I am fitting two kinds of models:
- Situation 1: the outcome is a ratio of multiple variables ((x_1 + x_2) / (x_3 + x_4)). In this situation, I am following the advice I found here of taking the logarithm and include an additional term corresponding to the logarithm of the denominator of the outcome.
- Situation 2: the exposure is a ratio of multiple variables. In this case I tought about including the exposure as \alpha \times log(exposure), although this would mean that the relation with the outcome is the same for both the numerator and the denominator. Since I believe the association with the outcome might differ, I thought about directly modeling the exposure as \alpha_1log(numerator) - \alpha_2log(denominator).
Is my reasoning correct?