1. Sample Sizes Considerations Joy C MacDermid

2. General Principles Why do we want many subjects? –Generalizability –Power –Subgroup Analysis –Why do we want a minimal number? –Cost –Time

3. What factors affect sample size? Type of measure Variability of measure Power we want to detect differences Risk we are willing to take of falsely declaring a difference where none exists Size of difference that is important

4. Types of Measurements Scale Nominal, Ordinal, Cardinal Range of possible responses The less detail of information in a measurement - the more numbers required to establish trends

5. Variability Variability is “background noise” which obscures our ability to see where true differences exist. The more variable a measurement/trait in a particular sample - the more numbers required to differentiate that the differences observed is true

6. Power Ability to detect a true difference Frequently set at 80% The more powerful you want to be - the more numbers you will need

7. Alpha Error Willingness to falsely declare a difference as real Usually set at 5% i.e. 95% confidence intervals, alpha=0.05 Considered worse to put into place a new treatment that is ineffective (and has side effects) than to miss a potentially useful one.

8. Clinically Important Difference How much will make an important difference? The least amount that you would consider important The smaller you make this - the more subjects you need

9. Choosing an Equation Depends on type of data/study Differences in size of two measurements i.e. means Difference in numbers of subjects- i.e. proportions

10. Difference in Means Sample size required per group N=(Z alpha + Z beta ) 2 standard deviation 2 Important difference 2 Z alpha usually 1.96; z beta usually 0.80

11. Difference in Proportions Sample size required per group N=(Z alpha + Z beta ) 2 [Pe(1-Pe) + Pc(1-Pc)]/ (Pe-Pc) 2 Z alpha usually 1.96; z beta usually 0.80

12. Special cases Repeated measures Unequal groups Affect of covariates

13. Reasons why sample sizes are underestimated Forget to take into account loss to follow-up Effectiveness of treatment of often over-estimated Selection criteria make exclude patients who get most benefit Controls improve - due to attention

14. Suggestions Use outcomes that have more detail Cardinal if possible Proportions - count serious and less serious occurrences Record time to events Use surrogate outcomes i.e. disease present versus death