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A note on random intensities and conditional survival functions

Published online by Cambridge University Press:  14 July 2016

Anatoli Yashin  and
Elja Arjas
Anatoli Yashin*
Affiliation:
Institute of Control Sciences, Moscow
Elja Arjas*
Affiliation:
University of Oulu
*
∗ Postal address: Institute of Control Sciences, Profsojusnaya 65, Moscow, USSR.
∗∗ Postal address: Department of Applied Mathematics and Statistics, University of Oulu, Linnanmaa, 90570 Oulu, Finland.
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Abstract

Failure intensities in which the evaluation of hazard is based on the observation of an auxiliary random process have become very popular in survival analysis. While their definition is well known, either as the derivative of a conditional failure probability or in the counting process and martingale framework, their relationship to conditional survival functions does not seem to be equally well understood. This paper gives a set of necessary and sufficient conditions for the so-called exponential formula in this context.

Keywords

HAZARD RATECOUNTING PROCESSMARTINGALEEXPONENTIAL FORMULA
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 630 - 635
Copyright
Copyright © Applied Probability Trust 1988 

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References

Aven, T. (1983) Optimal replacement under a minimal strategy—a general failure model. Adv. Appl. Prob. 15, 198–211.Google Scholar
Chou, C. S. and Meyer, P. A. (1974) Sur la representation des martingales comme integrales stochastiques dans les processus ponctuels. Lecture Notes in Mathematics 381, Springer-Verlag, Berlin.Google Scholar
Dellacherie, C. and Meyer, P. A. (1982) Probabilities and Potential. North-Holland, Amsterdam.Google Scholar
Flournoy, N. (1980) On the survivor and hazard functions. Paper read at the 1980 Joint Statistical Meetings, Houston, Texas. (Abstract published by the American Statistical Association.)Google Scholar
Jacod, J. (1975) Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Wahrscheinlichkeitsth. 31, 235–253.Google Scholar
Kalbfleisch, J. D. and Prentice, R. L. (1980) The Statistical Analysis of Failure Time Data. Wiley, New York.Google Scholar
Liptser, R. S. and Shiryayev, A. N. (1978) Statistics of Random Processes, Vol. II. Springer-Verlag, Heidelberg.Google Scholar
Pitman, J. W. and Speed, T. P. (1973) A note on random times. Stock. Proc. Appl. 1, 369–374.Google Scholar
Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V. Jr., Flournoy, N., Farewell, V. T. and Breslow, N. E. (1979) The analysis of failure times in the presence of competing risks. Biometrics 34, 541–554.Google Scholar
Yashin, A., Manton, K. and Stallard, E. (1986) Dependent competing risks: a stochastic process model. J. Math. Biol. 24, 119–140.Google Scholar