How do the three methods compare to survival curves (log-rank, Mantel-Haenszel, Gehan-Breslow-Wilcoxon) differ?
The log-rank test is equivalent to the Mantel-Haenszel method. Actually the two differ a bit in how they deal with multiple deaths at exactly the same time point. Prism uses the Mantel-Haenszel approach but uses the name 'log-rank' which is commonly used for both approaches. This method is also called the Mantel-Cox method.
When you compare two data sets, Prism 5 also calculates the Gehan-Breslow-Wilcoxon method. You don't have to (and cannot) choose -- Prism 5 simply reports both. The Gehan-Breslow-Wilcoxon method gives more weight to deaths at early time points, which makes lots of sense. But the results can be misleading when a large fraction of patients are censored at early time points.. In contrast, the log-rank test gives equal weight to all time points.
The log-rank test is more standard. It is the more powerful of the two tests if the assumption of proportional hazards is true. Proportional hazards means that the ratio of hazard functions (deaths per time) is the same at all time points. One example of proportional hazards would be if the control group died at twice the rate as treated group at all time points.
The Gehan-Breslow-Wilcoxon test does not require a consistent hazard ratio, but does require that one group consistently have a higher risk than the other.
If the two survival curves cross, then one group has a higher risk at early time points and the other group has a higher risk at late time points. This could just be a coincidence of random sampling, and the assumption of proportional hazards could still be valid. But if the sample size is large, neither the log-rank nor the Wilcoxon-Gehan test rests are helpful when the survival curves cross near the middle of the the time course.
Prism 6 adds two features. First, you can now choose whether you want to report log-rank or Gehan-Breslow-Wilcoxon or both. The default is for Prism to report both. Second, Prism can now perfrom the Gehan-Breslow-Wilcoxon test when you entered three or more data sets (Prism 5 could only do it for two data sets). Unfortuantely, there was a bug so Prism reported incorrect results for Gehan-Breslow-Wilcoxon for three or more data sets (but the results were correct for two data sets). Fixed in 6.03 and 6.0d.