I'm doing a logistic regression with 100 observations (of which 20 events), and a few predictors. One of the (binary) predictors is expected (theoretically) to be a quite strong predictor, but its value is missing for 30 records. By theory, we expect this variable to not be correlated with any of the other predictors, and its missingness to be MCAR. I have identified three possible strategies:
- Do multiple imputation, based only (or mostly) on the outcome as there is no (expected) relationship with the other variables
- Do a descriptive analysis with univariate and multivariate models based on complete data (maybe a model without the variable on the full data and one without on the subset of 70)
- Add a category 'missing' to the variable and perform analyses as usual. This is a quite clean approach but I've read that it can introduce bias even with MCAR
What would be the best approach?