Principles of sample size calculation - The EQUATOR Network
[Pages:21]Principles of sample size calculation
Jonathan Cook (with thanks to Doug Altman)
Centre for Statistics in Medicine, NDORMS, University of Oxford
EQUATOR ? OUCAGS training course 24 October 2015
Outline
Principles of study design Principles of study sample size calculation How to determine the sample size How to calculate in practice Summary
2
Study design ? general principles
Play of change could mislead
? The more subtle a question the more precise we need to be evaluation (i.e. more information that is more data)
We need to be clear about our question
? What exactly are we interested in? ? How precisely we want to know it?
Study (including sample size) should be fit for purpose
? Relevant ? Sufficient for the intended analysis
3
Study size ? how big?
Fundamental aspect of study design ? How many participants are needed?
Ethically and scientifically important ? legitimate experimentation ? Add to knowledge
Impact upon study conduct (e.g. 100 versus 2000) ? Management of project ? Timeframe ? Cost
4
Principles of sample size calculation
Aim
? We wish to compare the outcome between the treatments and determine if there is a difference between them
Typically approach for RCT sample size calculation
? Choose the key (primary) outcome and base the calculation on it ? Get a large enough sample size to have reassurance that we will be
able to detect a meaningful difference in the primary outcome
Main alternative approach
? Seek to estimate a quantity with a given precision
Same principles apply to all types of study
? What we are looking for may well differ
5
Reaching the wrong conclusion (1)
What can go wrong: May conclude that there is a difference in outcome
between active and control groups, when in fact no such difference exists Technically called a Type I error
? more usefully called a false-positive result
Probability of making such an error is designated , commonly known as the significance level
Risk of false-positive conclusion (Type I error) does not decrease as the sample size increases
6
Reaching the wrong conclusion (2)
May conclude that there is no evidence of a difference in outcomes between active and control groups, when in fact there is such a difference
Technically called a Type II error
? more usefully called a false-negative result
Probability of making such an error is often designated as (1- is commonly known as the statistical power)
Risk of missing an important difference (Type II error) decreases as the sample size increases
7
Type I and Type II errors
There really is a There really is difference no difference
Statistically significant
OK
Type I error
(false positive)
Statistically Type II error
OK
non-significant (false negative/
[1-power])
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