196 PART 4 Comparing Groups
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
RR
24 80 000
30 300 000
/
/
/
,
,
, 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 R
R
2
1 between two incidence rates if you wanted to, but in epi-
demiology, 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 pre-
cise it is. The exact calculation of a CI around RR is quite difficult, but if your
observed event counts are large enough (meaning ≥ 10), then the following
approximate formula for the 95 percent CI around an RR works reasonably well:
95% CI
/
to
RR Q
RR
Q where Q
e
N
N
1 96 1
1
1
2
.
/
/
.
For other confidence levels, you can replace the 1.96 in the Q formula with the
appropriate critical z value for the normal distribution.
So, for the 2023 adult Type II diabetes example, you would setN
N
1
2
30
24
,
, and
RR = 3.0. The equation would be Q
e1 96 1 24
1 30
.
/
/
, so the 95 percent lower and
upper confidence limits would be 3 0 1 71
.
.
/
and 3 0
1 71
.
.
, meaning the CI of the RR
would be from 1.75 to 5.13. You would interpret this by saying that that 2023 RR for
adult Type II diabetes incidence is 3.0 times the rate in City ABC compared to City
XYZ (95 percent CI 1.75 to 5.13).
Comparing two event rates
The examples in this chapter have compared incidence (or event) rates of adult
Type II diabetes in 2023 between City XYZ and City ABC. These two event rates are
represented as R1for City XYZ, andR2 for City ABC. They are based on City XYZ hav-
ing an N1 of 30 events and City ABC having an N 2 of 24 events, and on exposures
E1 and E2 for City XYZ and City ABC, respectively. The difference in event rates
between City XYZ and City ABC can be tested for significance by calculating the
95 percent CI around the RR, and observing whether that CI includes the value
of 1.0. Because the RR is a ratio, having 1.0 included in the CI indicates that
City XYZ’s and City ABC’s rates could be identical. If the 95 percent CI around the