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The logrank test, or log-rank test, is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored (technically, the censoring must be non-informative).
These three tests are asymptotically equivalent. For large enough N, they will give similar results. For small N, they may differ somewhat. The last row, "Score (logrank) test" is the result for the log-rank test, with p=0.011, the same result as the log-rank test, because the log-rank test is a special case of a Cox PH regression.
[1] [2] Choosing the right statistical test is not a trivial task. [1] The choice of the test depends on many properties of the research question. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use .
In some cases, one may wish to compare different Kaplan–Meier curves. This can be done by the log rank test, and the Cox proportional hazards test. Other statistics that may be of use with this estimator are pointwise confidence intervals, [13] the Hall-Wellner band [14] and the equal-precision band. [15]
The motivation to test differences between samples is that ranks are in some sense maximally invariant to monotone transformations. This may be important when there is outliers or when dealing with ordinal data .
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