1. Sample Size Considerations
A Carefully Planned Study is Crucial for Success
An Important Aspect of Most Studies:
Proper Sample Size Determination

2. 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
LSU-HSC School of Public Health Biostatistics

3. 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
LSU-HSC School of Public Health Biostatistics

4. 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.
LSU-HSC School of Public Health Biostatistics

5. 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

6. 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

7. Comparison of Topical Anesthetics Used in Tooth Restoration
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.

8. 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.

9. Specifying the hypothesis test on the mean: vs
Sample Size Example
Specifying the hypothesis test on the mean: vs

10. Specifying a significance level:  = 0.05 or 5% (Type I error rate)
Sample Size Example
Specifying a significance level:
 = 0.05 or 5%
(Type I error rate)

11. Specifying a clinically meaningful difference:
Sample Size Example
Specifying a clinically meaningful difference:

12. Effect size: Where  is the common standard deviation between groups
Sample Size Example
Effect size:
Where  is the common standard deviation between groups

13. Obtaining estimates of parameters (historical or pilot data)
Sample Size Example
Obtaining estimates of parameters (historical or pilot data)
Test
Standard 4 10 8 9 7 5

14. 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

15. Sample Size Considerations
Specifying a value of Power:
80% or 90%

16. Sample Size Considerations
Sample size per group for comparing means of two groups:

17. Sample Size Considerations
Sample size per group for comparing means of two groups:

18. Sample Size Considerations
Sample size per group for comparing means of two groups (80% Power):

19. Sample Size Considerations
Sample size per group for comparing means of two groups (90% Power):

20. 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

21. Sample Size for Equivalence Trials
One-sided equivalence testing
Non-inferiority
Is test drug at least as good as the std?

22. 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.

23. Sample Size for Equivalence Trials

24. Sample Size for Survival
Sample sizes based on hazard rates
=1/2
Parametric Models
Exponential
Weibull
Non-parametric

25. Sample Size for Survival
Parametric Models
Non-parametric
(result in slightly larger sample sizes)

26. Sample Size for Survival
Unbalanced treatment allocation

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