## OPTION 11

Sample size requirements for "proving" the null hypothesis

Ref:

- Blackwelder W C, "Proving the null hypothesis" in Clinical Trials, Controlled Clinical Trials 3: 395-353 (1982)
- Makuch R and Simon R,: Sample size requirements for evaluating a conservative therapy, Cancer Treat Rep 62: 1037-1040 (1978)

When designing a clinical trial to show whether a new or experimental therapy is as effective as a standard therapy (but not necessarily more effective), the usual null hypothesis of equality is inappropriate and leads to logical difficulties. Since therapies cannot be shown to be literally equivalent, the appropriate null hypothesis is that the experimental therapy is not less effective than the standard therapy by some tolerable amount. This type of hypothesis test is appropriate when the new therapy is desirable for other reasons than increasing the response rate of the subjects; the new treatment may be less toxic, less expensive or easier to administer. Hence the question is whether the new treatment is as effective as the standard - not, as in most studies, whether the new treatment is better.

When testing the null hypothesis of a specified difference, the roles of the Type I error and Type II error are reversed from the case of testing the usual null hypothesis. A type I error is now made if we conclude that the difference is greater than delta, i.e. we choose the experimental therapy when the standard is substantially better. We make a Type II error if we conclude that the difference is greater than delta when it is actually less than delta, i.e. we retain the standard therapy when the new experimental therapy is just as good.

This program accommodates either a dichotomous (binomial) or continuous (normal) response variable and computes any of the following:

- Required sample size - equal or unequal
- Maximum tolerable difference in response rates (or means)
- Power of the experiment
- One-sided alpha level for the confidence limit

when given the other three.

Of course, the immediate extension to unmatched case-referrent or cohort studies using binary incidence or exposure variables is obvious.