I'm aware that Logistic Regression works in odds, not probabilities. More specifically, it reports the variables in how they increase or decrease the odds. That makes sense, but when I think about it more, I'm wondering do probabilities really work like this in real life examples?
So if there is a variable with a large coefficient (say smoking for cancer), does it really only increase the probability of a cancer from 1 to 1.5% for people with low probability but 50 to 60% for mid-probability (see table below)? It just doesn't sit right.
I'm finding logistic regression tricky to present to business stakeholders because of this. When asked how certain variables change the probability, the answer that it depends on the underlying probability doesn't seem very satisfying.
If anyone could help clarify things that would be great!
odds p odds (50% increase) new p 0.01010101 0.01 0.015151515 0.014925373 0.176470588 0.15 0.264705882 0.209302326 0.428571429 0.3 0.642857143 0.391304348 1 0.5 1.5 0.6 2.333333333 0.7 3.5 0.777777778 5.666666667 0.85 8.5 0.894736842 99 0.99 148.5 0.993311037