# How do I adjust for age in comparing survival times of two different groups?

The usual way to compare distributions of deaths, or other "time to" events, is using survival analysis. In particular a survivor function of time, S.

S(age) = P(T>age | T>=age)

= Probability of living past a particular age given you have already attained that age.

Two methods are popularly used to evaluate S. Life table methods and the Kaplan-Meier estimate. Survival functions are cumulative probabilities which can take values from 1 to 0. These probabilities may be plotted for separate groups of individuals in the form of curves and compared using statistical procedures.

A useful property of survival curves is that they can utilise censored observations where only the lower bound of the time of an event (e.g. age of death) is known.There are three methods used for comparing Kaplan-Meier curves: the log-rank method, the Breslow test and Tarone-Ware. These may be fitted in SPSS by using analyze>survival>kaplan-meier.

A guide on choice of comparison method is presented below.

The short of it is that the log-rank method is best at detecting differences between the curves late in the time period of the study; the Breslow test is best at detecting early differences, and Tarone-Ware is an intermediate strategy.

Non-technical references:

Hosmer, D. W., and S. Lemeshow. 1999. Applied Survival Analysis. New York: John Wiley and Sons.

Kleinbaum, D. G. 1996. Survival Analysis: A Self-Learning Text. New York: Springer-Verlag.

Norusis, M. SPSS Advanced Statistical Procedures Companion. Upper Saddle-River, N.J.: Prentice Hall, Inc..

These are taken from the "Recommended Readings" in the Kaplan-Meier "case studies" at (Help > Case Studies).

Hosmer and Lemeshow give an example in which the log-rank and Breslow (which they call Wilcoxon) tests do not agree.

For a brief introduction to survival curves: Watson, P. 2005 Chapter 18 in A Handbook of Research Methods for Clinical and Health Psychology. Eds Miles and Gilbert. Oxford University Press. (in CBSU library).