Dear all, this is a summary of the replies i got to my question on the 
sample size calculation in non-inferiority trials:

(1)
Hi Ioanna,

You may find this article useful:

Irving K. Hwang & Toshihiko Morikawa, 1999. Design Issues in 
Noninferiority/Equivalence Trials. Drug Information Journal, 33(4): 1205-18.

Cheers,
Kylie.

(2)
Ioanna

I'm surprised there aren't regulatory guidelines on this  (eg the US FDA's
Committee on Veterinary Medicine's Bioequivalence Guidelines, or something 
from the European Agency of Evaluation of Medicinal Products). The trick is 
to find out which authority you are trying to satisfy, and what they want.

Duncan

Duncan Hedderley

Biometrician,
Crop & Food Research,
Palmerston North, New Zealand

(3)
Hi Ioanna,

The source article I have been using recently is the BMJ article by B Jones 
and P Jarvis 1996; 313:36-39.
Not sure if you've seen this but it gives the equations you need for 
equivalence (two-sided) and non-inferiority (one-sided).
Hope that helps,

Martyn.

(4)
I don't think you will find the answer to your question in any text book.  I 
assume that this is for a study which will be submitted to a regulatory 
authority.  If that is true, it is a question of what they will accept.
Mostly, they require a one-sided 0.025 test (which is equivalent to 
calculating the usual two-sided 95% interval).  In some cases (eg the E14 
guideline for QT prolongation studies) they indicate that they will accept a 
one-sided 0.05 test, giving a somewhat smaller sample size.

I hope that helps.  In practice, it usually doesn't make much difference to 
the sample size you get.  Far more crucial is the size of the margin (delta) 
you choose and the assumptions you make about the real effects of the 
treatment.


Dennis
Dr Dennis O. Chanter
Director, Statisfaction Statistical Consultancy Ltd


(5)
Presumably in a non-inferiority trial, you want to show there is no 
difference between the two drugs. If you lower your type 1 error (alpha), 
you're more likely to prove yourself right, cos it will be difficult for you 
to reject (unless your drug is very bad). SO rather than reducing alpha, I'd 
have thought you want to increase your alpha. But I haven't done any 
non-inferiority trial, so I don't know what the common practice is. But keep 
searching cos people have definitely discussed over it.

Tim



(6)
Ioanna Gioni asked for advice about calculating sample-size for a 
non-inferiority trial with Normal data. Specifically, she stated "I am not 
sure if I need to set my type error I (alpha) at half the conventional type 
I error used in two-sided confidence intervals." This would be better asked 
on the MedStats group, http://groups.google.com/group/MedStats, but some 
interest has already been sparked on Allstat.

The regulatory authorities such as the FDA and CHMP usually require the
Type I error in a non-inferiority trial to be 0.025. This corresponds to the 
lower limit of a 95% confidence interval for the difference between the 
means of two arms in a clinical trial being greater than a pre-specified 
tolerance.

Jay Warner asked for a quick guide to the medical stats jargon involved in 
this query, so here's an attempt. I am writing this from memory, which is an 
increasingly faulty storage mechanism in my case, so I may have made slips; 
but I think it explains the main terminology.

In a clinical trial with two groups (usually referred to as "arms") 
receiving different drugs (one of which may be a placebo), the primary aim 
is usually to compare the means (m1 and m2, say) of a specified response 
variable measured on all patients. Of most interest scientifically is an 
estimate of the difference between those means and the precision of the 
estimate, to show potential benefits to the patients. But in order to 
satisfy the rules of regulation when making a new drug application, a 
hypothesis test is carried out at a prescribed level of significance. The 
most common test is usually referred to as "superiority" of one drug over 
the other; in fact, this is a test of difference, with H0: m1 = m2. The
FDA requires this test to be carried out with alpha=0.05, which means in 
practice that the Type I error associated with claiming one drug to be 
better than another is 0.025, because no-one is interested in a new drug if 
the comparator works better.

When a drug is re-formulated, there is a requirement to demonstrate that the 
new formulation behaves like the old (say m1 is the mean for the new drug). 
A test of "equivalence" is then performed, using a pre-specified and 
medically accepted level of "tolerance" on the response scale: call it
t. The hypothesis tested is H0: (m1 > m2+t) OR (m1 < m2-t). The method is 
referred to by the abbreviation TOST (two one-sided tests) because it is 
carried out by testing the two components. If each component is tested using 
the same alpha, the Type I error of the full test is also alpha because the 
two cases are mutually exclusive. During the early development of a drug, 
equivalence tests of the pharmacokinetics of the drug (referred to as 
"bioequivalence tests") in small trials are usually accepted with 
alpha=0.05, so each component test is carried out with alpha=0.05. But in 
later development, in large confirmatory trials, alpha=0.025 is usually 
required.

A non-inferiority test is carried out when all that is needed is to 
demonstrate that a new drug or formulation is no worse than another. The 
hypothesis again relies on a tolerance level, and is H0: m1 < m2-t. The 
regulators usually require alpha=0.025.

The rules for significance levels are relaxed in some disease areas in which 
it is hard to recruit patients, and therefore hard to achieve statistical 
significance when a drug achieves a clinically important effect. But apart 
from this, and from the small trials used for bioequivalence testing, there 
is consistency in that there is a 1 in 40 chance of a trial being a 
"success" from the drug company's point of view, if the drug actually has no 
efficacy at all. To satisfy the FDA about a new drug, at least two trials 
have to succeed.

Peter Lane
Research Statistics Unit, GlaxoSmithKline


(7)
Dear Ioanna,

I've seen some useful replies, but none has explained why it is that 
equivalence trials are set up with different alpha and beta to the standard 
trial. I will try to remedy that now.

I would refer you to p166 of "Clinical Trials" by Steven Piantadosi - an 
excellent book ! But in case you can't get sight of it, I'll precis it 
below.

When performing an equivalence trial, the null hypothesis might be, "the 
treatments are different" when the alternative hypothesis would be, "the 
treatments are the same." This is a reversal of the standard test.

Furthermore, the test is one-sided because we are not testing for better or 
worse, only for equivalence. The roles of alpha and beta are reversed and 
must be selected with some thought.

Approaches to power and sample size for equivalence trials are discussed by 
Roebruck and Kuhn (1995), Statistics in Medicine, 14, 1583 - 1594 and by 
Farrington and Manning (1990), Statistics in Medicine, 9, 1447 - 1454

I hope that helps.

Best Wishes,

Martin Holt


Thank you all very much,

Ioanna





>From: ioanna gioni <[log in to unmask]>
>Reply-To: ioanna gioni <[log in to unmask]>
>To: [log in to unmask]
>Subject: sample size in non-inferiority trial
>Date: Thu, 26 Jan 2006 15:33:19 +0000
>
>Dear all,
>
>I need to calculate the sample size for a non-inferiority trial (normal 
>data).
>I have an issue with the choice of alpha in the sample size calculation 
>formula. I am not sure if I need to set my type error I (alpha) at half the 
>conventional type I error used in two-sided confidence intervals.
>Unfortunately, I don’t have access to any sample size calculations book 
>that deals with non-inferiority/equivalence issues.
>Searching in the Internet I found various examples where some calculate the 
>sample size setting alpha to be 0.05 and some setting alpha to be 0.025.
>I know that for the analysis I need to either calculate a two-sided 95% 
>confidence interval (equal-tailed) and then use the lower bound for testing 
>the hypothesis or calculate one-sided intervals with a coverage probability 
>of 97.5%.  My issue is if in the sample size calculation I set alpha as 
>0.05 or 0.025.
>
>Any help would be appreciated,
>
>Ioanna
>
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