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I have fifteen groups (factor levels) and I need to compare their crude mortality. Is Logrank test limited to two groups only? Which test would be correct to use in this case?

kjetil b halvorsen
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st4co4
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1 Answers1

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In principle, you could treat your groups as a 15-level categorical predictor and perform a Cox proportional hazards regression against that categorical predictor. That has the further advantage that covariates associated with outcome could be included in the model.

Provided that the proportional hazards assumption holds, ANOVA comparing models with and without that 15-level set of groups would document whether there were any differences in survival among the groups. Then the coefficient values associated with each of the groups could be used to determine specific between-group differences.

Two cautions, however. First, unless you have something on the order of 200 deaths you will be at risk of overfitting. You typically need about 10-20 events per predictor, and each of your groups beyond the first counts as a separate predictor.

Second, if you don't have some specific comparisons among groups in mind to start you will be faced with a major problem in correcting for multiple comparisons.

Depending on the goals of your study, you might instead consider a mixed-effect Cox model, for example with the coxme package in R, treating the groups as random effects. That would provide an estimate of the overall variability in outcomes associated with different groups, potentially working better with fewer events while still providing useful information.

EdM
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    Make sure that the groups are really groups. A good example of a grouping variable is country of origin. A bad example is groups created out of cross-classification and dichotomization of underlying variables. And how can it be the case that covariate adjustment is not needed? Did all the groups have equal opportunity for events, e.g. is the mean age of subjects the same across groups? – Frank Harrell Nov 14 '20 at 12:47
  • Thank you for the good answers. Just due to curiosity, is the log-rank test also suitable for this task? Or the number of comparison groups is limited in log-rank test? – st4co4 Jan 31 '21 at 19:09
  • @st4co4 the log-rank test is for comparing [two groups](https://en.wikipedia.org/wiki/Logrank_test). I suppose you could do all (15*14/2) or 105 pairwise comparisons between groups, but you would need stringent control for multiple comparisons. The score test in the Cox model can be considered an extension of the log-rank test to multiple groups. Most important, however, heed the warnings in the comment from Frank Harrell, and "make sure that the groups are really groups." – EdM Jan 31 '21 at 19:40