Sample sizes

Question 1

What is the standardised effect size/how is it calculated?

Answer 1

Δ = δ/σ
δ = the observed effect i.e. difference between two population means (assumed 0 under null hypothesis)
σ = standard deviation, assumed to be the same between the two groups

Question 2

How is the sample size calculated for normally distributed continuous data, comparing two means?

Answer 2

n(per groups) = 2σ^2(z(1-α/2)+z(1-β)^2/δ^2

The standard deviation and effect size are the planned values

Question 3

How is sample size calculated with a 5% significance and 80% power (simple formula)?

Answer 3

n(per group) = 16 (σ^2/δ^2) = 16/Δ^2
Planning values used

Change to 21 for 90% power

Question 4

How does sample size change with smaller value of α (e.g. 0.01 instead of 0.05)

Answer 4

Increases

Question 5

How does sample size change with a smaller value of β (larger power)?

Answer 5

Increases

Question 6

How does sample size change with a smaller planned effect size?

Answer 6

Increases

Question 7

How does sample size change with a smaller planned standard deviation?

Answer 7

Decreases

Question 8

How is effect size calculated for binary outcome data?

Answer 8

planned effect size = π1-π2

Where π1-π2 is the anticipated difference in proportions?

Question 9

How is sample size calculated for binary outcome data?

Answer 9

n(per group) = [π1(1-π1)+π2(1-π2)](z(1-α/2)+z(1-β)^2/δ^2

Question 10

Methods for calculating sample size with an unknown standard deviation?

Answer 10

1. Use first patients from trial to estimate SD –> sample size
2. Estimate SD by a relatively small pilot investigation (20-40 per group), then use this value
3. Specify the difference of interest directly in terms of unknown SD

Question 11

How can the SD be calculated from the estimated treatment difference/95% CI?

Answer 11

Upper limit - Lower limit = 4xSE
SE = s/√n
–> SD=(SE(d)x√n)/√2

Question 12

How is the sample size calculated for a prevalence study?

Answer 12

SE(p) = √p(1-p)/N
SEplan = Upper limit - lower limit (CI)/2x1.96
πplan used in place of p
N = πplan(1-πplan)/SE^2plan

Question 13

What are the four key ingredients for a sample size calculation for a two group RCT?

Answer 13

1. Type I error
2. Type II error
3. The variability of the outcome
4. The anticipated or target effect size