I am fitting a logistic regression with multiple binary variables as well as a single continuous variable (AGE) for which I have a linear and a quadratic term.
$$\log\frac P{1-P} = \text{constant} + a \cdot \text{AGE} + b \cdot \text{AGE}^2 + c \cdot\text{GENDER} + d \cdot\text{PREGNANCY} + \cdots$$
For any of the binary variables, it is custom to report their "odds ratio" (OR). For example, the OR for GENDER is
OR_GENDER = exp(c)
However, for AGE (which is continuous and has a non-linear effect), it is less clear what is the proper way to report an overall odds ratio.
What I am currently doing is reporting the ratio between the maximum and the minimum of the odds as a function of AGE within the range of ages in our data (0
OR_AGE = exp( max(a * AGE + b * AGE^2) - min(a * AGE + b * AGE^2) )
where the min and max are evaluated within the range 0-100 and so may appear either at the extreme points 0, or 100, or in the middle if the function has extremum within this range.
My questions are:
Is this method of reporting OR for non-linear variable ok and proper to do?
If so, is there a name for this procedure / or a reference I can cite?
If not, what would be a proper way to report overall ORs for AGE that can be compared on equal footings with those of GENDER, PREGNANCY and others?