2025 – PAGE 393 – 394 – STATISTICS
ODDS RATIO (OR)
Case control studies are typically used to study factors associated with rare events and diseases. Suppose that the actual risk of Reye syndrome in children exposed to aspirin is 1 in 10,000. In order to quantify that risk and compare it with the risk in unexposed children, we would need to follow 50,000 exposed children to find just 5 cases, clearly a difficult challenge. To overcome this problem, a case-control study starts by identifying a set of cases (e.g., of Reye Syndrome) and a set of comparable controls (e.g., without Reye Syndrome). The study then looks at the exposures in the two groups to see if the exposures can be blamed for the outcome. Here’s an example of a Case Control Study:
| Reye Syndrome | No Reye Syndrome | |
| Exposed | 4 | 3 |
| Not Exposed | 45 | 91 |
| TOTAL | 49 | 94 |
In the example above, there were 49 cases of Reye syndrome, of which 4 were exposed to aspirin. The ratio of exposed to non-exposed cases (4/45) is the odds of exposure in patients with the disease. The odds of exposure in the control subjects was 3/91. The odds ratio is (odds in cases)/(odds in controls) or, in this example, (4/45)/(3/91) = 2.7.
The general formula is:
What makes the odds ratio often easy to interpret is that when the disease is rare, the odds ratio is effectively equal to the relative risk. Thus, we can get a good idea of how exposure affects risk even when we do not know the absolute magnitude of the risks themselves.
PEARL: If you have a case-control study, then the results will generally be reported as an OR. If you have to do the calculation, it does not matter whether you divide the rows or columns first: (4/3)/(45/91) = (4/45)/(3/91).
CROSS-SECTIONAL STUDIES
Cross-sectional studies look at a population, or a representative subset, at one specific point in time in order to describe the relationship between a disease and other factors. They can provide data on prevalence of a disease, or possibly can be used to support inferences of cause and effect. For example, if it was found that the presence of active smoking correlated with lung disease, that would support the hypothesis that smoking may cause lung disease. These studies often use data already collected for other purposes (like a census) and are thus inexpensive but are NOT useful for rare conditions. Recall bias can also be a weakness. Cross-sectional studies are considered descriptive studies and lack any information on timing of exposure or outcome. This type of study is also most likely to yield valid information about the accuracy of a diagnostic test.
CASE STUDIES
Case studies look at individual cases in an effort to identify additional clinical questions surrounding rare diseases or events. An obvious weakness is that they only provide evidence for a single case, or a small number of cases.