From the Guidelines
To count an odds ratio, you need to organize your data in a 2x2 contingency table with exposure and outcome variables, and then calculate the odds ratio by dividing the odds of the outcome in the exposed group by the odds of the outcome in the unexposed group, using the formula OR = (a×d)/(b×c) 1. When calculating the odds ratio, it is essential to understand that it represents the odds of an outcome according to an explanatory variable, such as aspirin users versus non-users 1.
Key Steps to Calculate Odds Ratio
- Label your cells as a (exposed with outcome), b (exposed without outcome), c (unexposed with outcome), and d (unexposed without outcome)
- Calculate the odds ratio by dividing the odds of the outcome in the exposed group by the odds of the outcome in the unexposed group
- Use the formula OR = (a/b)/(c/d), which simplifies to OR = (a×d)/(b×c) For example, if 15 out of 25 exposed people have the outcome (a=15, b=10) and 5 out of 25 unexposed people have the outcome (c=5, d=20), the odds ratio would be (15×20)/(10×5) = 300/50 = 6, as described in the context of case-control studies and logistic regression analysis 1.
Interpreting Odds Ratio
- Values above 1 indicate increased odds with exposure
- Values below 1 suggest decreased odds
- An OR of 1 means the two practices are equally successful (no difference in reducing risk with respect to the outcome evaluated) 1
From the Research
Counting Odds Ratio
To count the odds ratio, we need to understand what it represents. The odds ratio is a measure of association between an exposure and an outcome.
- It represents the ratio of the odds of an event occurring in one group versus another group.
- The odds ratio can be calculated using the following formula: OR = (a/b) / (c/d), where a and b are the number of events and non-events in the exposed group, and c and d are the number of events and non-events in the non-exposed group.
Example from Studies
For example, in the study 2, the odds ratio for the risk of coronary artery disease (CAD) after COVID-19 vaccination was 1.70 (95% CrI: 1.11-2.57). This means that the odds of CAD were 1.70 times higher in the vaccinated group compared to the unvaccinated group.
- The study also found that the odds ratio for CAD after the second dose of the vaccine was 3.44 (95% CrI: 1.99-5.98), indicating a higher risk of CAD after the second dose.
- In contrast, the study found a protective effect on stroke (OR, 0.19; 95% CrI: 0.10-0.39) and myocardial infarction (OR, 0.003; 95% CrI: 0.001-0.006) after the third dose of the vaccine.
Calculation
The calculation of the odds ratio involves the use of a 2x2 contingency table, where the number of events and non-events are compared between the exposed and non-exposed groups.
- The odds ratio can be calculated using the formula: OR = (a/b) / (c/d), where a, b, c, and d are the cells in the 2x2 contingency table.
- The odds ratio can also be calculated using logistic regression analysis, which takes into account other covariates that may affect the association between the exposure and outcome.
Limitations
It's worth noting that the odds ratio has some limitations, such as it can be affected by the prevalence of the outcome in the population, and it can be difficult to interpret in terms of absolute risk.
- The odds ratio should be interpreted in the context of the study design, population, and outcome being measured.
- The confidence interval for the odds ratio should also be considered, as it provides a range of possible values for the true odds ratio.