I am running a Cox PH Survival analysis to determine if a biomarker is prognostic, predictive, both, or neither.

For a biomarker to be classed as prognostic, then the biomarker term must be significant. For a biomarker to be classed as predictive, the treatment:biomarker interaction term must be significant.

At the moment I'm running two models:

Prognostic model:
survival (1 or 0, with 1 as death) ~ **biomarker**

Predictive model:
survival (1 or 0, with 1 as death) ~ **biomarker** + treatment + biomarker:treatment

My question is - will the effect and hazard ratio for the biomarker alone (in bold) be the same in both models? If not, is it better to chose one model over another?