## How would you implement it? [BE/BA News]

Hi Helmut and all,

I was a little afraid of this. Thanks a lot for posting.

❝ Comparable median (≤ 20% difference) and range for Tmax

I am confused. I can see the point in regulating the matter, but I feel there is a lot that's left to be answered.

But let me ask all of you.

Question 1
Do you read this as: You need to be comparable (20% diff) for the median AND for the range? (i.e. is there also a 20% difference requirement for the range???)

❝ Calculating the ratio of values is a questionable procedure.

Question 2:
Whether we like it or not, we have to find a way forward. And this has a lot of degrees of freedom. In a nonparametric universe where we try to resolve it There could be all sorts of debate re. Hodges-Lehman, Kruskal-Wallis, Wilcoxon test, confidence levels, bootstrapping, pairing and what not.

So, kindly allow me to throw this on the table:

Imagine we have these Tmax levels for T and R in a BE trial, units could be hours.
Tmax.T=c(2.0, 2.5, 2.75, 2.5, 2.0, 2.5, 1.5, 2.0) Tmax.R=c(4.0, 3.0, 3.5, 3.75, 1.5, 3.5, 5.5, 4.5) 

Let us implement something that has the look and feel of a test along the lines of what regulators want.

Test1=wilcox.test(Tmax.T,  alt ="two.sided", conf.int = T, correct=T, conf.level=.90) Test1$conf.int; I am getting a CI of 1.999929-2.500036 (2 to 2.5). We can compare this with median(Tmax.R)*c(0.8, 1.2) The test fails. Would that be a way to go? No? then how about: Test2=wilcox.test(Tmax.T/Tmax.R, alt ="two.sided", conf.int = T, correct=T, conf.level=.90) Test2 Test2$conf.int;

I am getting 0.47-0.92. Not within 0.8 to 1.25, test fails.

Shoot me.
How would you prefer to implement the comparability exercise for Tmax? (I am not so much interested in your thoughts on alpha/confidence level, exact T or F, etc. I am mainly interested in a way to make the comparison itself, so please make me happy and focus on that ).

Mind you, the data above might be paired .... or it might not, depends on whether it was from an XO or not. This add complexity, all depending on the implementation.

And, question 3, if the comparability thing also applies to range, how to implement that?

And question 4, sample size calculation is going to get messy for these products, if we have to factor in comparability of Tmax at the 20% level. I am not outright saying I have a bad taste in my mouse, but I am leaning towards thinking this could easy translate into a complete showstopper for sponsors developing the products. What's your gut feeling?

At the end of the day answers to Q1-Q4 above hinge not only on what you think is the right thing to do; of equal importance is what you think regulators will accept.

Pass or fail!
ElMaestro