Ratio as independent variable for logistic regression

Question

I am trying to model the association between "previous 2 year history of no shows for consult (independent variable)" with current no shows (dependent variable) using a logistic regression model. The independent variable is measured as:

$\dfrac{number \thinspace of \thinspace missed \thinspace appointments \thinspace * 100 \thinspace }{total \thinspace number \thinspace of \thinspace appointments}$

The dependent variable is binary (Yes/No).

The Odds Ratio we observe = 14.05

The independent variable will be 0% for those who do not miss any appointments.

Questions:

1. What does this odds ratio tell us?

2. Is it ok to use the independent variable as a ratio ?

3. If answer on Question 2 is no, how can we model the independent variable?

Answer 1

This is similar to Ratios in Regression, aka Questions on Kronmal, although the question there is about linear regression. The advice in the linked paper there, which you should have a look at, is to use as regressor variables the numerator, inverse denominator, and their interaction (that is, the ratio). You could at least try that! (and tell us how it went)