A stochastic model for a progressive chronic disease.
For many progressive chronic diseases, there exist useful prognostic indicators for the course of the disease and the survival of the patient. The evolution of such an indicator is modelled as a monotone transformation of a pure birth process with killing. Explicit formulas are derived for the probability distribution of this process at an arbitrary time, the distribution of the first-passage times, the joint distribution of the survival time and the maximum of the process, and the marginals of this joint distribution. In two examples, the general formulas are evaluated in closed form.
Nagylaki
Thomas
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Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, Illinois 60637, USA.
D002908:Chronic Disease; D018450:Disease Progression; D006801:Humans; D008954:Models, Biological; D013269:Stochastic Processes; D016019:Survival Analysis