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Survival functions induced by stochastic covariate processes

Published online by Cambridge University Press:  14 July 2016

Lawrence E. Myers
Lawrence E. Myers*
Affiliation:
Duke Medical Center
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Abstract

A vector X of patient prognostic variables is modeled as a linear diffusion process with time-dependent, non-random, continuous coefficients. The instantaneous force of mortality (hazard function) operating on the patient is assumed to be a time-dependent, continuous quadratic functional of the prognostic vector. Conditional on initial data X0, the probability of surviving T units of time is expressed in terms of the solution of a Riccati equation, which can be evaluated in closed form if the coefficients of the process and the hazard are constant. This conditional expectation does not preserve proportional hazards.

Keywords

PROPORTIONAL HAZARDS MODELSTIME-DEPENDENT COVARIATESSURVIVAL FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 523 - 529
Copyright
Copyright © Applied Probability Trust 

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Footnotes

∗

Present address: Systems and Measurements Division, Research Triangle Institute, P.O. Box 12194, Research Triangle Park, NC 27709, U.S.A.

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