How to interpret and compare models in Cox regression?

#1
Hallo,

I am trying to interpret the results of a Cox regression; I am doing a PhD in medicine. I love statistics but my question is still pretty basic, I think, and I did not find an answer in previous threads.

I have to compare different models (just a couple of predictors in each; predictors are different, but sometimes the same predictor appears in different models; say, A+B, A+C, A+D, B+C) toward the same time-to-event variable.

How do I choose the “best” model? I am studying the underlying statistical principles, but I still don’t get whether I have to look at
- Which model has the highest log likelihood;
- Which model has the best p-value of the likelihood ratio test (LR chi2);
- Which model has all p-values of the HR coefficients (beta’s) of the covariates significant;
- Or any combination of the above (for instance, only consider the models where both the LR and the beta-coefficients of all covariates are significant, and among them choose the one with the highest log likelihood).

I understand that the significance of the LR and the significance of the beta-coefficients test different things, but still I need to select the model with, say, the “best predictive ability” or the “strongest association”.
I am using Stata.

Thank you in advance for your help!
Luca