198 PART 4 Comparing Groups

Estimating the Required Sample Size

As in all sample-size calculations, you need to specify the desired statistical power

and the α level of the test. Let’s set power to 80 percent and α to 0.05, as these are

common settings. When comparing event rates (R1 and R2) between two groups

with R1 as the reference group, you must also specify:»

» ^{The expected rate in the reference group (R}1^)»

» ^{The effect size of importance, expressed as the rate ratio RR}

R

R

2

1

/»

» ^{The expected ratio of exposure in the two groups E}

E

2

1

/

For example, suppose that you’re designing a study to test whether rotavirus gas-

troenteritis has a higher incidence in City XYZ compared to City ABC. You’ll enroll

an equal number City XYZ and City ABC residents, and follow them for one year to

see whether they get rotavirus. Suppose that the one-year incidence of rotavirus

in City XYZ is 1 case per 100 person-years (an incidence rate of 0.01 case per

patient-year, or 1 percent per year). You want to have an 80 percent likelihood of

getting a statistically significant result assuming p = 0.05 (you want to set power

at 80 percent and α = 0.05). When comparing the incidence rates, you are only

concerned if they differ by more than 25 percent, which translates to a RR of 1.25.

This means you expect to see 0.01 × 1.25 = 0.0125 cases per patient-year in City ABC.

If you want to use G*Power to do your power calculation (see Chapter 4), under

Test family, choose z tests for population-level tests. Under Statistical test, choose

Proportions: Difference between two independent proportions because the two rates are

independent. Under Type of power analysis, choose A priori: Compute required

sample size – given α, power and effect size, and under the Input Parameters section,

choose two tails so you can test if one is higher or lower than the other. Set Propor-

tion p1 to 0.01 (to represent City XYZ’s incidence rate), Proportion p2 to 0.0125 (to

represent City ABC’s expected incidence rate), α err prob (α) to 0.05, and Power

(1-β err prob) (power) to 0.8 for 80 percent, and keep a balanced Allocation ration

N2/N1 of 1. After clicking Calculate, you’ll see you need at least 27,937 person-

years of observation in each group, meaning observing 57,000 participants over a

one-year study. The shockingly large target sample size illustrates a challenge

when studying incidence rates of rare illnesses.