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I am using logistic regression for a binary outcome. When building a multivariate model, is including insignificant univariate variables with OR >0.5 and <1.5 appropriate? And why?

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Absolutely. In fact, it is not appropriate to exclude them on the basis of having a small OR alone. Here are some reasons why:

  1. We build models based on our knowledge and belief about a causal model for an outcome, not based on the data.
  2. The univariate associations between a predictor and an outcome are nonsense. These must be adjusted for other variables to make any sense.
  3. The types of adjustment variables needed to assess the relationship between a stratifying variable and an outcome are likely not available, and they are not part of the central hypothesis.
  4. We adjust for variables because they are prognostic or because they are confounders. It is possible that in a multivariate model, strong prognostic or confounding variables do not ultimately show a large OR in the final model.
  5. The OR depends on the scale of the variable which is relative.

Lastly, as a note. An odds ratio of 0.5 is 1/2. It's positive valued counterpart is 2.0 (2/1) not 1.5 (3/2).

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