based on the CI for N. Here’s how you calculate the CI for R:

1. Calculate the confidence interval (CI) for N.

Chapter 11 provides approximate SE and CI formulas based on the normal approximation to the

Poisson distribution (see Chapter 24). These approximations are reasonable when N is large —

meaning N ≥ 50 events:

2. Divide the lower and upper confidence limits for N by the exposure (E).

The answer is the CI for the incidence rate R.

Earlier in the chapter, we describe City ABC, which had a population of 80,000 adults without a

diagnosis of Type II diabetes. In 2023, 24 new diabetes cases were identified in adults in City ABC,

so the event count (N) is 24, and the exposure (E) is 80,000 person-years (because we are counting

80,000 persons for one year). Even though 24 is not that large, let’s use this example to demonstrate

calculating a CI for R. The incidence rate (R) is

, which is 24 per 80,000 person-years, or 30 per

100,000 person-years. How precise is this incidence rate?

To answer this, first, you should find the confidence limits for N. Using the approximate formula, the

95 percent CI around the event count of 24 is

, or 14.4 to 33.6 events.

Next, you divide the lower and upper confidence limits of N by the exposure using these formulas:

14.4/80,000 = 0.00018 for the lower limit, and 33.6/80,000 = 0.00042 for the upper limit. Finally, you

can express these limits as 18.0 to 42.0 events per 100,00 person-years — the CI for the incidence

rate. Your interpretation would be that City ABC’s 2023 incidence rate for Type II diabetes in adults

was 30.0 (95 percent CI 18.0 to 42.0) per 100,000 person-years.

Comparing incidences with the rate ratio

When comparing incidence rates between two populations, you should calculate a rate ratio

(RR) by dividing one incidence rate by the other. So for two groups with event counts

and

,

exposures

and

, and incidence rates

and

, respectively, you calculate the RR for Group

2 relative to Group 1 as a reference, like this:

Let’s revisit the example of 2023 incidence of Type II diabetes in adults in City XYZ compared to City

ABC. For City XYZ, you have N1 = 30 and E1 = 300,000. For City ABC, you have N1 = 24 and E2 =

80,000. The RR for City ABC relative to City XYZ is

, or 3.0,

indicating that City ABC has three times the adult Type II diabetes incidence in 2023 compared to City

XYZ. You could calculate the difference

between two incidence rates if you wanted to, but

in epidemiology, RRs are used much more often than rate differences.

Calculating confidence intervals for a rate ratio

Whenever you report an RR you’ve calculated, you should also indicate how precise it is. The exact

calculation of a CI around RR is quite difficult, but if your observed event counts are large enough