CHAPTER 14 Analyzing Incidence and Prevalence Rates in Epidemiologic Data 195

Random fluctuations in R are attributed entirely to fluctuations in the event

count (N). We are assuming the exposure (described earlier in this chapter as the

person-time in the denominator, abbreviated as E) is known exactly — or at least,

much more precisely than N. Therefore, the CI for the event rate is 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 approxima-

tions are reasonable when N is large — meaning N ≥ 50 events:

95

1 96

1 96

%

.

.

CI =

to

N

N

N

N

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 N E

/ , 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

24

1 96 24

24

.

to 24 +1.96

, 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 inci-

dence 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 N1 and N 2, exposures E1 and E2, and incidence rates R1 and R2, respec-

tively, you calculate the RR for Group 2 relative to Group 1 as a reference, like this:

RR

R

R

N

E

N

E

2

1

2

2

1

1

/

/