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I am running an analysis of various factors that determine whether an individual is likely to have an event. My outcome is binary (0 vs 1), and my explicative variables can be both quantitative or categorical. I also have a list of covariates known to be related to the dependent variable.

I'm unsure whether I should:

  • Perform a univariable logistic regression analysis for each explicative variable (without covariates), then use the significant ones (0.05 or Bonferroni-adjusted p-value?) in my final cox regression model;
  • Perform a univariable logistic regression analysis for each explicative variable adjusted for covariates (ex. age and sex), then use the significant ones (0.05 or Bonferroni-adjusted p-values?) in my final cox regression model; or
  • Use a backward stepwise regression model, then use the significant predictors (0.05 or Bonferroni-adjusted p-value?) in my final cox regression model?

By Bonferroni-adjusted, I mean adjusted for the total number of predictors.

I would be very grateful if you could help me with the process, and give me some explanations or references to better understand.

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    $\begingroup$ Where does Cox regression come from (there is no mention of any time-to-event endpoint)? What do you mean by univariate logistic regression without covariates? Or by univariate logistic regression adjusted for covariates? I am afraid your question needs clarification. Note that variable selection using univariate methods or by significance testing is usually not a good idea. $\endgroup$
    – ocram
    Commented Feb 3, 2022 at 9:33
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    $\begingroup$ Besides delineating Cox and logistic regression, not that multivariate does not apply here (hence my correction in the post title) because multivariate refers to having multiple dependent variables. This is a multivariable problem. And as @ocram said, stepwise variable selection is a very bad idea. Use subject matter knowledge and pre-specify your model. Stick to it, and don't remove "insignificant" variables. See here. $\endgroup$ Commented Feb 3, 2022 at 12:50

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