CHAPTER 13 Taking a Closer Look at Fourfold Tables 179

you would get if you had done a cohort study, so they produce estimates of relative

risk (see Chapter 7).

In a cohort study, the measure of relative risk used is called the risk ratio (also

called cumulative incidence ratio). To calculate the risk ratio, first calculate the

CIR in the exposed, calculate the CIR in the unexposed, then take a ratio of the CIR

in the exposed to the CIR in the unexposed. This formula could be expressed

as: RR

a r

c r

/

/

/

1

2 .

For this example, as calculated earlier, the CIR for the exposed was 0.667, and the

CIR for the unexposed was 0.308. Therefore, the risk-ratio calculation would be

0 667 0 308

.

/ .

, which is 2.17. So, in this cohort study, obese participants were slightly

more than twice as likely to be diagnosed as having HTN during follow-up than

non-obese subjects.

Calculating a risk ratio as a measure of relative risk is appropriate for a cohort

study. However, there are restrictions when creating measures of relative risk for

cross-sectional and case-control designs. In a cross-sectional study, you would

not calculate a CIR in the exposed and the unexposed because the exposure and

outcome are measured at the same time, so there’s no time for any participants to

experience any risk during the study. Instead, you would calculate the prevalence

of the outcome in the exposed — which is a r

/ 1 — and the prevalence of the out-

come in the unexposed — which is c r

/ 2 (read Chapter 14 to for a discussion of

prevalence). Notice that even though we use different wording, these are the same

formulas as for the CIR. Then, instead of a risk ratio, in a cross-sectional study

you would use a prevalence ratio, which is calculated the same way as the risk ratio:

PR = (a/r1)/(c/r2).

In a case-control study, for a measure of relative risk, you must use the odds ratio

(discussed later in the section “Odds ratio”). You cannot use the risk ratio or

prevalence ratio in a case-control study. The odds ratio can also be used as a mea-

sure of relative risk in a cross-sectional study, and can technically be used in a

cohort study, although the preferred measure is the risk ratio.

Let’s go back to discussing the risk ratio. You can calculate an approximate

95 percent confidence interval (CI) around the observed risk ratio using the fol-

lowing formulas, which assume that the logarithm of the risk ratio is normally

distributed:

1.

Calculate the standard error (SE) of the log of risk ratio using the follow-

ing formula:

SE

b

a

r

d

c

r

/ (

)

/ (

)

1

2