## Core concepts of survival analysis

Survival analysis deals with censored data, and it is very common that parametric models are unsuitable for explaining the lifetimes observed in clinical trials.

Let *T* denote the survival time, or the time to the event of interest, and we will naturally have , which is a continuous random variable. Suppose that the lifetime cumulative distribution is *F* and the associated density function is *f*. We define important concepts as required for further analysis. We will explore the concept of *survival function* next.

Suppose that *T* is the continuous random variable of a lifetime and that the associated cumulative distribution function is *F*. The survival function at time *t* is the probability the observation is still alive at the time, and it is defined by the following:

The survival function can take different forms. Let's go through some examples for each of the distributions to get a clearer picture of the difference in survival functions.

**Exponential Distribution...**