p-values in a Cox-Regression model

Question

I have a question regarding the output of a Cox-Model I obtained by stepwise model selection. My model includes now some variables with a p-value below 0.05 and some above 0.05. Since I want to interpret the selected variables with respect to the survival model. Would it be OK, to discuss the variables with p-values < 0.05 and skip the other variables/coefficients with the remark that they are not statistically significant with a threshold of 0.05? My understanding is that if a variable is not statistically significant, I cannot be sure that the hazard ratio is different from 1, in which case it does not have any impact on the hazard to die. Any comment is appreciated. THX

Answer 1

Discuss whatever you like. The lack of an expected effect may well be the most interesting thing about a study. Examine confidence intervals for hazard ratio estimates: can you in fact rule out hazard ratios of practical/theoretical importance or are more data needed? Bear in mind that the standard errors (& hence p-values & confidence intervals) aren't reliable after stepwise selection (see Algorithms for automatic model selection); it'd probably be better to derive the covariance matrix from that of the full model prior to variable selection. And if it was an observational study consider what potential confounders weren't included before making bold statements about variables having or not having an impact on the hazard of death.