, J. L. (1990). Locally adaptive hazard smoothing. Probab. Theory Related Fields 85 523-538.
35. MÜLLER, H. G. and WANG, J. L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics 50 61-76.
36. MÜLLER, H. G., WANG, J. L. and CAPRA, W. B. (1997). Estimating hazard functions from lifetables: the transformation approach. Biometrika. To appear.
37. PERLS, T. T. (1995). The Oldest-Old. Scientific American January 70-75.
38. RAMLAU-HANSEN, H. (1983). Smoothing counting process intensities by means of kernel functions. Ann. Statist. 11 453-466.
39. RICE, J. (1984). Bandwidth choice for nonparametric regression. Ann. Statist. 12 1215-1230.
40. SACKS, J. and YLVISAKER, D. (1970). Designs for regression problems with correlated errors III. Ann. Math. Statist. 41 2057-2074.
41. SEIFERT, B., GASSER, T. and WOLF, A. (1993). Nonparametric estimation of residual variance revisited. Biometrika 80 373-383.
42. SUZMAN, R. M., WILLIS, D. and MANTON, K. (1992). The Oldest Old. Oxford Univ. Press.
43. TANNER, M. and WONG, W. (1983). The estimation of the hazard function from randomly censored data by the kernel method. Ann. Statist. 11 989-993.
44. TANNER, M. and WONG, W. (1984). Data-based nonparametric estimation of the hazard function with applications to model diagnostics and exploratory analysis. J. Amer. Statist. Assoc. 79 174-182.
45. VAUPEL, J. W., JOHNSON, T. E. and LITHGOW, G. J. (1994). Rates of mortality in populations of Caenorhabditis Elegans. Science 266 826.
46. VAUPEL, J. W. and CAREY, J. R. (1993). Compositional interpretations of medfly mortality. Science 260 1666-1667.
47. VAUPEL, J. W., MANTON, K. G. and STALLARD, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16 439-454.
48. VAUPEL, J. W. and YASHIN, A. I. (1985). Heterogeneity's ruses: some surprising effects of selection on population dynamics. Amer. Statist. 39 176-185.
49. WANG, J. L., MÜLLER, H. G., CAPRA, W. B. and CAREY, J. R. (1994). Rates of mortality in populations of Caenorhabditis Elegans. Science 266 827-828.
50. WILSON, D. (1994). The analysis of survival (mortality) data: fitting Gompertz, Weibull, and logistic functions. Mechanisms of Ageing and Development 74 15-33.
51. YANDELL, B. S. (1983). Nonparametric inference for rates with censored survival data. Ann. Statist. 11 989-993.