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I have a group over about 500 subjects and want to perform a cox-regression to find predictors of an event taking into account the time to event. I have 12 potential predicting variables that I want to test. If there exist couple of collinear variable, I will remove one of those 2 variables. Beside this criterion, what is the best strategy to select the variables to include in the multiple model and why?

  • Is there a limit in the ratio $r = \frac{n_{variables}}{n_{subjects}}$ not to overcome?
  • Is it correct to first run a simple model for each of the 12 variables and then choose the variable with a p-value <0.10 to include in the multiple model?
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I think the answer to this question is generic. You pick the ones that theory supports or you have strong substantive reason to believe should be in the model.

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