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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. D:\840992600.doc