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.)
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.
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