Firstly, some background on the dataset:
I am performing survival analysis on a 28-event dataset. We found a genetic marker that predicts survival on a drug. Examining the data, the proportional hazards assumption appears to be met. I want to perform Cox regression with the goal of identifying potential confounders.
The issue is that with a 28-event dataset, I can't really fit more than 2 independent variables at a time to the data without risking overfitting. My approach has been to fit each potential confounder in turn together with my variable of interest (the genetic marker) and observe the impact on the regression.
My question is whether this is a valid approach for determining whether these other independent variables are confounders or not. Is there anything fundamentally wrong with this "pairwise" approach - aside from not being able to catch confounders which may have an impact on the regression together but not apart?