KaplanMeierestimatorer

The Kaplan Meier estimator is a non-parametric statistic used to estimate the survival function from lifetime data. The survival function, denoted as S(t), represents the probability that an individual survives beyond a certain time t. This estimator is particularly useful in medical research, where it is used to analyze the time until an event occurs, such as death, disease recurrence, or relapse.

The estimator works by calculating the proportion of individuals who are still alive at each observed event time. It starts with 100% of the individuals at the beginning of the study. As events occur, the proportion of survivors is updated. For each time point ti where an event occurs, the survival probability S(ti) is calculated by multiplying the survival probability at the previous event time (ti-1) by the proportion of individuals who survived past ti-1 and did not experience the event at ti.

A key feature of the Kaplan Meier estimator is its ability to handle censored data. Censoring occurs when the event of interest has not yet occurred for some individuals by the end of the study or when an individual is lost to follow-up. The estimator accounts for these individuals by only considering those who are still at risk of experiencing the event at each time point.

The output of the Kaplan Meier estimator is a step function that graphically represents the survival probabilities over time. This allows for visual comparison of survival experiences between different groups, such as a treatment group versus a control group. The estimator is a fundamental tool in survival analysis and is widely used to estimate survival curves and compare them between groups.