overfitting in univariable Cox model

I have seen an analysis where the predictive abiity of a number of predictors is each assessed individually by a univariable Cox PH model and the "AUC" reported (presumably Harrell's c-statistic, I will check). The model fitting and AUC calculation are performed on the same entire data set. Is this OK ? Overfitting is an issue when multivariate models are built and a correcion for optimism (test/training, crossvalidation or bootstrapping) a must. But even a single coefficient from a univariable model is overfitted in the sense of fine tuned to the data set its estimated from and will therefore predict that same data set better than new data.


Not a robit
It all depends on the purpose of the analyses and unfortunately sample sizes at times. Running a bunch of bivariate analyses, as you described, is typically frowned upon, since if there is collinearity or covariate interactions, etc. you won't know. Keep the questions coming if this didn't address your question.

To create generalizable results, the best use case scenario is the training, validating, and testing of models.