# Bioequivalence and Bioavailability Forum 09:09 CEST

GM
Junior

India,
2017-11-17 04:55
(edited by GM on 2017-11-17 05:07)

Posting: # 17986
Views: 2,240

## calculation of 90% CI for continuous variable in clinical endpoint studies [General Sta­tis­tics]

Hello All,

As I am new to the endpoint studies, how can we calculate 90% CI for continuous variable in clinical endpoint studies?

As per my understanding, there are two ways. One is ±20 rule for the difference of means and 80-120% rule for ratio of means of un-transformed data. Based on this reference 90% CI Calculation

But as per OGD, the 90%CI should lies in 80-125% for un-transformed data. Please see the point no.21 in the OGD (see Clindamycin Phosphate).

This is me a lot. Please clarify.

Best Regards,
GM
ElMaestro
Hero

Denmark,
2017-11-18 21:17

@ GM
Posting: # 17987
Views: 1,884

## calculation of 90% CI for continuous variable in clinical endpoint studies

Hi GM,

the tradition is to use 80.00%-125.00% for a ratio of continuous variables. This makes extremely good sense under a certain set of assumptions.

You refer to section 21 of the guidance, but this does not relate to continuous variables. It applies to dichotomous variables instead.

Rule of thumb: For a difference, the acceptance range is symmetric. For a ratio the lower acceptance limit equals the reciprocal upper limit, naturally. Most BE issues you will come across have elements of both if logs are involved.

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
GM
Junior

India,
2017-11-19 12:13

@ ElMaestro
Posting: # 17992
Views: 1,875

## calculation of 90% CI for continuous variable in clinical endpoint studies

Hello El-Maestro,

»
» the tradition is to use 80.00%-125.00% for a ratio of continuous variables. This makes extremely good sense under a certain set of assumptions.
»
Is it possible for untransformed data also? If possible what are the limits i.e., 80-125 or 80-120.

» You refer to section 21 of the guidance, but this does not relate to continuous variables. It applies to dichotomous variables instead.
»
Actually I need clarification on section 20 of the same guideline mentioned above. My apologies for mentioning wrong section earlier.

» Rule of thumb: For a difference, the acceptance range is symmetric. For a ratio the lower acceptance limit equals the reciprocal upper limit, naturally. Most BE issues you will come across have elements of both if logs are involved.

How can we will calculate 90% CI for ratio of means of untransformed continuous variable using PROC GLM in SAS.

Thankyou
GM.

Best Regards,
GM
ElMaestro
Hero

Denmark,
2017-11-20 20:41

@ GM
Posting: # 17993
Views: 1,805

## calculation of 90% CI for continuous variable in clinical endpoint studies

Hi GM,

» How can we will calculate 90% CI for ratio of means of untransformed continuous variable using PROC GLM in SAS.

Why is it that you want the endpoint to be untransformed?
Statistically normal distributions are wonderful because any two normal distributions added (= subtracted) will yield a new normal distrution. But try and divide them and you are facing a mathematical challenge that is in no way straightforward to deal with.
If you want to do a parametric CI on a ratio then the only way forward that I know of is a transformation one way or another so that the endpoint can reasonably be assumed normal.

So I am sorry that I cannot answer your question in the way you have asked it. Having said this I am of the impression that you don't really need a 90% CI for a ratio of untransformed means.

if (3) 4

Best regards,
ElMaestro

"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.
GM
Junior

India,
2017-11-21 06:02

@ ElMaestro
Posting: # 17995
Views: 1,805

## calculation of 90% CI for continuous variable in clinical endpoint studies

Hello El-Maestro,

Sorry I am understanding the guidance (see Clindamycin OGD)wrongly, as I already told "am new to endpoint studies".

As per the OGD section #6, the primary end point is, Percent change from baseline to week 12 in the inflammatory (papules and pustules) lesion count.

As per the OGD section #20, Equivalence Analysis

The compound hypothesis to be tested is:
H0: µT / µR ≤ θ1 or µT / µR ≥ θ2 versus HA : θ1 < µT / µR < θ2

Where µT = mean of test treatment, and µR = mean of reference treatment
Typically, we reject H0 with a type I error α = 0.05 (two 1-sided tests), if the 90% confidence interval for the ratio of means between test and reference products (µT / µR) is contained within the interval [θ1, θ2], where θ1 = 0.80 and θ2 = 1.25.

Here as per my understanding, the primary endpoint is untransformed data. That's why I had this confusion. and why 90% CI interval given as 00.80-1.25?

if the primary endpoint is ln-transformed data then there is no problem to calculate ratio of means or difference of means as you said earlier.

Sorry if I am confusing everybody. Kindly give me some idea on this.

GM

Best Regards,
GM
DavidManteigas
Regular

Portugal,
2017-11-21 10:01

@ GM
Posting: # 17996
Views: 1,770

## calculation of 90% CI for continuous variable in clinical endpoint studies

Hi GM,

As El Maestro explained, when your test hypothesis is a ratio (multiplicative model) then you must work with ln transformed data. The guidance is clear on that as it also defines the acceptance range as 0.8 to 1.25 (multiplicative model). If in some guideline they state the hypothesis as treatment differences (H0: u1-u2=0) and a symmetric equivalence range (0.8 to 1.2) then they would be suggesting an analysis on untransformed data. This is true regardless of the type of your endpoint as long as it is a continuous endpoint. As simple as that

Regards,
David
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