selviämisfunktiota

A selviämisfunktio, or survival function in English, is a fundamental concept in survival analysis. It describes the probability that a subject will survive beyond a specific time point. Mathematically, the survival function is often denoted by S(t), where 't' represents time. It is defined as the probability of an event (such as death, equipment failure, or disease relapse) not occurring by time 't'.

The survival function has several key properties. It is always between 0 and 1, inclusive. S(0) is typically 1, meaning at the start of observation, the probability of survival is certain. As time increases, the survival function generally decreases or stays constant, never increasing. The limit of S(t) as t approaches infinity represents the probability of surviving indefinitely.

Estimating the survival function from observed data is a primary goal in survival analysis. Common methods include the Kaplan-Meier estimator, which provides a non-parametric estimate, and parametric models that assume a specific distribution for survival times. These estimates are crucial for understanding the course of a process, comparing survival experiences between different groups, and making predictions about future outcomes. The area under the survival curve can also represent the mean survival time, providing another summary statistic.