# 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.
• 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.