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?
Absolutely. In fact, it is not appropriate to exclude them on the basis of having a small OR alone. Here are some reasons why:
- We build models based on our knowledge and belief about a causal model for an outcome, not based on the data.
- The univariate associations between a predictor and an outcome are nonsense. These must be adjusted for other variables to make any sense.
- 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.
- 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.
- 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).