I'm conducting a survival analysis for my dissertation and have run into a bit of a road block about which test to use to look for differences in Kaplan-Meier curves between treatments.

A previous study that was similar in design to mine used the Wilcox-Gehan D test, but I want to make sure I am choosing the test with the most power for my study design. Briefly, I have two groups with relatively small sample sizes (n=10, n=27). In the control group, I randomly right-censored individuals to pair clinical findings with the experimental group mortalities.

Does anyone have strong opinions about which test would be most appropriate?

The tests I know of are:

  1. Mantel-Haenzel logrank test
  2. Peto & Peto logrank test
  3. Gehan generalized Wilcoxon ranksum test
  4. Peto & Peto & Prentice generalized Wilcoxon test
  5. Tarone & Ware modified Wilcoxon test

If I missed any please let me know! Thanks in advance!


1 Answer 1


From time 0 to time T, at some specific time points, events happened. At each event time point, we have observed # of events in each group and expected # of event also. The different between observed # and expected # is used the measure the difference between groups. But we have more then one event time point, So we need to summarize them together. When we summarize them, the weights are needed. All of these test methods are differed by the different methods of assigning weights. Some of them assign the weight according to # of subjects at the risk at that time. Some of them follow the estimated survival probability. Here is the description of some methods and corresponding weights https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_lifetest_a0000000265.htm . Because the mess of the names, I am not sure what weights scheme is used in your named methods, But you can find them from where you get the names. After you know the weight scheme for each method, you can select one that you love.

Suppose you have two survival curves for two groups. They begin from survival probability = 0 at time 0 and end to survival probability to 0 at at time T. Between time 0 and T, the two curves should not overlap together completely. It means there are some difference between two curves. The importance of these differences is the base for you to select weights. For example, if you think importance are the them then assign weigh 1 to all of them (log-rank test). If you think early differences is more importance, you can use Wilcoxon test, because at early stage, the # of subjects on risk is high than later stage.

  • $\begingroup$ thanks for the fast response! I am still not sure how to decide which of the weights would be most appropriate for my study design. $\endgroup$
    – derp4herps
    Nov 16, 2018 at 21:36
  • $\begingroup$ Understandable? Any questions? $\endgroup$
    – user158565
    Nov 16, 2018 at 21:40
  • $\begingroup$ How do I decide which weight to use? Which situation should each weight be used for? $\endgroup$
    – derp4herps
    Nov 16, 2018 at 21:43
  • $\begingroup$ See last paragraph is Answer. Too long such that comment does not accept it. $\endgroup$
    – user158565
    Nov 16, 2018 at 21:56

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