calculating sample size for a case-control study
TRANSCRIPT
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