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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?

Thank you for your thoughts!

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Backward selection is not a good method of variable selection, this has been discussed here many times. Combining it with univariate screening can only make it worse.

However, one reason for the behavior you describe is that the two variables are correlated.

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  • $\begingroup$ 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? $\endgroup$ – Frank Harrell Mar 28 '13 at 12:21

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