I have two groups of patients, let’s say groups A and B, who have the same disease with a well-known genetic cause. My main goal is to see whether there is a difference in survivals by the type of underlying mutation (x and y) in all patients. The sample sizes are ~55:145 for A:B and when I estimate survivals by the group variable, group A has a better survival with log-rank p<0.05. I don’t know what might cause this difference. It may be due to selection bias and possibly some other factors. In this case, would it be appropriate to “pool” these 2 groups with different survivals and compare survivals by gene (x/y) variable in A+B? How would you approach this question? Thank you!
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$\begingroup$ Have you tried the stratified logrank test? stratified by group A or B. $\endgroup$– John LCommented Feb 11, 2021 at 16:55
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You shouldn't put too much weight on survival models with just one or a few predictors, which is what you do with a simple log-rank test or a stratified log-rank test (as recommended in a comment). There is clearly some substantial association of Group with survival, which also leads to a question whether the association of genotype with outcome will differ between Group A and Group B. Unless you investigate those issues you run a risk of missing something important.
To address those issues it's best to use a survival model that includes as many predictors reasonably related to outcome as possible without overfitting. That helps deal with correlations among predictors, effects of some predictors that depend on the values of others, and a general bias in Cox models when you omit any predictor associated with outcome, similar to the case with logistic regression. A rule of thumb is that you can include 1 predictor for every 10-20 events without too much risk of overfitting. So if you have about 50% survival in your 200 cases you should be able to evaluate 5-10 predictors.
With that in mind, I'd start with a survival model on all of your data, and include the Group membership as a predictor along with the genotype and other clinical variables that might be expected to be associated with survival. You could include interactions between Group and other predictors (in particular, genotype) if you suspect that the associations of the other predictors with outcome depend on a patient's Group membership.
