Abstract
Abstract Since the pioneering work of O.O. Aalen (1975, 1978), the statistical theory of continuous‐time survival analysis and event history analysis has been based on the probabilistic theory of counting processes, martingales, and stochastic integrals. The important features are a full mathematical theory of censoring, the most important feature of these areas of applied statistics, and a master central limit theorem for martingales that allows a general asymptotic theory of many functionals used for parametric and nonparametric estimation and hypothesis testing. In this way, the tool of counting processes has provided a uniform background for what used to be scattered results. While survival analysis is the basic example of these techniques, more detailed statistical models are also covered, including competing risk models and multistate processes including illness‐death models.
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