# Inter-experimental variation in survival experiment - how to estimate variability?

In my animal experiments, I do survival studies, which generate Kaplan-Meier survival curves for each group, which I then compare with an appropriate log rank test.

My question is: If I have run a survival experiment with identical variables, say, five times, and the final outcome (in very layman's terms) happens to be slightly different each time, is there a test that I can do estimate the variability (variance) of my experimental runs?

One major confounding factor is the fact that survival is a continuous variable over time. Therefore, it is difficult to reduce it to a single statistic (that can then be compared with a test). A lot of people use the median survival (expressed in units of time) as a single statistic surrogate for survival, but it can often be misleading - depending upon the slope of the survival curve, and may not represent the true nature of the survival outcome.

Can someone here help? Please also let me know if further clarifications are needed.

• Can you provide an example of the outcomes you consider in your experiments? What is your sample size (in each group)?
– chl
Commented Sep 30, 2010 at 18:43
• I'm a bit confused what the goal is as well. Is there a reason examining a plot of each of the 5 hazard functions (and/or their confidence intervals) is insufficient? Do you need a test statistic to state where the curves intersect? As chl suggested in a comment to Thylacoleo's answer pooling seems inappropriate with different outcomes. Commented Oct 1, 2010 at 15:29
• Sorry about the late comment. I just received the book that Thylacoleo recommended. To answer your questions: Chl - the outcome is survival (i.e. no death) over a period of time. The sample size in each group varies from, say, 5-8. Andy - survival experiments suffer from inherent variabilities. I do indeed examine the Kaplan Meier plots of the groups by a log rank test. But I am more interested in finding out if there is a test that can evaluate inter-experimental variabilities of survival experiments. Commented Nov 15, 2010 at 20:47

I suggest you read Section 2.3 & 2.4 pp40-73 of Hosmer & Lemeshow's 1999 edition of Applied Survival Analysis. This gives variances of various statistics of survivorship functions, such as 1) each time (allowing confidence interval estimation), 2) mean survival, etc. I'm not clear from your question what aspect experimental variability you want to summarise.

You will be aware there are several test statistics which can be used to compare KM survival functions, such as the log-rank test you mention. They differ on the weighting applied to variance estimates of deaths at different survival times. However, the pooled result, which forms the test statistic, is not usually regarded as a variance estimate, in the same way that a chi-squared statistic is not a variance estimator, but a test of whether the sample distribution of the variance follows what is expected from the null hypothesis.

• I was thinking of confidence intervals, but the question is not clear to me because there seems to be different outcomes each time (but may I don't understand the question) which would prevent from pooling anything at all.
– chl
Commented Oct 1, 2010 at 10:56