Stochastic mortality theory and the mortality potential: A biophysical model for certain competing risks

The theory of competing risks cannot be based entirely on the analysis of postmortem pathology data. It is necessary also to know the prevalence and residence times of the diseases in question, separately and jointly, in the living population at risk. It is also necessary to have a conceptual model of the transition process from health to disease, or from one disease state to another, within the organism, so that the formal transition probabilities estimated from epidemiological data can be interpreted in biophysical terms as arising from changes in the physico-chemical state of the organism. This paper offers such a model for transition processes arising from fluctuations of physiological state (for example, lapse into diabetic coma or insulin shock as a result of extreme high or low excursions of the blood sugar level). A Gaussian fluctuation process is postulated, and the transition probability, or incidence rate, is calculated as the frequency with which the state variable fluctuates beyond a specified distance, Λ, from the mean state. An explicit solution is given for the limiting, but biologically reasonable, case that such an excursion is a rare event. In this case, the transition probability varies exponentially for linear displacement of Λ or of the dispersion of fluctuations, σ. If Λ decreases, and/or σ increases, as a linear function of age, this model yields an exponential (Gompertzian) relation of disease incidence to age. Generalization to more than one variable is accomplished by introducing the concept of a mortality potential surface, in which the disease transitions are geometrized as saddle points, or “passes”, on the surface.