# PROPHET StatGuide: Survival function comparison tests

##
For survival data recorded for individuals,
test the null hypothesis
that two more more samples are from
populations
that follow the same survival function,
using the Mantel-Cox
log-rank test, the Gehan-Breslow test,
or the Tarone-Ware test.

### Assumptions:

Within each sample, the exact survival times are independent
and identically distributed.
(The Mantel-Cox, Gehan-Breslow,
and Tarone-Ware tests are all
nonparametric
tests. We need not specify or know what the
distribution is,
only that all the survival times for each sample
follow the same discrete distribution.)

Each sample of subjects is a random sample
from the population(s) of
interest, so that they are independent of
each other, both within each sample and among samples.

If any survival values are censored,
they are randomly censored, and the distribution of censoring times
for each sample is independent
of the exact survival times for that samples. 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.

### Guidance:

**Ways to detect** before
performing a survival test whether your data violate any
assumptions.

**Ways to examine**
survival test results to detect assumption violations.

**Possible alternatives** if your data
or survival test results indicate assumption violations.

To properly analyze and interpret
results of *survival tests*, 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
*survival tests* 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.
- Miller, Rupert G. Jr. 1981.
*Survival Analysis. * New York: John Wiley & Sons.
- Rosner, Bernard. 1995.
*Fundamentals of Biostatistics.*
4th ed. Belmont, California: Duxbury Press.

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##### Last modified: February 20, 1997

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