Calculating Confidence Interval and P-Value for Odds Ratio

Understanding Odds Ratio

An odds ratio expresses the relative likelihood of an event occurring in one group compared to another group. It is used to assess the association between two categorical variables. The odds ratio formula is given below:

OR = ab / cd 

where:

* a: Number of individuals with both property A and B * b: Number of individuals with property B but not A * c: Number of individuals with property A but not B * d: Number of individuals with neither property A nor B

Calculating Confidence Interval

The confidence interval for an odds ratio provides a range of values within which the true odds ratio is likely to fall. The 95% confidence interval is calculated using the formula:

CI = exp(log(OR) ± 1.96 * SE) 

where:

* OR: Odds ratio * SE: Standard error of the odds ratio

Calculating P-Value

The p-value is a measure of statistical significance that provides evidence for rejecting the null hypothesis (i.e., there is no association between the two variables). The p-value for an odds ratio is calculated using the chi-square test or Fisher's exact test.

Interpretation

An odds ratio greater than 1 indicates a positive association, while an odds ratio less than 1 indicates a negative association. A narrow confidence interval and a small p-value (<0.05) provide stronger evidence for a significant association.