calculating sample size for a case-control study

Calculating sample size for a case-control study

Statistical Power Statistical power is the probability

of finding an effect if it’s real.

Factors Affecting Power

1. Size of the effect2. Standard deviation of the

characteristic3. Bigger sample size 4. Significance level desired

Sample size calculations Based on these elements, you can

write a formal mathematical equation that relates power, sample size, effect size, standard deviation, and significance level.

Calculating sample size for a case-control study: binary exposure

Use difference in proportions formula…

formula for difference in proportions

221

2/2

)(p

)Z)(1)(()1

(p

Zpp

r

rn

Sample size in the case group

Represents the desired power (typically .84 for 80% power).

Represents the desired level of statistical significance (typically 1.96).

A measure of variability (similar to standard deviation)

Effect Size (the difference in proportions)

r=ratio of controls to cases

Example How many cases and controls do

you need assuming… 80% power You want to detect an odds ratio of

2.0 or greater An equal number of cases and

controls (r=1) The proportion exposed in the control

group is 20%

Example, continued…

221

2/2

)(p

)Z)(1)(()1

(p

Zpp

r

rn

For 80% power, Z=.84 For 0.05 significance level, Z=1.96 r=1 (equal number of cases and controls) The proportion exposed in the control group is 20% To get proportion of cases exposed:

1)1(exp

expexp

ORp

ORpp

controls

controlscase

33.20.1

40.

1)10.2)(20(.

)20(.0.2exp

casep

Average proportion exposed = (.33+.20)/2=.265

Example, continued…

181)20.33.(

)96.184)(.265.1)(265(.2

2

2

n

221

2/2

)(p

)Z)(1)(()1

(p

Zpp

r

rn

Therefore, n=362 (181 cases, 181 controls)

Calculating sample size for a case-control study: continuous exposure

Use difference in means formula…

formula for difference in means

Sample size in the case group

Represents the desired power (typically .84 for 80% power).

Represents the desired level of statistical significance (typically 1.96).

Standard deviation of the outcome variable

Effect Size (the difference in means)

2

2/2

2

)ifference(

)Z()1

(d

Z

r

rn

r=ratio of controls to cases

Example How many cases and controls do you

need assuming… 80% power The standard deviation of the characteristic

you are comparing is 10.0 You want to detect a difference in your

characteristic of 5.0 (one half standard deviation)

An equal number of cases and controls (r=1)

Example, continued…

For 80% power, Z=.84 For 0.05 significance level, Z=1.96 r=1 (equal number of cases and controls) =10.0 Difference = 5.0

2

2/2

2

)ifference(

)Z()1

(d

Z

r

rn

Example, continued…

Therefore, n=126 (63 cases, 63 controls)

63)84.7(2)2()5(

)84.7(10)2( 2

2

2

n

2

2/2

2

)ifference(

)Z()1

(d

Z

r

rn