Sample Size Determination

Donna McClish

Issues in sample size determination

• Sample size formulas depend on– Study design– Outcome measure

• Dichotomous• Ordered• Continuous• Time to event (survival)

Issues in sample size determination

• Sample size is a function of– Type II error (beta)– Effect size– Type I error (alpha)– Variability of measures

Sample Size Formula(continuous data)

N= 2*(Zalpha + Zbeta )2 ( StandardDeviation)2

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Difference2

Type I error

• Type I error (alpha) is probability of incorrectly rejecting the null hypothesis (finding an association when there really isn’t one)

• Usually set to 5%, Zalpha=1.96

Type II error

• Probability of not rejecting the null hypothesis, when it is true (I.e., probability of missing a true association)

• Power=1-Type II error

• Usually no greater than 20 % (i.e., power is at least 80%) ; Zbeta=1.28 or Zbeta=0.84

Effect size

• Magnitude of the association between predictor and outcome we want to detect

– At least 5 mmHg change in DBP between groups– Difference in proportion of people with controlled BP– Relative risk of at least 2 for a risk factor

Variability of measurement

• The greater the variability in outcome measure, the more likely the values of groups will overlap and the harder it will be to detect differences

Strategies for minimizing sample size

• Decrease Power– Usually can’t make this less than 80%

• Use continuous variables– Detecting differences in means requires

smaller sample size than detecting differences in proportions

• Increase the effect size of interest– Be realistic

Strategies for minimizing sample size (cont’d)

• Decrease variability– Standardize measurement methods– Train and certify observers– Refine the measuring instrument– Switch to a more precise measurement– Automate (avoid human observers, errors)– Use mean of multiple measurements– Enroll from a more homogeneous population

Strategies for minimizing sample size (cont’d)

• Use paired measurements– Change from baseline

• Use a matched design– Pair matching– Crossover design (self matching)

• Use a more common outcome– E.g. all cause mortality instead of a specific

cause

Strategies for minimizing sample size (cont’d)

• Extend the follow up period– Sample size is related to number of events;

this give more time for outcome to occur

• Enroll subjects at higher risk of having the outcome– Increases the number of outcomes that occur– Decreases generalizability

Other things to do when sample size is too large

• Unequal group size – Increases total sample size required– May be easier or less expensive to enroll

certain types of patients• Multiple controls for each case• People more willing to participate if they are more

likely to receive treatment• More people in group receiving less expensive

intervention

Other things to do when sample size is too large (cont’d)

• Become a multi-center study

Other Issues-Compliance and Dropout

• Noncompliance - subjects don’t follow protocol exactly (usually take less meds, do less exercise, etc)

• Contamination – subjects in one group are exposed to the treatment in the other group (usually control group is exposed to the treatment)

• Both noncompliance and contamination result in decreased effect sizes by making comparison groups look more similar

Other Issues - Dropout

• Not all subjects complete the study and provide final outcome information

• Reduces sample size for analysis

• Biases comparisons– In clinical trial, groups are no longer “random”