# PROPHET StatGuide: Life tables

## 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.)

• 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 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:

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.
• Miller, Rupert G. Jr. 1981. Survival Analysis. New York: John Wiley & Sons.
• Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.