Mis on Nelson-Aalen hinnang?

The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function in survival analysis. It is used to estimate the risk of occurrence of an event (e.g., death or failure) over time, based on observed data with censoring.

Formally, the estimate is constructed as the sum of the inverse values of the number of individuals under observation at the times when events occur:

[ \hat{H}(t) = \sum_{t_i \le t} \frac{d_i}{n_i} ]

where:

• (t_i) are the event times,
• (d_i) is the number of events at time (t_i),
• (n_i) is the number of individuals under observation immediately before (t_i).

The Nelson-Aalen estimator is often used to construct survival function estimates through the relationship with the cumulative hazard function, and as a fundamental tool for group comparison and model building in survival analysis.