Slide 1 Calculating sample size for a case-control study

Slide 2 ### Statistical Power

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

Slide 3 ### Factors Affecting Power

1. Size of the effect

2. Standard deviation of the characteristic

3. Bigger sample size

4. Significance level desired

Slide 4 ### 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.

Slide 5 ### Calculating sample size for a case-control study: binary exposure

- Use difference in proportions formula…

Slide 6 Represents the desired 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

Slide 7 ### 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%

Slide 8 ### Example, continued…

- 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

Slide 9 ### Example, continued…

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

Slide 10 ### Calculating sample size for a case-control study: continuous exposure

- Use difference in means formula…

Slide 11 Sample size 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

Slide 12 ### 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)

Slide 13 ### 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

Slide 14 ### Example, continued…

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