the unexposed, then take a ratio of the CIR in the exposed to the CIR in the unexposed. This formula

could be expressed as:

.

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

, 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

— and the prevalence of the outcome

in the unexposed — which is

(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 measure 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 following 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 following formula:

2. Calculate Q with the following formula:

where Q is simply a convenient

intermediate quantity that will be used in the next part of the calculation, and e is the

mathematical constant 2.718.

3. Find the lower and upper limits of the CI with the following formula:

For confidence levels other than 95 percent, replace the z-score of 1.96 in Step 2 with the

corresponding z-score shown in Table 10-1 of Chapter 10. As an example, for 90 percent confidence

levels, use 1.64, and for 99 percent confidence levels, use 2.58.

For the example in Figure 13-2, you calculate 95 percent CI around the observed risk ratio as follows: