Bioequivalence and Bioavailability Forum

Helmut
★★★

Vienna, Austria,
2013-01-13 16:54
(4504 d 07:30 ago)

Posting: # 9834
Views: 16,119

FDA’s aggregate BE for NTIDs: example [RSABE / ABEL]

Dear all,

I tried to implement FDA’s aggregate BE according to the warfarin guidance in Phoenix/WinNonlin 6.3. For a discussion see also this thread. In order to demonstrate BE a study has to pass three criteria:

RSABE based on θ=[ln(1.11111)/0.1]²: crit. bound ≤0.
unscaled ABE: 90% CI within 80.00–125.00%.
comparison of σ_WT with σ_WR: upper 95% CL of s_WT/s_WR ≤2.5.

For an example data set (20kB xls) I got:

critbound: -0.0098283 (passed)
CI: 93.90–103.35% (passed)
upper CL: 1.0453 (passed)

Can you check in your installation – or other software – whether I screwed up?^*

I did. Not for the first time. See this post. Ergo:
upper CL: 0.68427 (passed)

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

d_labes ★★★ Berlin, Germany, 2013-01-13 20:06 (4504 d 04:18 ago) @ Helmut Posting: # 9835 Views: 14,990	404 Post reply
	Dear Helmut, ❝ For an example data set (20kB xls) I got: And I got: SORRY, a ‘404 Not Found Error’ occurred! — Regards, Detlew

Helmut
★★★

Vienna, Austria,
2013-01-13 21:49
(4504 d 02:35 ago)

@ d_labes
Posting: # 9836
Views: 14,999

URL corrected

Post reply

Dear Detlew,

❝ ❝ For an example data set (20kB xls) I got:

❝ And I got:

❝ SORRY, a ‘404 Not Found Error’ occurred!

Correct response of the server since I posted a wrong link. :not really:

Should work by now.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-14 22:09 (4503 d 02:16 ago) @ Helmut Posting: # 9838 Views: 14,893	URL corrected Post reply
	Hi Helmut, SAS. Working on the last line... So far I have: 95% upper confidence bound or critbound:-0.009828289 Unscaled 90% CI:93.8971-103.353. Pt Est:98.5117 John

Helmut
★★★

Vienna, Austria,
2013-01-14 22:50
(4503 d 01:34 ago)

@ jag009
Posting: # 9840
Views: 14,920

THX!

Post reply

Hi John,

THX for the help!

❝ 95% upper confidence bound or critbound:-0.009828289

OK, if you want to get more figures -0.00982828898913271. [image]

❝ Unscaled 90% CI:96.7557-106.500. Pt Est:101.511

❝ The 90% CI is different from yours though... I checked and I didn't see anything wrong.

Would you mind checking your code? If I code ‘T’ as the reference (in SAS-speak: TRT -1 1 instead of TRT 1 -1) I get
CI 96.75557–106.49961, PE 101.51074…

Ah I see – you edited your post. Therefore

❝ Unscaled 90% CI:93.8971-103.353. Pt Est:98.5117

Dont’t forget FDA’s rounding to two decimals. ;-)

However, the easiest part of the game:
93.8971–103.3532, 98.5117 [image]

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-14 22:53 (4503 d 01:32 ago) @ Helmut Posting: # 9841 Views: 15,037	THX! Post reply
	Sorry you were right (see my edited message). CI is same as your. Just the last computation now (the 90% CI for wt/wr) John

Helmut
★★★

Vienna, Austria,
2013-01-14 23:07
(4503 d 01:17 ago)

@ jag009
Posting: # 9842
Views: 14,948

Home stretch

Post reply

Hi John,

these are the wonders of modern communications. Two one-way streets.

❝ Just the last computation now (the 90% CI for wt/wr)

THX again. Have to have dinner now. Did you see my other post?

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-14 23:24 (4503 d 01:00 ago) @ Helmut Posting: # 9843 Views: 14,894	Home stretch Post reply
	Hi Helmut, ❝ THX again. Have to have dinner now. Did you see my other post? Yes sorry I thought the codes are the same! John

K2K ★ India, 2013-01-16 05:48 (4501 d 18:36 ago) (edited on 2013-01-16 13:19) @ Helmut Posting: # 9859 Views: 14,663	estimate Post reply
	Hi John & helmut, ❝ Would you mind checking your code? If I code ‘T’ as the reference (in SAS-speak: `TRT -1 1` instead of `TRT 1 -1`) I get ❝ CI 96.75557–106.49961, PE 101.51074… according to warfin sas code `REPEATED/GRP=TRT SUB=SUBJ;ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1;ods output`. when we want to choose 'T vs. R' TRT 1 -1 or T vs. R' TRT -1 1. — thanks and regards Karthik

Helmut
★★★

Vienna, Austria,
2013-01-16 15:00
(4501 d 09:24 ago)

@ K2K
Posting: # 9864
Views: 14,740

only a typo in John’s code

Post reply

Hi Karthik,

❝ according to warfin sas code REPEATED/GRP=TRT SUB=SUBJ;ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1;ods output.

❝

❝ when we want to choose 'T vs. R' TRT 1 -1 or T vs. R' TRT -1 1.

Never. By coding TRT 1 -1 you would compare reference with test – that’s the opposite of what we want.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

K2K ★ India, 2013-01-17 05:46 (4500 d 18:39 ago) @ Helmut Posting: # 9882 Views: 14,634	only a typo in John’s code Post reply
	Hi helmut, ❝ Never. By coding `TRT 1 -1` you would compare reference with test – that’s the opposite of what we want. thanks for your reply. — thanks and regards Karthik

jag009 ★★★ NJ, 2013-01-15 00:04 (4503 d 00:20 ago) @ Helmut Posting: # 9844 Views: 14,870	FDA’s aggregate BE for NTIDs: example Post reply
	Hi Helmut, Stuck at the last one.. ❝ 3. `upper CL: 1.0453` (passed) Did you get these values for std dev of T and R? I pulled them from PROC MIXED when running the unscaled BE steps as suggested by the warfarin guidance: S_WT2=0.003281; S_WR2=0.02483 Turning brain dead on Monday (5pm->home time)... Can't get the 90% CI. John

Helmut
★★★

Vienna, Austria,
2013-01-15 16:41
(4502 d 07:43 ago)

@ jag009
Posting: # 9848
Views: 14,792

Variances from ABE: different model

Post reply

Hi John,

❝ Did you get these values for std dev of T and R? I pulled them from PROC MIXED when running the unscaled BE steps as suggested by the warfarin guidance:

❝ S_WT2=0.003281; S_WR2=0.02483

Good point. Same values if I extract them from unscaled ABE. But in my understanding FDA wants to use the D_ij-analysis (the individual R₁-R₂ contrast with fixed effect sequence). That’s different to the unscaled ABE-model and results agree with FDA’s 2001 guidance model for PBE/IBE. For s²_WT I coded the D_ij-model for test and got:

                            s²_WT      CV_WT    s²_WR     CV_WR

unscaled ABE:              0.0032813 5.73%  0.024829 15.86%

← like your result


scaled ABE:                0.0031048 5.58%  0.015474 12.49%

scaled ABE (2001 PBE/IBE): 0.0031048 5.58%  0.015474 12.49%

Too bad that FDA does not give an example data set. :-(

If you want you can also check a more nasty set-up: Imbalanced and incomplete. I deleted subject 18 and the last period (R) of subject 17 and got:

critbound: -0.010150 (passed)
CI: 93.32–103.59% (passed)
upper CL: 1.0643 0.68354 (passed)

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009
★★★

NJ,
2013-01-15 18:58
(4502 d 05:26 ago)

@ Helmut
Posting: # 9851
Views: 14,746

Variances from ABE: different model

Post reply

Hi Helmut,

❝ s²_WT CV_WT s²_WR CV_WR

❝ unscaled ABE: 0.0032813 5.73% 0.024829 15.86% ← like your result

❝ scaled ABE: 0.0031048 5.58% 0.015474 12.49%

❝ scaled ABE (2001 PBE/IBE): 0.0031048 5.58% 0.015474 12.49%

❝ Too bad that FDA does not give an example data set. :-(

Yes I confirmed your above values based on scaled ABE with SAS :-)

Working backward on the 90% CI computation for the ratio of std deviation of within subject T/R... Your v1 and v2, the 2 degrees of freedom are 16 and 16 right?

John

Helmut
★★★

Vienna, Austria,
2013-01-15 19:09
(4502 d 05:15 ago)

@ jag009
Posting: # 9852
Views: 14,674

Variances from ABE: different model

Post reply

Hi John,

❝ Yes I confirmed your above values based on scaled ABE with SAS :-)

Nice. BTW, didn’t know that you have PHX 6.3 as well. ;-)

❝ Working backward on the 90% CI computation for the ratio of std deviation of within subject T/R... Your v1 and v2, the 2 degrees of freedom are 16 and 16 right?

Correct; n-m, where m=2 in the fully replicated. Therefore, my F-values are 2.333484 and 0.4285438 (from R, since not accessible in PHX).

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009
★★★

NJ,
2013-01-15 19:17
(4502 d 05:07 ago)

(edited on 2013-01-15 20:00)
@ Helmut
Posting: # 9853
Views: 14,888

Variances from ABE: different model

Post reply

Hi Helmut,

❝ Correct; n-m, where m=2 in the fully replicated. Therefore, my F-values are 2.333484 and 0.4285438 (from R, since not accessible in PHX).

Yes I got those results as well in SAS. How do you come up with the CL value? I need food, hungry, can't think (damn lunch time here)...

According to the equation in the warfarin guidance
(1-alpha)100%CI = (SWT/SWR)/Sqrt(F₁), (SWT/SWR)/Sqrt(F₂), where
F₁=F_{alpha/2,v1,v2}, F₂=F_{1-alpha/2,v1,v2}

I ended up getting 0.13134956, 0.306502082???

I am not smoking weed at this moment, its illegal anyway...

John

Helmut
★★★

Vienna, Austria,
2013-01-16 00:30
(4501 d 23:54 ago)

@ jag009
Posting: # 9857
Views: 14,761

Yep. Almost there.

Post reply

Hi John,

❝ […] How do you come up with the CL value?

By ignoring the √… Unbelievable, since printed in such a large font.

❝ According to the equation in the warfarin guidance

❝ (1-alpha)100%CI = (SWT/SWR)/Sqrt(F₁), (SWT/SWR)/Sqrt(F₂),

❝ where F₁=F_{alpha/2,v1,v2}, F₂=F_{1-alpha/2,v1,v2}

❝

❝ I ended up getting 0.13134956, 0.306502082???

Duno. My steps:


 s²_WT        s²_WR

0.0031048  0.015474

 s_WT         s_WR      s_WT/s_WR

0.055721   0.12440   0.44794

α 0.1, therefore,


 F_0.05,16,16   F_0.95,16,16

2.3335       0.42854

√F_0.05,16,16  √F_0.95,16,16

1.5278       0.65463

CL_lo      CL_hi

0.29324   0.68427

❝ I am not smoking weed at this moment, its illegal anyway...

Well,

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-16 17:14 (4501 d 07:10 ago) @ Helmut Posting: # 9868 Views: 14,629	Yep. Almost there. Post reply
	Hi Helmut, ❝ `CL_lo CL_hi` ❝ `0.29324 0.68427` ❝ ❝ ❝ I am not smoking weed at this moment, its illegal anyway... ❝ ❝ Well, So your initial CL value of 1.04xxx was incorrect? Confirmed your number. I was not smoking but drinking, sort of. hehe John

Helmut
★★★

Vienna, Austria,
2013-01-20 13:58
(4497 d 10:27 ago)

@ jag009
Posting: # 9894
Views: 14,534

Done

Post reply

Hi John,

❝ ❝ CL_lo CL_hi

❝ ❝ 0.29324 0.68427

❝ So your initial CL value of 1.04xxx was incorrect? :-D

Yes, forgot to take the square-root of the Fs.

❝ Confirmed your number.

Finally. THX.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-15 19:19 (4502 d 05:06 ago) @ Helmut Posting: # 9854 Views: 14,696	Variances from ABE: different model Post reply
	❝ ❝ Yes I confirmed your above values based on scaled ABE with SAS ❝ ❝ Nice. BTW, didn’t know that you have PHX 6.3 as well. I use it for modelling and IVIVC By the way, do you know Laszlo Endrenyi? He was actually my grad prof John

Helmut
★★★

Vienna, Austria,
2013-01-15 19:29
(4502 d 04:55 ago)

@ jag009
Posting: # 9855
Views: 14,747

Variances from ABE: different model

Post reply

Hi John,

❝ ❝ Nice. BTW, didn’t know that you have PHX 6.3 as well. ;-)

❝

❝ I use it for modelling and IVIVC :-)

❝ By the way, do you know Laszlo Endrenyi? He was actually my grad prof

Oh yes, he is a very nice guy! We’ll be giving a workshop together in Romania this March. :cool:

So you were hanging around in Toronto’s underground shopping malls instead of getting frost boils in wintertime?

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

jag009 ★★★ NJ, 2013-01-15 20:49 (4502 d 03:36 ago) @ Helmut Posting: # 9856 Views: 14,713	Variances from ABE: different model Post reply
	Hi Helmut, Haha yeah it's freaking cold during the winter up there with windchill. The underground shopping malls or tunnels are not as big as the catacombs in Paris

jag009 ★★★ NJ, 2013-01-16 20:35 (4501 d 03:50 ago) @ Helmut Posting: # 9877 Views: 14,606	Variances from ABE: different model Post reply
	Hi Helmut, ❝ Oh yes, he is a very nice guy! We’ll be giving a workshop together in Romania this March. Where? Vlad's castle? John

Helmut
★★★

Vienna, Austria,
2013-01-16 20:39
(4501 d 03:46 ago)

@ jag009
Posting: # 9878
Views: 14,631

Variances from ABE: different model

Post reply

Hi John,

❝ ❝ Oh yes, he is a very nice guy! We’ll be giving a workshop together in Romania this March. :cool:

❝

❝ Where? Vlad's castle?

I’m afraid not, though it’s a hotel now. In a more urban area.

—
Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

FDA’s aggregate BE for NTIDs: example [RSABE / ABEL]

404

URL corrected

URL corrected

THX!

THX!

Home stretch

Home stretch

estimate

only a typo in John’s code

only a typo in John’s code

FDA’s aggregate BE for NTIDs: example

Variances from ABE: different model

Variances from ABE: different model

Variances from ABE: different model

Variances from ABE: different model

Yep. Almost there.

Yep. Almost there.

Done

Variances from ABE: different model

Variances from ABE: different model

Variances from ABE: different model

Variances from ABE: different model

Variances from ABE: different model