## Understanding Odds Ratio (OR)

- The Odds Ratio (OR) represents the likelihood of an event occurring in one group compared to another group.
- Specifically, it’s the ratio of the odds of an event happening in the treatment group (a/b) to the odds of the same event happening in the control group (c/d).

**Generic Formula for Odds Ratio**

- The odds ratio can be expressed as:

`Odds Ratio = (a/b)/(c/d) = (a×d)/(b×c)`

## Example Dataset

Let’s consider a medical survey with the following data:

- Treatment group (IV drug users):
- HIV+: a cases
- HIV-: b cases

- Control group (non-drug users):
- HIV+: c cases
- HIV-: d cases

## Calculating Odds Ratio in Excel

- Suppose the data is in cells
**C5**(HIV+ in drug users) through**D6**(HIV- in non-drug users).

- To calculate the odds ratio, enter the following formula in cell
**E5**:

`=(C5/D5)/(C6/D6)`

**Interpretation:**

The result (e.g., **2.14**) indicates that those who are HIV+ are 2.14 times more likely to also be IV drug users than to be non-drug users.

**Read More: **How to Calculate Ratio of 3 Numbers in Excel

## Confidence Intervals (CI) for Odds Ratio

- Confidence intervals provide a range of values within which the true odds ratio likely falls.
- The generic formula for the 95% confidence interval is:

**Confidence Interval = e^(ln(OR)±1.96×√(1/a+1/b+1/c+1/d))**

- To calculate the lower 95% confidence interval, use this formula in cell F5:

`=EXP(LN(E5)-1.96*SQRT(1/C5+1/D5+1/C6+1/D6))`

- For the upper 95% confidence interval, use this formula in cell
**G5**:

`=EXP(LN(E5)+1.96*SQRT(1/C5+1/D5+1/C6+1/D6))`

## Interpreting Results

- Remember that an OR > 1 generally indicates a higher likelihood of the event occurring.
- An OR < 1 suggests the opposite.
- Avoid concluding that
**IV**drug users are**2.14**times more likely to become**HIV+**; instead, interpret it the other way around.

**Download Practice Workbook**

You can download the practice workbook from here:

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