I have a question regarding a translation in odds ratio curve OR(x). More specifically, let's say we have an OR(x) which we get using logistic regression. We look at the interval bounded with 25% and 75% percentiles of the variable X and denote the value of interval with X25-75. For further interpretation of the odds ratio we want to have OR(X25-75) = 1, however in our case we get X50 = 1.02. So my question is: how do we translate the odds ratio curve to get the OR(X25-75) = 1? In other words: How do we get the OR estimates for different percentile intervals?
See for example table 4 from this paper or table 2 from this paper.
