Cox regression and covariate selection



When selecting covariates to adjust for baseline confounding, such as sex and age, in a Cox regression, do we evaluate change in estimate for each covariate to decide whether to include in the model as we would in logistic regression?

Thanks much!


As explained in detail in my book Regression Modeling Strategies, it is not good statistical practice to “play” with the model. There are many reasons for this, including

  • the judgement of how big a “change” is arbitrary
  • this procedure will result in biased (low) estimates of standard errors of the parameter estimates

My recommendation is to pre-specify the model and to include all the pre-specified covariates no matter how insignificant they are.

I assume you have an observational study.


yes, it’s an observational study. i agree i would normally select covariates based on literature review and biological relevance and then draw a DAG. just wanted to make sure i am not missing anything.

many thanks!


I guess another reason not to use change-in-estimates is that it cannot distinguish between confounders and mediators, right?


You don’t need to think that deeply. Just use that fact that the change-in-estimates method is not based on any statistical principles and it ruins estimates of uncertainty. It also suggests that parsimony is a good thing. I suggest never using it.