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:
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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...