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I'm looking at a dataset of survival times of animals in two different groups. While there is some early mortality in the first group, the Kaplan-Meier survival curves overlap, the log-rank test and the Cox proportional hazard model are not significant, which would lead me to conclude that there is no evidence that the survival rate would be different in the two groups.

However, I can also tally the number of live and dead animals in the two groups at particular time points, and run a Fisher's exact test to see if there is an association between the group membership and the survival status. Lo and behold, some of these turn out to be significant at some time points, which would lead me to conclude that ther is an association between survival and membership in the two groups.

Which of these results should I trust? Is the Fisher's test appropriate here and if it is not, then why not?

All your insights would be highly appreciated!

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    $\begingroup$ Is there censoring (i.e. cases not observed until either death or end of a fixed observation period that is the same for all)? If so, I would strongly mistrust methods that do not account for it and go with the survival analysis. $\endgroup$ – Björn Dec 9 '16 at 12:25
  • $\begingroup$ Use a principled pre-specified statistical analysis plan. Otherwise it becomes p-hacking. The two methods should disagree. Time to event analysis is more appropriate. And note that Fisher's "exact" test is not very accurate and is discouraged. $\endgroup$ – Frank Harrell Feb 9 '19 at 13:11
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Overlapping survival curves indicate that the hazard rate is not proportional between the groups. This means that Cox model assumptions are not met, and it might not have the power to detect the type of effect that you have there.

On the other hand, if you are repeating a Fisher's test at every time point of observation, you are doing multiple (auto-correlated, I believe) tests. If I had to go this way, I at least apply some overly conservative multiple testing correction. I am not sure if it is possible to fit a survival model with non-proportional hazards - maybe other posters will be able to help with that.

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    $\begingroup$ Multiple testing is clearly an issue. As a side ntoe: the Cox model essentially corresponds to a log-rank test (plus minus exact handling of tied event times) so that it provides a valid test even when hazards are not proportional (like the log-rank test it may not have good power - but neither will Fisher's exact test necessarily), it is simply not straightforward to interpret the model estimates when proportional hazards are not fulfilled. $\endgroup$ – Björn Dec 9 '16 at 12:26
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    $\begingroup$ Survival curves can overlap because of noise; that doesn't necessarily mean non-proportional hazards is present. And to the original question, don't make the "absence of evidence is not evidence for absence" error. And Fisher's exact test is not meant for this situation, and is not very accurate in the situations for which it is meant. $\endgroup$ – Frank Harrell Jun 16 '18 at 12:21

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