A comparison of counting process models for complicated life histories

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Abstract
The modern statistical theory for counting processes lends itself to flexible non‐parametric analyses of complicated life histories. Its application rests upon a statistical model of multiplicative intensities, adequately constructed for the objectives of the analysis and usually derived from an underlying stochastic model of an individual course of disease. It is shown how survival times and suitable stochastic partitionings of the time axis can yield statistical models of intermittent and multi‐state exposure to a risk of death which otherwise are deduced, under stronger assumptions, from Markovian illness–death processes. Aalen's linear regression model for counting processes is applied in a non‐standard context of intermittent exposure.

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