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# Calculating sample size for a case-control study - PowerPoint PPT Presentation

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 effect 2. Standard deviation of the characteristic 3. Bigger sample size 4. Significance level desired .

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### Calculating sample size for a case-control study

• Statistical power is the probability of finding an effect if it’s real.

1. Size of the effect

2. Standard deviation of the characteristic

3. Bigger sample size

4. Significance level desired

• Based on these elements, you can write a formal mathematical equation that relates power, sample size, effect size, standard deviation, and significance level.

• Use difference in proportions formula…

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

r=ratio of controls to cases

Sample size in the case group

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

A measure of variability (similar to standard deviation)

Effect Size (the difference in proportions)

formula for difference in proportions

Example exposure

• 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… exposure

• 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:

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

Example, continued… exposure

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

• Use difference in means formula…

Sample size exposure in the case group

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

r=ratio of controls to cases

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

Standard deviation of the outcome variable

Effect Size (the difference in means)

formula for difference in means

Example exposure

• 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… exposure

• 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

Example, continued… exposure

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