# Odds Ratio Interpretation and Predicted Probabilities

I am conducting research on the association between smoking and Tuberculosis (TB), and I need to clarify what the odds ratio is telling me. I am getting the Odds Ratio value from the table of a research paper, not directly from a statistical model. So if an Odds Ratio comparing smokers to nonsmoker is equal to 1.5, can I make the following interpretations?

1. The odds of developing TB among smokers is 1.5 that of nonsmokers.
2. The odds of developing TB among smokers is 50 % higher that of nonsmokers.

I think interpretation 1 and 2 are the same, but not sure if one is more suitable than the other. Now the other part of my question relates to "predicted probabilities" from ORs as described in this response https://stats.stackexchange.com/a/18115/208860. Is it possible to get that probability if I just have my OR and its confidence interval?

You cannot recover the predicted probabilities from only the odds ratios. If you have the baseline odds, you could. The baseline odds in your case is the odds of TB for a non-smoker. Say the odds of having TB among non-smokers is $$0.01$$, i.e. we expect to find 1 non-smoker with TB for every 100 non-smokers without TB. Than with your odds ratio, the odds of having TB for smokers is $$1.5\times0.01=0.015$$. To transform odds to odds ratios we use $$p = \frac{o}{1+o}$$, where $$p$$ is the probability and $$o$$ is the odds. So in this case the predicted probabilities are $$\frac{0.01}{1+0.01}\approx 0.0099$$ for non-smokers and $$\frac{0.015}{1+0.015}\approx 0.0148$$ for smokers. This computation was only possible because I had both the baseline odds and the odds ratio.