Sample Size Considerations

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Sample Size Considerations

• A Carefully Planned Study is Crucial for Success
• An Important Aspect of Most Studies
• Proper Sample Size Determination

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Sample Size Study Goals

• Sample size estimation (SSE) should be related
  to the goals of the experiment.
• It should not be too small or too big

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Sample Size Study Goals

• Too small a study
• Scientifically - Cannot detect clinically
  important effects
• Economically - waste resources without capability
  of producing useful results.
• Ethically Expose subjects to potentially harmful
  treatments without advancing knowledge

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Sample Size Study Goals

• Too large a study
• Scientifically - demonstrate scientifically
  (clinically) irrelevant, but statistically
  significant effects.
• Economically - waste resources by using more than
  necessary.
• Ethically Expose unnecessary number of subjects
  to potentially harmful treatments or subjects
  denied potentially beneficial ones.

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Components of Sample Size

• Sample size estimation should incorporate
• clinical or scientific effects of interest
• Precision (error variance)
• study design

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Sample Size Considerations

• Power approach to sample estimation
• - Specifying the hypothesis
• - Specifying a significance level
• - Specifying an effect size or clinical
  difference
• - Obtaining estimates of parameters (historical
  or pilot data)
• - Specifying a value of power

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Sample Size Example

• Comparison of Topical Anesthetics
• Used in Tooth Restoration
•  
• A two-group parallel randomized double-blind
  study is planned in patients undergoing dental
  restoration.
• Each patient will be randomly assigned to receive
  either a new topical anesthetic or the standard
  topical anesthetic before dental restoration.

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Sample Size Example

• The sample sizes in each group will be equal.
• The primary outcome measure will be the number of
  minutes until complete numbness is achieved,
  which will be compared between the two groups.
• The research hypothesis is that the mean time to
  numbness in the restoration area will be
  significantly different for the two anesthetic
  groups.

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Sample Size Example

• Specifying the hypothesis test on the mean
• vs

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Sample Size Example

• Specifying a significance level
• ? 0.05 or 5
• (Type I error rate)

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Sample Size Example

• Specifying a clinically meaningful difference

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Sample Size Example

• Effect size
• Where ? is the common standard deviation between
  groups

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Sample Size Example

• Obtaining estimates of parameters (historical or
  pilot data)

Test Standard
4 10
8 9
7 5
5 9
7 8
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Sample Size Example

• From Pilot Data we obtain estimates
• Test Group
• Mean 6.8 minutes
• S.D. 1.64
• n 5
• Standard Group
• Mean 8.2 minutes
• S.D. 1.92
• n 5

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Sample Size Considerations

• Specifying a value of Power
• 80 or 90

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Sample Size Considerations

• Sample size per group for comparing means of two
  groups

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Sample Size Considerations

• Sample size per group for comparing means of two
  groups

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Sample Size Considerations

• Sample size per group for comparing means of two
  groups (80 Power)

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Sample Size Considerations

• Sample size per group for comparing means of two
  groups (90 Power)

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Sample Size Considerations

• Two group t-test of equal means (equal n's)
• Power 80 90
• Test significance level 0.05 0.05
• 1 or 2 sided test? 2 2
• Difference in means 1.4 1.4
• Common std deviation 1.78 1.78
• Effect size 1.07 1.07
• n per group 26 34

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Sample Size for Equivalence Trials

• One-sided equivalence testing
• Non-inferiority
• Is test drug at least as good as the std?

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Sample Size for Equivalence Trials

• Two-sided equivalence testing
• Bio-equivalence testing
• Is test drug neither better nor worse than the
  std?
• Usually carried out as two-one-side CIs.
• If equivalence limit ? is contained in both.

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Sample Size for Equivalence Trials
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Sample Size for Survival

• Sample sizes based on hazard rates
• ??1/?2
• Parametric Models
• Exponential
• Weibull
• Non-parametric

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Sample Size for Survival

• Parametric Models
• Non-parametric
• (result in slightly larger sample sizes)

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Sample Size for Survival

• Unbalanced treatment allocation

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Account for Accrual

• Accrual models can be incorporated into sample
  size projections.
• Poisson distribution can be used as distribution
  for accrual times.

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