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Abstract:
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In survival analysis the focus is usually on the mere occurrence of events. Not much emphasis is placed on understanding the processes leading up to these events. The simple reason for this is that these processes are usually unobserved. However, one may consider the structure of possible underlying processes and draw some general conclusions from this. For instance, a practically important issue is why hazard rates assume various specific shapes, e.g. why do we often see hazard rates that first increase and then decrease? We shall show the usefulness of the concept of quasi-stationarity. These are stationary distributions that arise in stochastic processes where probability mass is continuously being lost to some set of absorbing states. Due to this leaking of probability mass, the limiting distribution is just stationary in a conditional sense that is, conditioned on nonabsorption.
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