Bioequivalence and Bioavailability Forum

Hi ElMaestro,

❝ a 90% CI that doesn't spanover 1.0 should generally be no problem. It means that Test and Ref differ but so be it; all products differ and sometimes we can even detect it as a significant treatment effect as in your case. The primary equivalence criterion is still just a 90% CI within the acceptance range. Statistically different isn't necessarily clinically relevant.

This is my take on it as well and how I plan on pushing it (gently). What do you mean by "quality-focused"?

Thank you for your feedback.

❝ Adding to what ElMaestro said my two cents: Maybe you can point out (in a polite way I’m not an expert in) that if one increases the sample size sooner or later any study will show a significant difference if the ratio is not exactly (!) 1. See this post. I don’t know your CV and sample size, but the sponsor cannot be blamed to have performed a study in “too” many subjects (I would avoid the term overpowered).

In turns out the client and assessor haven't mentioned anything specific about the CI not overlapping with unity. What the client focused on was the F-test for treatment effect (which, I guess, comes into play if the study was overpowered). I'll take a look at the assumptions in the sample size estimation and take it from there. Thanks for the lead.

Goodmorning,

❝ Adding to what ElMaestro said my two cents: Maybe you can point out (in a polite way I’m not an expert in) that if one increases the sample size sooner or later any study will show a significant difference if the ratio is not exactly (!) 1. See this post. I don’t know your CV and sample size, but the sponsor cannot be blamed to have performed a study in “too” many subjects (I would avoid the term overpowered).

Just as a follow-up, would it be fair to twist a bit what you said and express it this way: "...that if one increases the sample size sooner or later any study will show a significant treatment difference if the ratio is not exactly one." Or is that too much wishful thinking?

The reason I'm asking is that the significant treatment effect is what seems to bother the assessor and not the fact that the ratio doesn't include unity (maybe both are linked statistically, but that's beyond my understanding).

Thank you.

Dear kumarnaidu,

the Marzo/Balant¹⁾ formula is one of the numerous approximate quick calculation formulas for estimating the sample size which arose in the good old ages where computers were rare and software for exact sample size estimation seldom available.

The formula is very simple:
n = 392 * CV^2
It was derived under the following prerequisites from a large sample approximation of the number of subjects (see ²⁾):
log-normal data, 2x2 crossover design, power = 0.8, 'true' ratio T/R=1, intra-subject variance ~ CV^2.

Especially the restriction to T/R = 1 makes the formula nowadays obsolete. These days sample size estimations usually uses a 'true' T/R of 0.95 or something similar.

A slightly better approximation for higher CV's is obtained by using
n = 392 * se^2 with se^2 = log(CV^2 + 1) (marzo2).

Here a comparison of the exact results (PowerTOST) and the Marzo/Balant formula(s):
  CV   exact marzo marzo2
0.100    6     4↓     4↓
0.125    8     6↓     6↓
0.150   10    10     10
0.175   14    12↓    12↓
0.200   16    16     16
0.225   20    20     20
0.250   24    24     24
0.275   28    30↑    30↑
0.300   32    36↑    34↑
0.325   36    42↑    40↑
0.350   42    48↑    46↑
0.375   48    56↑    52↑
0.400   54    64↑    58↑
uneven numbers in marzo, marzo2 rounded to next even
↓ too low, ↑ too high

In the current modern times there is no need for such formulas and they shouldn't be used any longer. Just fire up R-project and use the PowerTOST-package for your sample size estimation .

---

¹⁾Marzo, A.; Balant, L. P.
"Bioequivalence: an updated reappraisal addressed to applications o interchangeable multi-sorce pharmaceutical products"
Arzneim. – Forsch./Drug Res., Aulendorf, v. 45, n.2, p. 109-115, 1995

²⁾
Steven A. Julious
"Sample Sizes for Clinical Trials"
Chapman & Hall/CRC, Boca Raton, 2010
Chapter 7.2.1.2