Sample size estimation Flashcards
Why use sample size calculations
Required by ethical committees
• Required by grant giving bodies and funding
agencies.
• Required by CONSORT in checklist for writing
up papers.
• Forms part of ‘quality assessment’ for metaanalysis.
Why not use sample size
calculations
Rarely enough information for precise calculations.
• Very sensitive to assumptions.
• Based on only one outcome/endpoint.
• Main criteria are usually availability of patients,
finance, resources and time.
Statistical reasons for sample size
calculation
The results of any study are subject to the
possibility of error.
• The purpose of the sample size calculation is
to reduce the risk of errors due to chance to a
level we will accept
No impact on bias or cofounding though
Why is there a difference in
Type I and Type II error rates?
Conventionally a minimum power of 0.80 is required.
• So the Type I error, α, (of 0.05) is less than the Type II
error, β, (of 0.20).
• Why this difference in error rates?
• The simple answer is that researchers are innately
conservative.
Sample sizes for comparison of
two independent groups
If the outcome is assumed to be Normally
distributed, then the best summary statistic for the
data is the sample mean, and the difference in
means between the two groups is an appropriate
comparative summary measure.
• The usual hypothesis test for a difference in mean
population parameters between two independent
samples is the two-sample t test
Standardised effect size equation
effect size/SD
comparing 2 measures formula
SD2(z1-a/2+z1-b)/effect size
z1-α/2 and z1-β are values from the standard Normal distribution
To get them you would use the table in the folder
simple equation
For the situation where we want a 5% significance
level and 80% power, the sample size formula can be
approximated with:
16(SD plan/effect sizeplan)
For 90% power and 5% (two-sided) significance the
numerator is changed from 16 to 21.
Sample size ingredients
Ingredients for determining sample size for a two group
superiority RCT with a continuous outcome are:
1. The target or anticipated effect size δPlan = μPlan,T – μPlan,C ,
which is the size of the planned difference between the two
treatments.
• This is usually, but not always, the smallest difference or
minimum important difference (MID) that is considered
clinically or practically important
2.The variability or standard deviation (SD) of the outcome
measure, σPlan, usually assumed the same in the test and
control groups.
- Power (typically 80% or 90%) or (1 - probability of a Type II
error (β)). - The significance (α) level of the statistical test (typically 0.05
or 0.01) to be used in the analysis (the probability of a Type I
error).
Sample size formula for Continuous
data
N per group=
2SD2plan (Z1-a/2+z1-b2)/ effectsize 2
what happens if the sample size goes up
- Goes up for smaller α (sig level
- Goes up for smaller β (i.e. larger power)
- Goes up for smaller δPlan (EFFECT SIZE)
what happens if the sample size goes down
Goes down for smaller SD
Sample size formula for
Binary outcome data
At the planning stage we need to specify the planned or
anticipated difference in proportions- p1-p2
equlation
n per group= [p1(1-p1) +p2(1-p2) (Z1-a/2+Z1-b)2/ effect size2
what do you do if Unknown Standard Deviation
If no estimate of the SD is available there are several
approaches:
1. Start the trial and use the data for the first patients to
estimate the SD and then the sample size needed.
2. Estimate the SD by a relatively small pilot investigation,
with 20 to 40 subjects per group, and then use this value.
3. Specify the difference of interest directly in terms of the
unknown SD.
Tips on obtaining the unknown SD
Often papers only give an estimate of the treatment effect
with a 95% CI.
• We need the standard deviation, s.
• If we let U be upper limit of CI and L be lower limit of the 95%
CI.
• U - L is about 4 times the standard error, SE.
• Use the fact that 𝑆
