# Backward selection in a Cox regression model

My goal is to fit a cox regression model in SAS, for which I use the PROC PHREG statement. As I am still new to regression methods, I would appreciate a little of your help. My procedure is as follows:

First, I check all variables in a univariate regression and select those, which have a p-value less than 0.25. The next step is that these significant variables (p-value < 0.25) are considered in a model with backward selection. Variables with a p-value less than 0.167 (according to the AIC criterion) are removed from the model. The reduced model should then include the best explanatory variables.

My question now is, whether I can find out, why one variable is removed in the backward selection or which variable rather explains the influence? I am surprised, that this variable drops out, although it is very significant in the univariate regression. Furthermore, I have deleted a variable from the backward selection, as this one is removed later anyway, and see, my "problem variable" remains in the model. How does this work?

• In addition to Peter's excellent answer, univariate screening has been shown to convert a really terrible stepwise variable selection algorithm into a total disaster. How did you get the idea that building models based on $P$-values is statistically valid? – Frank Harrell Mar 28 '13 at 12:21