I want to compare several logistic regression models. The different models are built using the same initial dataset. The models differ with respect to the explanatory variables included.

Many of the explanatory variables, however, have missing values. When estimating a model, I remove the observations for which one of the explanatory variables is NA. As a result, since observations will remain or be removed depending on the explanatory variables selected, the datasets used to estimate the different models are different. The datasets' size vary from around 150 observations to 500 observations depending on the combination of explanatory variables chosen.

Given the potential large difference in data size I do not solely compare models anymore which seems undesirable.

Would imputation here be advised such that I compare the models? Are there any other strategies I could follow?