I'm comparing three LASSO-regression models for classifying two patient types. Each model has increasingly complex variables, which are less likely to be available. Consequently, the last model has more missing data compared to the first model.
As I understand it, LASSO regression requires non-missing data. Do I need to perform a complete case analysis or can I utilize all available data for each model? Does using all data affect model comparability due to inherent differences in the datasets and increased observations? I am using the AUC as model performance parameter.
I am using R and I am splitting my data into training and test sets and using 10-fold cross validation for the determination of the optimal Lambda value. I thought about imputation already, but my mentor dissuaded me from it.