I have the following data: Predictor X: positive count data (range 0 to 43), in this case the number of symptoms present out of a total of 43. Outcome Y: binary
I want to test, whether (or to what extend) the predictor (i.e. the number of symptoms present) is associated with the binary outcome in a logistic regression.
The predictor variable obviously is not normal and it is zero-inflated.
If I treat X as a linear predictor, I feel I would lose information as I won't be able to discriminate between the lower values of X (which are most of them). Larger values (higher number of symptoms) possibly are due to reporting bias rather than due to a much worse symptomatology. From a clinical perspective it would make sense to give more weight to 1 point increases in the lower end than in the upper end.
How do I incorporate this information into my regression model? How should I transform the X variable for this type of data?
Thank you for your help.