17.6.1.2 Algorithms (Kaplan-Meier Estimator)

The Kaplan-Meier estimate of the survival probabilities is a step function, let \(t_i\,\!\), i = 1, 2, 3, ..., n. denotes the ordered distinct time for the observed event occurred, the survivorship function can be calculate by:

\(\hat S(t)=\prod_{j=1}^i(\frac{n_j-d_j}{n_j})\),

wheres \(n_j\,\!\) is the sample number at time \(t_j\,\!\) and \(d_j\,\!\) is the number of observed events and censored observations at time \(t_j\,\!\).