I would like to learn more about how unbalanced binary predictors affect type I or type II error in regression models. I am aware that having unbalanced binary outcomes can increase type II error.
I am using regression to test for an association between a binary predictor and continuous outcome. I am also testing if a binary predictor (ex. drug treatment yes/no) is associated with other binary predictors (ex. disease status yes/no). The regression model has sex, age, body mass index as covariates and then 1 binary predictor; I am iterating through each binary variable as predictors. So far I am using a case:control ratio of 1:2 for binary outcomes and the minimum sample size requirement is 200. I am not using over- or under-sampling techniques.
So should I also have my binary predictors have the case:control ratio of 1:2? I have looked at this and this thread but they focus on the situation when the unbalanced data is the outcome and not the predictor variable. I also read this list of assumptions on binary logistic regression from a university online resource and it does not touch upon unbalanced classes in the predictor data set.
I appreciate everyone's help!