# Kaplan-Meier plot

Kaplan-Meier plots display estimates of the survival function for survival data recorded for individuals.

The Kaplan-Meier estimate is also known as the product-limit estimate.

### Assumptions:

• The exact survival times are independent and identically distributed. (The Kaplan-Meier estimator is a nonparametric method. We need not specify or know what the distribution is, only that all the survival times follow the same discrete distribution.)
• The subjects are a random sample from the population of interest, so that they are independent of each other.
• If any survival values are censored, they are randomly censored, and the distribution of censoring times is independent of the exact survival times. The values that happen to be censored come from the same survival distribution as those that are not censored. The amount and pattern of censoring should be comparable across the groups.
• The time during which the subjects are observed is partitioned into intervals such that each distinct (unique) noncensored time of death is in a separate interval. The probability of survival remains constant throughout a given interval; the survival times are assumed to be sufficiently closely spaced so that this assumption is reasonable, and so that the probability of tied death values is small. If there are no censored survival times, and each subject happens to fall into a different interval, the life table survival estimates will be the same as the Kaplan-Meier estimates.
• Subjects that are censored are considered to have survived until just after the time at which they were last observed alive. This means that if a censoring and survival time have the same value, the subject with the noncensored time is considered to have died just before the subject with the censored time. In the interval ending with time T, the subjects at exposed (at risk) include all those with censoring or survival times greater than or equal to T.
• The Kaplan-Meier survival estimate is a step function that changes at every distinct survival time, but does not change at censoring times (unless a survival time happens to be tied to a censoring time). If the final observation is a noncensored survival time T, then the Kaplan-Meier survival estimate for all times greater than T is 0. The Kaplan-Meier estimator is not defined past the final noncensored survival time. If the final observation is a censoring time instead of a survival time, then the final Kaplan-Meier estimator will be greater than 0, and occur at the last uncensored survival time. In this situation, the survival estimate conventionally is often represented as continuing indefinitely at the value calculated at the final noncensored survival time.

### Guidance:

• Ways to detect before calculating a Kaplan-Meier estimate whether your data violate any assumptions.
• Ways to examine Kaplan-Meier results to detect assumption violations.
• Possible alternatives if your data or Kaplan-Meier results indicate assumption violations.

To properly analyze and interpret results of Kaplan-Meier plots, you should be familiar with the following terms and concepts:

If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply Kaplan-Meier plots may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:

• Cox, D. R. and Oakes, D. 1984. Analysis of Survival Data. London: Chapman and Hall.
• Elandt-Johnson, Regina C. and Johnson, Norman L. 1980. Survival Models and Data Analysis. New York: John Wiley & Sons.
• Kalbfleisch, John D. and Prentice, Ross L. 1980. The Statistical Analysis of Failure Time Data. New York: John Wiley & Sons.
• Lawless, J. F. 1982. Statistical Models and Methods for Lifetime Data. New York: John Wiley & Sons.
• Lee, Elisa T. 1992. Statistical Methods for Survival Data Analysis. 2nd ed. New York: John Wiley & Sons.
• Marubini, Ettore, and Valsecchi, Maria Grazia. 1995. Analysing Survival Data from Clinical Trials and Observational Studies. New York: John Wiley & Sons.
• Miller, Rupert G. Jr. 1981. Survival Analysis. New York: John Wiley & Sons.
• Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.