Fractional odds are the ratio of the amount (profit) won to the stake;Odds ratio can be calculated either with odds of exposure or odds of outcome In casecontrol design, you would only know odds of exposure like you described In a different design, ratio of odds of outcome is the way to go These are the same mathematically which can be seen by playing with the 2 x 2 table Relative risk, risk ratio, orThis brings us to today's topic Odds Ratio (OR) vs Relative Risk (RR) Odds vs Probability why we love them and why these two cousin statistics continue to confuse us Anyone with a math, science, or medical background has been taught this, and if
Converting An Odds Ratio To A Range Of Plausible Relative Risks For Better Communication Of Research Findings The Bmj