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 MeansSample size required per group • N=(Z alpha + Z beta )2 standard deviation2 Important difference2 Z alpha usually 1.96; z beta usually 0.80

11. Difference in ProportionsSample 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