I have an imbalanced data set of 300 observations with an adverse event rate of 8%. I have 4 features that I believe to be relevant based on expertise in the field. I am interested only in inference (not prediction) and assessing potential relevance of one of the features for protection against the adverse event, so I'm using logistic regression which has good interpretability. This is not meant to be a decisive paper since I'm aware of the limitations of the data, merely to elucidate potential for further research into the field.
1) How should these results - positive or negative - be presented in a paper? Do I need more to present more than odds ratios with associated confidence intervals and p-values?
2) Since the event rate is low and sample size relatively small (and thus underpowered logistic regression), is cross-validation applicable? It seemed like it might give misleading results. If I were doing machine learning/prediction, I'd re-sample to balance (oversample or undersample with something like SMOTE), but I'm also not interested at all in accuracy or other metrics like F1, just the parameter estimates.
In general, what are my options for assessing the results of logistic regression given that I am not interested in prediction?