Transcript Sample Size Estimation - LSUHSC School of Public Health

Sample Size Considerations
A Carefully Planned Study is Crucial for Success
An Important Aspect of Most Studies:
Proper Sample Size Determination
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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Biostatistics
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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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Biostatistics
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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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Biostatistics
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Components of Sample Size
Sample size estimation should incorporate:
– clinical or scientific effects of interest
– Precision (error variance)
– study design
LSU-HSC School of Public Health
Biostatistics
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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
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.
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.
Sample Size Example
Specifying the hypothesis test on the mean:
H o : t  s
vs
H A : t  s
Sample Size Example
Specifying a significance level:
 = 0.05 or 5%
(Type I error rate)
Sample Size Example
Specifying a clinically meaningful difference:
t  s
Sample Size Example
Effect size:
t   s

Where  is the common standard deviation
between groups
Sample Size Example
Obtaining estimates of parameters (historical or pilot data)
Test
Standard
4
10
8
9
7
5
5
9
7
8
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
Sample Size Considerations
Specifying a value of Power:
80% or 90%
Sample Size Considerations
Sample size per group for comparing means of
two groups:
variability   error rates 

n
2
 expected difference 
2
Sample Size Considerations
Sample size per group for comparing means of
two groups:
2


 2   z1  z1 
2
2



 2
 , where  2  1
2
n
2
2
 1  2 
2
Sample Size Considerations
Sample size per group for comparing means of
two groups (80% Power):
2*1.78  1.96  0.84

n
2
8.2  6.8
2
2
n  25.44, choose n  26
Sample Size Considerations
Sample size per group for comparing means of
two groups (90% Power):
2*1.78  1.96  1.28

n
2
8.2  6.8
2
2
n  33.93, choose n  34
Sample Size Considerations
Two group t-test of equal means (equal n's)
Power
Test significance level
1 or 2 sided test?
Difference in means
Common std deviation
Effect size
n per group
80%
0.05
2
1.4
1.78
1.07
26
90%
0.05
2
1.4
1.78
1.07
34
Sample Size for Equivalence Trials
One-sided equivalence testing
• Non-inferiority
Is test drug at least as good as the std?
H 0 :  T   S   vs H1 :  T   S  
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 CI’s.
• If equivalence limit  is contained in both.
Sample Size for Equivalence Trials
n2
Z


 Z    1 1   1    2 1   2  
2
   1   2  
2

Sample Size for Survival
• Sample sizes based on hazard rates
• =1/2
Parametric Models
• Exponential
• Weibull
Non-parametric
Sample Size for Survival
Parametric Models
Z

D  2n  4

 Z 
2
log()
Non-parametric
(result in slightly larger
sample sizes)
2
 Z  Z      1
2
D  2n  4
   1
2
2
Sample Size for Survival
Unbalanced treatment allocation
 r  1   Z  Z  
n

2
 r   log()
2
Account for Accrual
Accrual models can be
incorporated into
sample size projections.
Poisson distribution can
be used as distribution
for accrual times.
n
Z

 Z 
2
T log    
2