Biostatistics For Dummies, 2nd Edition (Monika Wahi, John Pezzullo)

CHAPTER 13 Taking a Closer Look at Fourfold Tables 183

Find the limits of the confidence interval with the following formula:

95% CI

to (

OR Q

Like with the risk ratio CI, 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

OR as follows:

1 14

1 7

1 12

1 27

, which is 0.5785.

e^{1.96 0.5785}, which is 3.11.

95% CI

4.50 3.11 to (4.50

3.11), which is 1.45 to 14.0.

Using these calculations, the OR is estimated as 4.5, and the 95 percent CI as 1.45

to 14.0.

To do this operation in R, you would follow the same steps as listed at the end of

the previous section, except in Step 3, the command you’d run on the matrix is

oddsratio.wald() using this code: oddsratio.wald(obese_HTN). The output is laid out

the same way as shown in Listing 13-1, with a $measure section titled odds ratio

with a 95% C.I. In that section, it indicates that the lower and upper confidence

limits are 1.448095 (rounded to 1.45) and 13.98389 (rounded to 13.98), respec-

tively. This time, R’s estimate of the 95 percent CI was close to the one you got

with your manual calculation, but slightly narrower.

A wide 95 percent CI is the sign of an unstable (and not very useful) estimate.

Consider a 95 percent CI for an OR that goes from 1.45 to 14.0. If you are interpret-

ing the results of a cohort study, you are saying that obesity could increase the

odds of getting HTN by as little as 1.45, or as much as 14! Most researchers try to

solve this problem by increasing their sample size to reduce the size of their SE,

which will in turn reduce the width of the CI.

Evaluating diagnostic procedures

Many diagnostic procedures provide a positive or negative test result — such as a

COVID-19 test. Ideally, this result should correspond to the true presence or

absence of the medical condition for which the test was administered — meaning

a positive COVID-19 test should mean you have COVID-19, and a negative test

should mean you do not. The true presence or absence of a medical condition is