My dataset has many biomarkers and the boxplots of these variables show the presence of many outliers. However, these 'outliers' are real data and not misread observations. I want to use elastic net logistic regression to see the association of these biomarkers with a binary outcome. Because my sample size is small and some biomarkers are correlated, I need some regularization. However, I'm not sure if the presence of outliers is a problem for elastic net logistic regressions (I assume it's going to affect the fit adversely because the estimation is still likelihood based). I could only find an R package called enetLTS that does a robust version of the elastic net regression.
I'd like to know if it's better to use this technique or there are other methods that I didn't find. Is there a package that can help identify the outliers and influential observations appropriately so that I can remove those and rerun the regression (if that is suggested at all)? I have found a link that shows sometimes fitting a GLM with the selected variables fails to identify the outliers.