Several statistical tests have been proposed for comparing survival distributions or Kaplan-Meier curves between two or more groups. It seems that 99% of the time in clinical research the log-rank test is used but it is not clear in most situations whether this test is the best choice compared to Breslow (generalized Wilcoxon), Tarone-Ware, or Peto-Prentice, except that statisticians say it depends on when the failure times occur (earlier versus later) and on the pattern of censoring. Apparently, the various tests use different weights, making them more or less likely to detect earlier or later group differences.
Can someone suggest a useful and more objective way of making this decision because even visually inspecting the KM curves, while important, does not always make it obvious as to which test is preferred?
Thanks all!
This is the proportionality of hazards (PH) assumption (also needed for Cox models). Try the Log Minus Log (LML) plot. If the lines are roughly paralel, use log-rank test. If PH assumption doesn't hold, then the consequence for log-rank test will be loss of power (inflated type II error).
In general, log-rank Test tends to perform best towards the right side of the survival curves, the Wilcoxon Test tends to perform best on the left side of the survival curves, and the Tarone-Ware Test tends to perform best in the middle.
You don't mention the software used. SPSS has to be tricked to provide the observed LML plot, instead of theoretical (predicted by Cox model) LML survivals (always perfectly parallel, so useless)
If the proportional hazard assumption is questionable, you can also explore direct adjustments of survival curves, which compares the survival outcome of an 'average' patient/treatment unit using standarized differences. For a SAS example: http://support.sas.com/documentation/cdl/en/statug/66859/HTML/default/viewer.htm#statug_phreg_examples08.htm
based on the work in the link
Article Variance Calculations for Direct Adjusted Survival Curves, w...
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