Frailty Models Based On Levy Processes

Generalizing the standard frailty models of survival analysis, we propose to model frailty as a weighted Levy process. Hence, the frailty of an individual is not a fixed quantity, but develops overtime. Formulae for the population hazard and survival functions are derived. The power variance function Levy process is a prominent example. In many cases, notably for compound Poisson processes, quasi-stationary distributions of survivors may arise. Quasi-stationarity implies limiting population hazard rates that are constant, in spite of the continual increase of the individual hazards. A brief discussion is given of the biological relevance of this finding.