11.5 Survival Function

\[ S(t) = Pr(T>t) \]

• \(T\) is the time of ‘death’ or other event under consideration.

• \(S(t)\) is the probability of surviving up to time \(t\).

• But we dont observe \(T\) ! Rather we observe \(Y\):

\[ Y = min(T,C)\]

where C is the time of censoring. We also need to observe a status indicator:

\[ \delta = \left\{ \begin{array}{c l} 1, & \text{if } T \leq C \\ 0, & \text{if } T > C \end{array} \right. \]

• These pairs \((y_n, \delta_n)\) represent the survival data. (In R, they are combined to make a survival object using Surv)