Proportional Hazard fit with changing significance by reducing indepedent variables

Question

Hello,

I am still wondering about; when I create a proportional fit model with n independent variables - and then subsequently delete the non-significant one in a stepwise approach - my logrank or significance for the residual independent variables change as well.

Like in my example to an extreme - where I first tested n variables - then reduced it to 2 by deleting the non-significant ones - leaving weight and age, which appear highly signifikant -  but if I delete one or the other - the other remaining, as singular independent variable is not significant any more ?

Could you kindly explain this ? - And is it now significant or not ?

Many thanks, Marc

dale_lehman · Accepted Answer

You will probably get more sophisticated ideas from others in this forum, but I will offer a few insights.  Clearly the model with both weight and age is far superior to the one with weight alone (look at the fit diagnostics).  So, the lack of significance for weight alone appears to mean that weight is a noisy predictor unless you also account for age.  Once age is accounted for, it is clear that weight matters - I suspect if you examine the relationship between weight and age you will find some rationale for these results.  Having said that, I don't think it is so meaningful to focus on the presence or lack of statistical significance - what matters more is that the inclusion of both variables provides a much more informative model.  It appears that weight reduces survival risk while age increases it.  The fact that weight alone does not appear to influence survival time probably reflects the likely fact that weight increases with age (so that without accounting for age, it appears that weight is not systematically related to survival).