Person-time at risk sums durations during which individuals are observed and susceptible to the event.
An event is interval-censored when it is known only to have occurred between two observation times.
A competing risks model assigns cause-specific hazards to mutually exclusive event types.
The Cox model writes with an unspecified baseline hazard.
The Cox partial likelihood conditions each event on its risk set, eliminating the baseline hazard.
A stratified Cox model gives each stratum its own baseline hazard while sharing regression coefficients.
A stratum is a subgroup assigned its own nuisance baseline.
Left truncation includes an individual only after survival to a delayed entry time.
The Kaplan-Meier product-limit estimator multiplies factors over event times.
A piecewise-exponential model takes the hazard to be constant on fixed time intervals.

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Survival analysis is a branch of statistics focused on analyzing the time until an event of interest occurs. This event is often referred to as a "failure" or "death," although it can represent any type of event, such as recovery from a disease, mechanical breakdown, or customer churn. Key concepts in survival analysis include: 1. **Survival Time**: The duration until the event occurs. This can be measured in various units, such as days, months, or years.