I've got a study with 55 patients having undergone surgery. 80% were happy with the surgery while 20% weren't.
I'm looking at predictors that may be able to predict surgery satisfaction.
The problem is the N is low so I'm not sure if I can run a multiple regression model. I thought perhaps changing the study to an association study using ttest and chi2 and just reporting that? Maybe regularization models?
How would you approach such a study statistically?
For biomedical studies, a general rule of thumb to avoid overfitting in an unpenalized logistic regression model is to have on the order of 10-20 minority-class cases per evaluated predictor. You have 11 cases in the minority class, so without penalization should only be evaluating 1 predictor. That predictor would need to be pre-selected based on your knowledge of the subject matter, as using the data to identify the predictor invalidates the assumptions needed to calculate p-values and confidence intervals.
If you did multiple association tests of outcome against each predictor as you propose you would at least have to correct for multiple comparisons and you would not be able to control for the values of the other predictors.
LASSO tends to return a number of predictors similar to the number that would be allowed under the rule of thumb in the first paragraph: so maybe only 1 or 2 in this case.
Logistic ridge regression (L2 penalty) might be the best way to start working with this small data set. All of your predictors would be included in the model, but their coefficients would be heavily penalized to avoid overfitting.
