Notice that the output is organized under the following headings: $data, $measure, $p.value, and

$correction. Under the $measure section is a centered title that says risk ratio with 95% C.I. —

which is more than a hint! Under that is a table with the following column headings: Predictor,

estimate, lower, and upper. The estimate column has the risk ratio estimate (which you already

calculated by hand and rounded off to 2.17). The lower and upper columns have the confidence limits,

which R calculated as 1.09512 (round to 1.10) and 3.938939 (round to 3.94), respectively. You may

notice that because R used a slightly different SE formula than our manual calculation, R’s CI was

slightly wider.

Odds ratio

The odds of an event occurring is the probability of it happening divided by the probability of it not

happening. Assuming you use p to represent a probability, you could write the odds equation this way:

. In a fourfold table, you would represent the odds of the outcome in the exposed as a/b. You

would also represent the odds of the outcome in the unexposed as c/d.

Let’s apply this to the scenario depicted in Figure 13-2. This is a study of 60 individuals, where the

exposure is obesity status (yes/no) and the outcome is HTN status (yes/no). Using the data from Figure

13-2, the odds of having the outcome for exposed participants would be calculated as

, which

would be

, which is 2.00. And the odds of having the outcome in the unexposed participants is

c/d, which would be

, which is 0.444.

Odds have no units. They are not expressed as percentages. See Chapter 3 for a more detailed

discussion of odds.

When considering cross-sectional and cohort studies, the odds ratio (OR) represents the ratio

of the odds of the outcome in the exposed to the odds of the outcome in the unexposed. In case-

control studies, because of the sampling approach, the OR represents the ratio of the odds of

exposure among those with the outcome to the odds of exposure among those without the outcome.

But because any fourfold table has only one OR no matter how you calculate it, the actual value of

the OR stays the same, but how it is described and interpreted depends upon the study design.

Let’s assume that Figure 13-2 presents data on a cross-sectional study, so we will look at the OR from

that perspective. Because you calculate the odds in the exposed as a/b, and the odds in the unexposed

as c/d, the odds ratio is calculated by dividing a/b by b/c like this:

For this example, the OR is

, which is

, which is 4.50. In this sample,

assuming a cross-sectional study, participants who were positive for the exposure had 4.5 times the

odds of also being positive for the outcome compared to participants who were negative for the

exposure. In other words, obese participants had 4.5 times the odds of also having HTN compared to

non-obese participants.

You can calculate an approximate 95 percent CI around the observed OR using the following formulas,

which assume that the logarithm of the OR is normally distributed: