A brief review of hypothesis testing

We discussed hypothesis testing in some detail in Chapter 6. For present purposes, the role of hypothesis testing in confirmatory clinical trials can be restated simply as follows  

Hypothesis testing provides an objective way to make a decision to proceed as if the drug is either effective or not effective based on the sample data, while also limiting the probability of making either decision in error. 

For a superiority trial the null hypothesis is that the treatment effect is zero. Sponsors of drug trials would like to generate sufficient evidence, in the form of the test statistic, to reject the null hypothesis in favor of the alternate hypothesis, thereby providing compelling evidence that the treatment effect is not zero. The null hypothesis may be rejected if the treatment effect favors the test drug, and also if it favors the placebo (as discussed, we have to acknowledge this possibility). 

The decision to reject the null hypothesis depends on the value of the test statistic relative to the distribution of its values under the null hypothesis. Rejection of the null hypothesis means one of two things  

There really is a difference between the two treatments, that is, the alternate hypothesis is true. 

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