For grouped survival data, life tables calculate estimates of
time to failure distributions,
such as the survival function, the probability density function,
and the hazard function.
Assumptions:
The exact survival times are independent
and identically distributed.
(The life table estimate
is a nonparametric
method. We need not specify or know what the
distribution is,
only that all the survival times follow the same 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 time during which the subjects are observed is partitioned into
intervals (usually equal intervals). The probability of survival
remains constant throughout a given interval.
Subjects that survive to the beginning of an interval are
considered exposed (at risk) throughout the previous interval.
For the actuarial method of survival function estimation,
subjects that are censored during an interval are
considered at risk for half that interval, relying
on the assumption that the deaths and censorings occur randomly
throughout the interval, following a uniform distribution.
Guidance:
Ways to detect before
constructing a life table whether your data violate any
assumptions.
Ways to examine life
table results to detect assumption violations.
Possible alternatives if your data
or life table results indicate assumption violations.
To properly analyze and interpret results of life tables,
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
life tables 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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