I'm reviewing a paper that includes some survival plots for patients stratified to 3 groups (low, intermediate and high value of certain parameter), with p-value given for each plot. My understanding of Logrank test was that it only compares two groups. For 3 groups, we can have 3 comparisons (low/high, low/intermediate, intermediate/high), so for me it's not clear what does this p-value correspond to. Am I missing something? Would it be correct to request authors to specify which comparison is characterized by the p-value they show, or there are some default agreements for this kind of things?
P.S. it's especially unclear for me because on their examples 'Low' and 'High' groups behave similarly and only 'Intermediate' group has markedly different survival, so we can't say it's some unidirectional trend.
Best Answer
What's called a "log-rank" test in this context might be either of two things.
One possibility (used by the
survdiff()function in R) is a generalization of the chi-square test illustrated by Bland and Altman for a 2-group logrank test. With more than 2 groups, the null hypothesis is that there are no differences at all among the groups.It might alternatively be a score test of the overall null hypothesis that there are no differences in survival curves in a Cox model (null hypothesis that all regression coefficients are 0). This is one of 3 tests of that null hypothesis often displayed in Cox proportional hazard analysis results, as shown on this page where it is labeled "Score (logrank) test." If there were only 2 groups and no ties in event times, then the score test and the log-rank test would be identical.
This answer nicely explains the differences between the log-rank and the 2 other tests (likelihood ratio and Wald tests) typically reported for Cox regressions and other analyses in which models are estimated by maximizing a likelihood or partial likelihood.