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I want to conduct a multivariable cox regression model to assess predictors of "Mortality" variable. Assume there are three independent variable as follows:
Gender --> (dichotomous= 1,2)
Type --> (nominal = "Athlete", "Sedentary", "Normal")
Age --> Continuous

I want first conduct univariable analysis for each variables and then select variables with significant p-vlaue < 0.1 to incorporate into multivariable coxph.

For choosing significant variables in univariable analysis, which one I have to look for:
1- significant level of the var in univar analysis
2- or model significance(wald's test or LR test)
3- or more precisely to say, Both of them!

But how to deal with sometimes inconsistent results, for example significant p value for variable in the model but not for model itself, and vice versa.

Which variables should I include in multivariable analysis based on univariable analysis(based on assumption of p-value < 0.1)

Also for nominal variables with more than two values, how can I choose if some of the values of the variable is significant in comparison to reference value but some not( for example "Sedentary" to "Athlete" is significant but "Normal" to "Athlete" is not.

In this setting, should I look just at Robustness test such as LR test or Wald test to choose variable?

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Univariable screening has terrible performance and should be avoided. It invalidates later parameter estimates and especially their standard errors, so frequentist operating characteristics such as $\alpha$ are distorted. Use subject matter knowledge to fully pre-specify the model. You will know you are doing this correctly when there is at least one "insignificant" parameter in the model. Don't be tempted to remove it. Details and references are in RMS book and course notes.

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