Effects of unobserved and partially observed covariate processes on system failure: A review of models and estimation strategies

Statistical Science

Volumn 12, Issue 1, 1997, Pages 20-34

  Yashin, Anatoli I ^a   Manton, Kenneth G ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Cameron Martin; Conditional Gaussian processes; Kalman Filters; Martingales; Quadratic hazard functions; Random covariates; Stochastic hazards; Wiener processes

Indexed keywords

EID: 0002942685     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1029963259     Document Type: Article

References (42)

1. Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Continuing Processes. Springer, New York.
2. Arjas, E. (1989). Survival models and martingale dynamics. Scand. J. Statist. 16 177-225.
3. Cameron, R. and Martin, W. (1944). The Wiener measure of Hilbert neighborhoods in the space of real continuous functions. J. Math. Phys. 23 195-209.
4. Colantonio, a., Kasl, S. W. and Ostfeld, a. M. (1992). Level of function predicts first stroke in the elderly. Stroke 23 1355-1357.
5. Diggle, P. and Kenward, M. G. (1994). Informative drop-out in longitudinal data analysis. J. Roy. Statist. Soc. Ser. C 41 4993.
6. FINCH, C. E. (1990). Longevity, Senescence, and the Genome. Univ. Chicago Press.
7. FINCH, C. and Pike, M. (1996). Maximum life span predictions from the Gompertz mortality model. Journal of Gerontology: Biological Sciences 51 B183-B194.
8. Kasch, F. W., Boyer, J. L., Van Camp, S. P., Verity, L. S. and Wallace, J. P. (1993). Effect of exercise on cardiovascular ageing. Age and Ageing 22 5-10.
9. Khametov, V. M. and Yashin, A. I. (1983). Efficient solution to the interpolation problem on the basis of observations of jump processes. Problems Inform. Transmission 19 38-51.
10. Law, M. R., Wald, N. J. and Thompson, S. G. (1994). By how much and how quickly does reduction in serum cholesterol concentration lower risk of ischaemic heart disease? British Medical Journal 308 367-373.
11. Law, M. R., Wald, N. J., Wu, T., Hackshaw, a. and Bailey, A. (1994). Systematic underestimation of association between serum cholesterol concentration and ischaemic heart disease in observational studies: data from the BUPA study British Medical Journal 308 363-366.
12. Liptser, R. S. and Shiryayev, a. N. (1977). Statistics of Random Processes 1. General Theory. Springer, New York.
13. Liptser, R. S. and Shiryayev, a. N. (1988). The Theory ofMar-tingales. Springer, New York.
14. Manton, K. G., Corder, L. S. and Stallard, E. (1993). Estimates of change in chronic disability and institutional incidence and prevalence rates in the U.S. elderly population from the 1982, 1984, and 1989 National Long Term Care Survey Journal of Gerontology: Social Sciences 47 S153-S166.
15. Manton, K. G. and Stallard, E. (1988). Chronic Disease Modeling: Measurement and Evaluation of the Risks of Chronic Disease Processes. Griffin, London.
16. Manton, K. G., Stallard, E. and Singer, B. H. (1994). Methods for projecting the future size and health status of the U.S. elderly population. In Studies of the Economics of Aging (D. Wise, ed.) 41-77. National Bureau of Economic Research, Univ. Chicago Press.
17. Manton, K. G., Stallard, E., Woodbury, M. a. and Dowd, J. (1994). Time-varying covariates in models of human mortality and aging: multidimensional generalization of the Gom-pertz. Journal of Gerontology: Biological Sciences 49 B169-B190.
18. Manton, K. G., Woodbury, M. a. and Tolley, H. (1994). Statistical Applications Using Fuzzy Sets. Wiley, New York.
19. Myers, L. E. (1981). Survival functions induced by stochastic covariate processes. J. Appl. Probab. 18 523-529.
20. Pekkanen, J., Manton, K., Stallard, E., Nissinen, a. and Kar-Vonen, M. (1992). Risk factor dynamics, mortality and life expectancy differences between eastern and western Finland: the Finnish cohorts of the seven countries studies. International Journal Epidemiology 21 406-419.
21. Rosenberg, a., Kemeny, G., Smith, L. G., Skurnick, I. D. and Bandurski, M. J. (1973). The kinetics and thermodynamics of death in multicellular organisms. Mechanisms of Aging and Development 2 275-293.
22. Sacher, G. A. and Trucco, E. (1962). The stochastic theory of mortality Ann. New York Acad. Sci. 96 985.
23. Selikoff, I. J. (1981). Disability compensation for asbestos-associated disease in the United States. Report to the U.S. Dept. Labor Environmental Sciences Laboratory, Mount Sinai School of Medicine, New York. (Contract No. J-9-M-8-0165.)
24. Singpurwalla, N. D. (1995). Survival in dynamic environments. Statist. Sci. 10 86-103.
25. Stebbing, A. D. (1987). Growth hormesis: a by-product of control. Health Physics 52 543-547.
26. Strehler, B. L. (1977). Time, Cells and Aging. Academic Press, New York.
27. Strehler, B. L. and Mildvan, a. S. (1960). General theory of mortality and aging. Science 132 14-21.
28. Vaupel, J., Manton, K. and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality Demography 16 439-454.
29. Vaupel, J. and Yashin, a. I. (1985). Heterogeneity ruses: some surprising effects of selection on population dynamics. American Statistician 39 176-185.
30. Witteman, J. M., Grobbee, D. E., Valkenburg, H. A., van Hemert, A. M., Stijnen, T., Burger, H. and Hofman, A. (1994). J-shaped relation between change in diastolic blood pressure and progression of aortic atherosclerosis. The Lancet 343 504-507.
31. Woodbury, M. a. and Manton, K. G. (1977). A random-walk model of human mortality and aging. Theoret. Population Biol. 11 37-48.
32. Woodbury, M. a., Manton, K. G. and Tolley, H. D. (1996). Convex models of high dimensional discrete data. Ann. Inst. Statist. Math. To appear.
33. Wu, M. C. and Bailey, K. R. (1988). Analyzing changes in the presence of right censoring caused by death and withdrawal. Statistics in Medicine 7 337-346.
34. Wu, M. C. and Carroll, R. (1988). Estimation and comparison of changes in the presence of right censoring by modeling the censoring process. Biometrics 44 175-188.
35. Wu, M. and Ware, J. (1979). On the use of repeated measurements of regression analysis with dichotomous responses. Biometrics 35 513-521.
36. Yashin, a. I. (1980). Conditional Gaussian estimation of dynamic systems under jumping observations. Automat. Remote Control 5 618-626. (Translated from Russian.)
37. Yashin, A. I. (1985). Dynamics in survival analysis: conditional Gaussian property versus Cameron-Martin formula. In Statistics and Control of Stochastic Processes (N. V. Krylov, R. Sh. Liptser and A. A. Novikov, eds.) 466-475. Springer, New York.
38. Yashin, a. I. (1993). An extension of the Cameron-Martin result. J. Appl. Probab. 30 247-251.
39. Yashin, a. I. and Arjas, E. (1988). A note on random intensities and conditional survival functions. J. Appl. Probab. 25 630-635.
40. Yashin, A. I. and Manton, K. G. (1994). Modifications of the EM algorithm for survival influenced by an unobserved stochastic process. Stochastic Process. Appl. 54 257-274.
41. Yashin, a. I., Manton, K. G. and Stallard, E. (1986a). Dependent competing risks: a stochastic process model. J. Math. Biol. 24 119-140.
42. Yashin, a. I., Manton, K. G. and Stallard, E. (1986b). Evaluating the effects of observed and unobserved diffusion processes. Survival Analysis Modelling 7 1353-1363.