182 PART 4 Comparing Groups

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

viduals, 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 a b

/

, which would be 14 7

/ , which

is 2.00. And the odds of having the outcome in the unexposed participants is c/d,

which would be 12 27

/

, 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) repre-

sents the ratio of the odds of the outcome in the exposed to the odds of the out-

come 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 four-

fold 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 divid-

ing a/b by b/c like this: OR

a b

c

d

/

/

/

.

For this example, the OR is (

/ ) / (

/

)

14 7

12 27 , which is 2 00 0 444

.

/ .

, 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 com-

pared 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:

1.

Calculate the standard error of the log of the OR with the following

formula:

SE

a

b

c

d

1

1

1

1

/

/

/

/

2.

Calculate Q with the following formula: Q

e^{1.96 SE}, 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.