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Statistics Support. Journal Club. Tuesday 30 March 2010
Haybittle-Peto stopping rule
Often an interim analysis take place to identify early if there is clear evidence of benefit or harm of the
intervention. If a clear difference were visible, it may be unethical to continue a trial. The Haybittle-Peto
stopping rule states the trial should be stopped if there is a very significant difference p<0.001 at interim
analysis. The threshold is lower than the conventional p<0.05 to avoid a Type I error.
Null hypothesis
The null hypothesis states that the results observed in a study are no different from what might have
occurred as a result of chance or randomness.
Alternative hypothesis
The alternative hypothesis is the opposite of the null hypothesis. It states that any observed effect in a study
is real and not the result of chance or randomness.
You decide to…
Reject the null hypothesis
(test is statistically significant)
Not reject the null hypothesis
(test is not statistically significant)
The null hypothesis is actually…
True
False
Incorrect
Correct
Correct
Incorrect
Type I error
Declaring a difference (between the study and control group) which doesn’t exist. The probability of a type I
error is denoted by the greek letter α (alpha) and is the same as the p value. Therefore p<0.05 means that
there is a 0.05 or 5% probability of declaring a difference which doesn’t exist. α is the same as the false
positive rate.
Type II error
Declaring no difference (between the study and control group) when there really is a difference. The
probability of a type II error is denoted by the greek letter β (beta). β is the same as the false negative rate.
There is a trade-off between type I and type II errors. If you reduce your threshold for a type I error, then you
may be more likely to make a type II error instead and vice versa. This is analogous to sensitivity and
specificity of a test.
Power
The power of a statistical test is the probability that it will reject the null hypothesis when the alternative
hypothesis is true. This is the opposite of a type II error; it is the probability of correctly declaring a difference
(between the study and control group). Power is often denoted as 1- β. 80% is the usual level set for power.
Probabilities of different outcomes
Test statistically significant
Null hypothesis is true
Alternative hypothesis is true
Yes
No
Type I error (α)
Power (1- β)
Type II error (β)
Sample size calculation
1. Agree type I error rate threshold (α) usually <0.05.
2. Agree Power. Usually 80%.
3. Predict anticipated standard deviation of outcome measure. This may be based on previous studies.
4. Anticipate effect size. Researchers must consider an effect that would make the treatment worthwhile
and tailor the study to this, or the study may just prove an effect that is too small to be useful clinically.
These components are combined statistically to calculate an appropriate size for the study group.
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