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Published online by Cambridge University Press: 14 July 2016
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.
Present address: Systems and Measurements Division, Research Triangle Institute, P.O. Box 12194, Research Triangle Park, NC 27709, U.S.A.