## 1.3 Some notation

We are now ready to introduce basic mathematical terminology and notation for survival analysis.

Let $$T$$ the random variable that denotes the survival time, i.e., the time to an event. Since $$T$$ denotes time, its possible values include all nonnegative numbers; that is, $$T$$ can be any number equal to or greater than zero. Furthermore, $$t$$ will be any specific value of interest for the random variable $$T$$.

Additionally, when each subject has a random right censoring time $$C_i$$ that is independent of their failure time $$T_i$$, the data is represented by $$(Y_i, \Delta_i)$$ where $$Y_i = \min(T_i, C_i)$$ and $$\Delta_i = I(T_i \le C_i)$$, this $$\Delta$$ define a $$(0,1)$$ random variable indicating either failure or censorship. That is, $$\Delta = 1$$ for failure if the event occurs during the study period, or $$\Delta = 0$$ if the survival time is censored by the end of the study period.