Reporting Generalized Wilcoxon for Survival Analysis


I was retrospectively comparing those who received treatment (radiotherapy) and those who did not in a cohort of patients, with regards to their time-to-death outcome. This disease is characterized by a high event rate, typically within months from registration. For the group that did not receive treatment, virtually all cases died within 25 months.

However, there is one case in that [inferior] arm that survived for 10 years.

Assuming proportionality of hazards (no?), logrank’s p = 0.2. This, for me, seems to undermine the differences in the survival experience between the two groups. Having looked at the KM plots, I thought I could give the Generalized Wilcoxon test (Breslow’s) a try, since it is a weighted test, and I got p = 0.03.

Baring in mind that I’ve used the logrank for all the other comparisons and the Generalized Wilcoxon is ad hoc, how should I report this scenario?

Thank you,
E. Maher

but you must need an adjusted analysis here i think. You could do adjusted KM but id probably start with cox. regarding log rank v wilcoxon, suitability depends on the prop hazards, becasue the curves dont cross i would think log rank is reasonable, although i dont understand the discrepancy between p-values, it’s unexpected to me. you maybe want to do an influence analysis regarding the extreme survival time. I recommend david collett’s book for survival analysis

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Thank you for your response. I am actually going to attempt Cox, but I am not expecting too much reasonable adjustment with the sample size at hand.

Re difference between p-values, I was under the impression that it resulted from that 10-year survivor, with GW giving more weight to earlier events (and thus not affected much by such outlier).

I’ll check Collet’s book out, thank you!

It is seldom the case that a comparison with “those who did not receive treatment” is a valid comparison. It could have been valid if

  • there is a magic time zero such as day of diagnosis at which treatments are initiated
  • all confounders were measured and adjusted for

Your case seems to be more likely to involve a time-dependent treatment, and you need to give survival credit for all the pre-treatment days. This can be done, with a little luck, using a time-dependent treatment covariate in a Cox model if you are able to adjust for an array of baseline confounders and possibly adjust for time-dependent (updated) confounders.


If you do not receive radiotherapy when it is apparently indicated in the great majority of cases, there is probably a serious clinical reason why not. Either the clinical picture did not offer the prospect of radiology intervention making any difference or the patient was too frail already (from comorbidity, for example).

You can do a statistical test on data like this, but you don’t know what you are testing because you don’t know the data generation process – you don’t know why the patients ended up in the groups they are in.