# Issues in Sample Size Determination

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```					          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
______________________________________________

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
• 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”

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 views: 0 posted: 7/19/2013 language: English pages: 15