Issues in Sample Size Determination

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					          Issues in sample size

• Sample size formulas depend on
  – Study design
  – Outcome measure
     •   Dichotomous
     •   Ordered
     •   Continuous
     •   Time to event (survival)
          Issues in sample size
• 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

               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
• 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
• 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
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
  – 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
 Other things to do when sample
    size is too large (cont’d)
• Become a multi-center study
    Other Issues-Compliance and
• Noncompliance - subjects don’t follow protocol
  exactly (usually take less meds, do less exercise,
• 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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