2 Survival, Hazard and Cumulative Hazard

The distribution of a survival time can be described in several equivalent ways. The distribution function and density of ordinary statistics are less natural here than two functions designed for time-to-event data: the survival function, the probability of lasting beyond each time, and the hazard function, the instantaneous risk of the event at each time among those who have lasted so far. The hazard is the central idea of the subject: it is what doctors and engineers think in (“the risk is highest in the first month”), and it is what the regression models later in the course describe. This section defines these functions, shows how each determines the others, and computes summaries such as the mean and median.

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