When the number of events is too low compared to the number of adjustment variables, we consider a possible overfitting. An approximate rule to avoid overfitting is to have at least 10 events per covariate whether for a logistic (Peduzzi et al. 1996) or a Cox (Peduzzi et al. 1995) model.
Covariates on the pathway
A confounder must be a cause of exposure. The adjustement on a consequence of the exposure would result in under-estimating the true causal effect of exposure.