Sample Size Considerations

A Carefully Planned Study is Crucial for Success

An Important Aspect of Most Studies:

Proper Sample Size Determination

LSU-HSC School of Public Health Biostatistics

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

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:

vs

:o t sH

:A t sH

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:

Where is the common standard deviation between groups

t s

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 minutesS.D. = 1.64n = 5

Standard Group: Mean = 8.2 minutes

S.D. = 1.92n = 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:

2

2

variability error rates

expected differencen

Sample Size Considerations

Sample size per group for comparing means of two groups:

2

21 2 21

2 2 1 22

1 2

2

, where 2

z z

n

Sample Size Considerations

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

22

2

2*1.78 1.96 0.84

8.2 6.8n

25.44, choose 26n n

Sample Size Considerations

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

22

2

2*1.78 1.96 1.28

8.2 6.8n

33.93, choose 34n n

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

Sample Size for Equivalence TrialsOne-sided equivalence testing

• Non-inferiority

Is test drug at least as good as the std?

0 1: vs :T S T SH H

Sample Size for Equivalence TrialsTwo-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

2

1 1 2 2

2 2

1 2

1 1Z Zn

Sample Size for Survival

• Sample sizes based on hazard rates

=1/2

Parametric Models• Exponential• Weibull

Non-parametric

Sample Size for Survival

Parametric Models

Non-parametric

(result in slightly larger sample sizes)

2

22 4log( )

Z ZD n

2 2

2

12 4

1

Z ZD n

Sample Size for Survival

Unbalanced treatment allocation

2

2

1

log( )

Z Zrn

r

Account for Accrual

Accrual models can be incorporated into sample size projections.

Poisson distribution can be used as distribution for accrual times.

2

2log

Z Zn

T