Intensity models

Survival analysis has been one of the most important branch of statistics for decades. During this time, the range of methodology has expanded considerably, but still the most common methods such as the Cox proportional hazards model and the Kaplan-Meier method date back to the 1970’s or before that. These methods have various advantages, but more modern methods can provide more detailed insight in cases where more information has been recorded on life events. A (non-) homogenous Poisson process parameterized by a hazard function has independent increments i.e. the number of events between two time points does not depend on the number or timing of events before that time interval (history).

Intensity (or Cox point) processes (see, for example, Arjas 1989 or Andersen et al. 1993) have been developed as an extension to Poisson point processes. These methods allow observed event history prior to some time point to be incorporated in the statistical model to predict the future risk after that time. The intensity process models are very flexible, but the drawback is that most statistical software packages provide only a limited set of tools for practical applications.