Understanding odds ratios
The odds ratio (OR) is the ratio of the odds of an event occurring in the exposed group to the odds in the unexposed group. An OR of 1 indicates no association. An OR greater than 1 suggests increased odds with exposure; less than 1 suggests decreased odds.
Odds ratios are particularly useful in case-control studies where direct risk calculation is not possible. The 95% confidence interval is computed using the Woolf (log) method. If the CI does not include 1, the association is statistically significant at the 5% level.
OR = (a × d) / (b × c)
Odds ratio from a 2x2 table: cross-product ratio of the four cells.
ln(OR) ± 1.96 × √(1/a + 1/b + 1/c + 1/d)
95% confidence interval using the Woolf method on the log scale.