Sample Sizes Considerations Joy C MacDermid

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

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

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

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

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

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.

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

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

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

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

Special cases Repeated measures Unequal groups Affect of covariates

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

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