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Calculating sample size for a case-control study






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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 .
Calculating sample size for a case-control study

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Calculating sample size for a case control study l.jpgSlide 1

Calculating sample size for a case-control study

Statistical power l.jpgSlide 2

Statistical Power

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

Factors affecting power l.jpgSlide 3

Factors Affecting Power

1. Size of the effect

2. Standard deviation of the characteristic

3. Bigger sample size

4. Significance level desired

Sample size calculations l.jpgSlide 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.

Calculating sample size for a case control study binary exposure l.jpgSlide 5

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

  • Use difference in proportions formula…

Formula for difference in proportions l.jpgSlide 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

Example l.jpgSlide 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%

Example continued l.jpgSlide 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

Example continued9 l.jpgSlide 9

Example, continued…

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

Calculating sample size for a case control study continuous exposure l.jpgSlide 10

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

  • Use difference in means formula…

Formula for difference in means l.jpgSlide 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

Example12 l.jpgSlide 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)

Example continued13 l.jpgSlide 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

Example continued14 l.jpgSlide 14

Example, continued…

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


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