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)