Assuming that we perform a Cox regression as presented in the example here. I am wondering what we should expect in the output of the Cox regression if, for example, we perform the fit again but this we replace the values of the predictor variable 'ph.karno: Karnofsky performance score (bad=0-good=100) rated by physician' with new values given from a new team of physicians who, for example, have shown that their score is statistically significant in detecting lung cancer by its own.
beta HR (95% CI for HR) wald.test p.value age 0.019 1 (1-1) 4.1 0.042 sex -0.53 0.59 (0.42-0.82) 10 0.0015 ph.karno -0.016 0.98 (0.97-1) 7.9 0.005 ph.ecog 0.48 1.6 (1.3-2) 18 2.7e-05 wt.loss 0.0013 1 (0.99-1) 0.05 0.83
I am wondering what we should expect to change in the coefficients of this and the other covariates (if we can expect something to change apriori) by performing the fit again. E.g. do we expect that this known change in predicting lung cancer on its own will have a specific impact on age, sex etc.?
In a nutshell, I'm interested to know if there is a mathematical connection or empirical proof on the effect of replacing the values of a predictor variable with new values that we already know that are statistically significant in detecting the effect by themselves.