Confidence Interval for a Rate Difference
Similar to the other measures of association covered so far, the 95% confidence interval for the rate difference can be calculated to provide us with a range of plausible rate differences based on our sample. Like the risk difference, the rate difference is normally distributed, so we can calculate the confidence interval for the rate difference directly and do not need to transform it to the log-scale.
The formula for the 95% Confidence Interval for the rate difference is as follows:
Rate Difference + [1.96 x SE(Rate Difference)]
Let's walk through this formula step-by-step, using the smoking and lung cancer data as an example.
- Step 1: Calculate the standard error of the rate difference:
- Step 2: Calculate the lower and upper confidence bounds
-The lower bound of the 95% confidence interval of the rate difference is:
- The upper bound of the 95% confidence interval of the rate difference is:
- Step 3: Report and interpret the estimate and the confidence interval.
Post-menopausal women who received HRT had 62 fewer cases of coronary artery disease per 100,000 person-years compared to post-menopausal women who did not receive hormone replacement therapy. Based on this sample, we are 95% confident that the true risk difference lies between 97 and 27 fewer cases of coronary artery disease per 100,000 person-years among post-menopausal women who received HRT compared to those who did not.
As a rule of thumb, you should use the following wording when interpreting the 95% confidence interval for the rate difference. "Based on this sample, we are 95% confident that the true rate difference lies between [lower bound] and [upper bound] excess/fewer cases of [disease] per [number] person-years."