Calculating sample size for a case-control study

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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

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1. Calculating sample size for a case-control study

2. Statistical Power Statistical power is the probability of finding an effect if it?s real. What things are going to help statistical power?What things are going to help statistical power?

3. Factors Affecting Power 1. Size of the effect 2. Standard deviation of the characteristic 3. Bigger sample size 4. Significance level desired It turns out that if you were to go out and sample many, many times, most sample statistics that you could calculate would follow a normal distribution. What are the 2 parameters (from last time) that define any normal distribution? Remember that a normal curve is characterized by two parameters, a mean and a variability (SD) What do you think the mean value of a sample statistic would be? The standard deviation? Remember standard deviation is natural variability of the population Standard error can be standard error of the mean or standard error of the odds ratio or standard error of the difference of 2 means, etc. The standard error of any sample statistic.It turns out that if you were to go out and sample many, many times, most sample statistics that you could calculate would follow a normal distribution. What are the 2 parameters (from last time) that define any normal distribution? Remember that a normal curve is characterized by two parameters, a mean and a variability (SD) What do you think the mean value of a sample statistic would be? The standard deviation? Remember standard deviation is natural variability of the population Standard error can be standard error of the mean or standard error of the odds ratio or standard error of the difference of 2 means, etc. The standard error of any sample statistic.

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.

5. Calculating sample size for a case-control study: binary exposure Use difference in proportions formula?

6. formula for difference in proportions

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%

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:

9. Example, continued?

10. Calculating sample size for a case-control study: continuous exposure Use difference in means formula?

11. formula for difference in means

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)

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

14. Example, continued?


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