On 1/18/2012 10:05 AM, Marsh Roy wrote:
> This question was posed to me by a public health information analyst
> the other day "Can you work out NNT in a non-inferiority trial?' I
> think not. Because the finding is equivalence. So you can't do it
> (can you?) But I have come across trials that call themselves
> 'non-inferiority' but clearly show superiority, at least for some
> outcomes. And work out NNT for those outcomes (though not for the
> equivalent outcomes). Presumably the trials had to demonstrate that
> they were powered enough to detect superiority ... and then went and
> found it (even though that wasn't the actual aim)? Why call
> themselves 'non-inferiority' anyway, if they have to be as powerful
> as 'normal' trials? What does 'non-inferiority' add to my
> understanding of a trial? example: Diggle L, Deeks JJ, Pollard AJ.
> Effect of needle size on immunogenicity and reactogenicity of
> vaccines in infants: randomisedcontrolled trial. BMJ 2006;333:571.
> http://www.bmj.com/content/333/7568/571
Let's think about this a bit. Suppose the new therapy had an absolute
risk reduction ARR of 20% and the 95% confidence interval (CI) went from
10% to 30%. Then the NNT is 5 and the CI is 10 to 3.3. Normally we'd
reverse this, of course and say the CI is from 3.3 to 10.
Now suppose that the ARR is -20% (implying that the control treatment is
superior) and the CI is -30% to -10%. Then your value is a NNH since
your new therapy is doing more harm than good. Bear with me on this,
because we don't usually talk about NNH in this context. The NNH is 5
and the CI is 3.3 to 10.
Now let's suppose that the ARR is 20% but the CI goes from -10% to 50%.
The NNT is 5, but now you have two confidence intervals. You are 95%
confident that the NNT is more than 2 (1/0.5) and you are also 95%
confident that the NNH is more than 10 (1/0.1).
Some people will talk about the interval including infinity, and that's
a fine way to present it. But the point is that if your confidence
interval contains zero (as it is likely to do in a non-inferiority
study), then you have bounds on how much better the new therapy might be
(NNT is between 2 and infinity) and you have bounds on how much worse
the new therapy might be (NNH is between 10 and infinity).
I would argue that the bound on NNH is the more critical one in a
non-inferiority study. If you can argue that the savings in cost, the
greater tolerability of the drug, the fewer side effects, etc. are
valuable enough that we would be willing to tolerate one fewer cure
among every 10 patients, then the CI on NNH establishes non-inferiority.
In fact, I would argue that the NNH is the only logical way to set an
non-inferiority margin. Look at the benefits of switching relative to
the benefits of seeing a cure. If the cure is "worth" 10 times as much,
then you want a non-inferiority margin which is equivalent to an NNH of
10 or higher.
As far as what you call a study, I think that a study powered to
demonstrate non-inferiority can be taken as evidence of superiority if
you are lucky enough to get a CI for the ARR that has only positive
values. There's some controversy about this, however, and not everyone
would be as liberal as I am on this issue.
Steve Simon, [log in to unmask], Standard Disclaimer.
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