Wednesday, September 26, 2007

Dueling with anideulafungin

Our letter to the editor of the NEJM regarding the anidulafungin article (described in a blog post in July - see below) was published today and can be seen at: .

To say the least, I am disappointed in the authors' response, particularly in regards to the non-inferiority and superiority issues.

The "two-step" process they describe for sequential determination of non-inferiority followed by superiority is simply the way that a non-inferiority trial is conducted. Superiority is declared in a non-inferiority trial if the CI of the point estimate does not include zero. (See .

The "debate" among statisticians that they refer to is not really a debate at all, but relates to the distinction between a non-inferiority trial and an equivalence trial - in the latter, the CI of the point estimate must not include negative delta; in this case that would mean the 95% CI would have to fall so far to the left of zero that it did not include minus 20, or the pre-specified margin of non-inferiority. Obviously, the choice of a non-inferiority trial rather than an equivalence trial makes it easier to declare superiority. And this choice can create, as it did in this case, an apparent contradiction that the authors try to gloss over by restating the definition of superiority they chose when designing the trial.

Here is the contradiction, the violation of logic. The drug is declared superior because the 95% CI does not cross zero, but of course, that 95% CI is derived from a point estimate, in this case 15.4%. So, 15.4% is sufficient for the drug to be superior. But if your very design implied that a difference less than 20% is clinically negligible (a requirement for the rational determination of a delta, a prespecified margin of non-inferiority), aren't you obliged by reason and fairness to qualify the declaration of superiority by saying something like "but, we think that a 15.4% difference is clinically negligible?"

There is no rule that states that you must qualify it in this way, but I think it's only fair. Perhaps we, the medical community, should create a rule - namely that you cannot claim superiority in a non-inferiority trial, only in an equivalence trial. This would prevent the industry from getting one of the "free lunches" they currently get when they conduct these trials, and the apparent contradictions that sometimes arise from them.

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