NelsonAalenSchätzung

NelsonAalenSchätzung refers to the Nelson-Aalen estimator, a non-parametric method used in survival analysis to estimate the cumulative hazard function. The cumulative hazard function, denoted by H(t), represents the accumulated risk of an event occurring up to time t. This estimator is particularly useful when event times are not known precisely, or when dealing with censored data.

The Nelson-Aalen estimator is calculated as the sum of the increments of the estimated hazard at each observed event time. For each distinct event time t_i, the estimated hazard rate is the number of events occurring at t_i divided by the number of individuals at risk just before t_i. The cumulative hazard at time t is then the sum of these estimated hazard rates for all observed event times less than or equal to t.

This estimator is known to be a consistent and asymptotically normal estimator for the true cumulative hazard function. It is also a lower-bounded estimator, meaning it will never overestimate the true cumulative hazard. The Nelson-Aalen estimator is a fundamental tool in survival analysis, providing a way to understand the risk progression over time without making strong assumptions about the underlying hazard distribution. It is often used in conjunction with methods for estimating the survival function, such as the Kaplan-Meier estimator.