Calculating sample size for a case-control study

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Calculating sample size for a case-control study
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Statistical Power

• Statistical power is the probability of finding
  an effect if its real.

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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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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.

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Calculating sample size for a case-control study
binary exposure

• Use difference in proportions formula

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formula for difference in proportions
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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 (r1)
• The proportion exposed in the control group is 20

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Example, continued

• For 80 power, Z?.84
• For 0.05 significance level, Z?1.96
• r1 (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

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Example, continued

• Therefore, n362 (181 cases, 181 controls)

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Calculating sample size for a case-control study
continuous exposure

• Use difference in means formula

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formula for difference in means
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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 (r1)

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Example, continued

• For 80 power, Z?.84
• For 0.05 significance level, Z?1.96
• r1 (equal number of cases and controls)
• ?10.0
• Difference 5.0

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Example, continued

• Therefore, n126 (63 cases, 63 controls)