Suppose I have a dataset where 100 patients have the disease (e.g. information such as height, smoking, weight, age, disease status) and 10000 patients do not have the disease (i.e. class imbalance).
I am interested in using Logistic Regression to try and understand what patient characteristics appear to influence the odds of having the disease or not. As such, there are significantly more patients without the disease compared to those who do not.
I fear that fitting a Logistic Regression on the entire dataset might partly invalidate the results as patients without the disease will have more influence in the model estimates. To potentially mitigate this problem, I am thinking of using Propensity Score Matching to select 100 patients who do not have the disease - in a way such that we only select patients without the disease so that they have an "approximate analog" in the disease set. As a result, I will have a dataset with only 200 patients and the the ratio of disease to non-disease will be balanced.
I had the following question: By using this Propensity Score Matching approach, I will end up discarding lots of information corresponding to the non-diseased patients and a result might be forfeiting large amounts of valuable information that might be beneficial to the model. However, by including this information, I fear that I risk "flooding" the model with too much information corresponding to the "non-diseased patients" and suppressing information belonging to the diseased patients.
In general - can Propensity Score Matching be used to mitigate problems/biases associated with class imbalance when fitting regression models to such types of problems?