INTRODUCTION
The odds ratio (OR) is a measure of association or relationship, and compares the odds of disease or an event in those exposed to the odds of disease or an event in the unexposed group.1 Other measures of association are relative risk ratio, hazard risk, mean difference, et cetera. Odds ratios are related to the probability of a binary or categorical outcome (an outcome that is either present or absent) but not exactly related to the probability of events. Relative risk ratio is the ratio of the probabilities of outcome in both exposed and unexposed.2
Odds Ratio (OR) has also been defined as a numeric expression of the strength of the association between cause and an effect when both are expressed as categorical variables. In clinical medicine, odds ratios can be used to present the strength of association between risk factors and outcomes where the null value is 1.
There is a difference between probability and odds. Probability is the likelihood of an event happening. However, the odds of an event represent the ratio of the probability that the event will occur and probability that the event will not occur for a given exposure/risk factor. Odds Ratio (OR) serves to determine the relationship between exposure and outcome of an event. While odds can be calculated for any event, odds ratio is always with reference to two different outcomes e.g. (cases and controls, alive or dead, et cetera). The OR can be used to evaluate whether the odds of an event are same for two groups in a study sample. The OR measures the ratio of the odds that an outcome will occur given a particular exposure or event to the odds of the outcome occurring in the absence of the exposure or event3, 4. When the probability is small, odds are virtually identical to the probability and will be small2. The smaller the OR, the lesser the effect on the outcome, and the converse is true for a larger OR1.
For example, if the probability of developing bladder cancer in a chimney worker is 0.20 (20%), then the probability that the event will not occur is 1– 0.20 = 0.80, or 80%. The odds of a chimney worker developing bladder cancer is 0.2/0.8 = 0.25. Same probability and odds for developing bladder cancer can be calculated for a group of workers not exposed to chimney smoke. A comparison of the odds of developing bladder cancer in both groups is termed odds ratio.
Clinicians and researchers are usually interested in knowing probabilities, level of association and relationship between two or more variables, whereas gamblers think in terms of odds. Odds are useful when betting because they represent fair payouts or cash outs. If one were to bet $100 on winning a match, a payout of $300 is necessary to have an even chance of winning your money back. From the gambler’s perspective, a payout smaller than $300 is unfavorable and greater than $300 is favorable. Similarly, odds with a minus sign (like -$100) indicate that you must risk more than you will win. In OR, a negative value suggests a protective effect on the intervention compared to the control. A gambler has a fallacy that a certain random event is less or more likely to occur based on previous results. However, OR is more finite, the probability that an event will occur is the fraction of times you expect to see that event in many trials3. The OR can also be a measure of the effect size. Formula for calculating OR = (odds of disease in exposed)/ (odds of disease in the unexposed).
Most odds ratio calculations are set up as two by two tables. Therefore, the preferred significance statistic is the Maximum Likelihood Ratio Chi-Square. However, in some instances the Fisher’s Exact Probability statistics or Pearson’s Chi-Square can also be used.5