Assuming three variables are exactly related as:
C = A + B
Is it reasonable to run a logistic regression including both C and A as independent variables? If it is reasonable, how would the estimate for each be interpreted?
For example, for some binary outcome, I'd like to estimate the effect of the number of cardiovascular related hospitalizations in the year prior, ("A" in the above equation) controlling for the total number of hospitalizations (any type) in the prior year ("C" in the above equation). "B" in the above equation would be "number of non-cardiovascular related hospitalizations, and would not be included in the model. This model "runs" without error, but I am really struggling with interpretation.
I have also considered categorizing the counts - (e.g. estimating the effect of a three category variable: 0, low, or high number of cardiovascular related hospitalizations, while controlling for 0, low, or high number of overall hospitalizations).