Bioequivalence and Bioavailability Forum • FDA's HVD SAS Code from Progesterone Guidance

jag009
★★★

NJ,
2013-04-22 18:39
(4380 d 03:25 ago)

Posting: # 10458
Views: 29,735

FDA's HVD SAS Code from Progesterone Guidance [RSABE / ABEL]

Hi everyone,

I am getting some strange results using the FDA Progesterone Scaled Average Bioequivalence SAS Code → The portion to compute the Unscaled Average 90% C.I.

PROC MIXED

data=pk;

CLASSES SEQ SUBJ PER TRT;

MODEL LAUCT = SEQ PER TRT/ DDFM=SATTERTH;

RANDOM TRT/TYPE=FA0(2) SUB=SUBJ G;

REPEATED/GRP=TRT SUB=SUJ;

ESTIMATE 'T vs. R' TRT 1 -1/CL ALPHA=0.1;

ods output Estimates=unsc1;

title1 'unscaled BE 90% CI - guidance version';

title2 'AUCt';

run; data unsc1;

set unsc1;

unscabe_lower=exp(lower);

unscabe_upper=exp(upper);

run;

Should the Test/Reference Ratio from the Scaled Average BE computation be similar (if not the same) as the ratio computed from the above Unscaled Average BE code?

Thanks
John

Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2013-04-22 19:47
(4380 d 02:17 ago)

@ jag009
Posting: # 10460
Views: 25,543

Proc MIXED vs. Proc GLM

Post reply

Hi John,

❝ Should the Test/Reference Ratio from the Scaled Average BE computation be similar (if not the same) as the ratio computed from the above Unscaled Average BE code?

More details, pleeze! Define similar. ;-)

Note that FDA’s ABE is evaluated by a Proc MIXED and the partial replicate by Proc GLM. You will see differences for incomplete data-sets (GLM drops subjects, MIXED keeps them).

Even for a fully replicated design (but imbalanced and incomplete like EMA’s data set I) SAS’ merge will drop subjects. In Phoenix I get PEs of 1.1546132 (RSABE) and 1.1565765 (ABE).

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

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jag009
★★★

NJ,
2013-04-22 22:33
(4379 d 23:30 ago)

@ Helmut
Posting: # 10464
Views: 25,450

Proc MIXED vs. Proc GLM

Post reply

Hi Helmut,

Can you try this and let me know? Yes there are missing datapoints. The other 2 parameters worked out fine. I ran data from another study and everything worked as well. Only this dataset is giving me the finger. The difference is the missing values as other datasets had values for all subjects. Maybe the missing data is messing things up?

Data columns are Subject Period Sequence Formulation PK-parameter

My SAS SCABE for this parameter is

Theta    Bound y    (S2wr)    (sWR)   (T/R) Pt Est  95% Upper Crit

0.79669   -0.22198  0.41135  0.64137    89.8994     -0.18423

I ran Unscaled Avg BE (Progesterone guidance SAS code)

T/R Ratio     90% CI

101.021    80.7739 - 126.343

Sequence 1=ABB, 2=BAB, 3=BBA

1 3 BBA A 31.432

2 1 ABB A 23.746

4 1 ABB A 41.258

5 3 BBA A 24.887

6 2 BAB A 237.003

7 3 BBA A 35.132

8 1 ABB A 22.399

9 2 BAB A 77.187

10 2 BAB A 180.386

11 3 BBA A 40.623

12 1 ABB A 15.382

14 2 BAB A -

15 3 BBA A 75.768

17 1 ABB A 15.219

18 2 BAB A 136.554

19 1 ABB A 53.966

20 2 BAB A 18.509

21 3 BBA A 24.439

23 2 BAB A 23.710

25 2 BAB A 16.264

26 3 BBA A 41.160

27 1 ABB A 63.364

28 3 BBA A 46.344

29 1 ABB A 66.059

30 2 BAB A 2.539

31 3 BBA A -

32 1 ABB A 34.002

33 2 BAB A 61.070

34 3 BBA A 149.674

35 2 BAB A 26.440

36 1 ABB A 54.400

37 2 BAB A 39.185

38 3 BBA A 201.983

39 1 ABB A 17.831

40 3 BBA A 85.293

1 1 BBA B 40.705

1 2 BBA B 68.864

2 2 ABB B 13.020

2 3 ABB B 36.121

4 2 ABB B 102.646

4 3 ABB B 54.459

5 1 BBA B 9.396

5 2 BBA B 22.999

6 1 BAB B 309.754

6 3 BAB B 163.058

7 1 BBA B 41.710

7 2 BBA B 44.472

8 2 ABB B 2.915

8 3 ABB B -

9 1 BAB B 88.910

9 3 BAB B 109.897

10 1 BAB B 373.070

10 3 BAB B 529.088

11 1 BBA B 74.469

11 2 BBA B 80.379

12 2 ABB B 26.124

12 3 ABB B 18.094

14 1 BAB B 2.280

14 3 BAB B -

15 1 BBA B 99.409

15 2 BBA B 134.023

17 2 ABB B -

17 3 ABB B 3.694

18 1 BAB B 49.218

18 3 BAB B 42.806

19 2 ABB B 61.764

19 3 ABB B 47.537

20 1 BAB B 74.644

20 3 BAB B 36.181

21 1 BBA B 47.737

21 2 BBA B 30.634

23 1 BAB B 11.766

23 3 BAB B 14.121

25 1 BAB B 29.943

25 3 BAB B 20.244

26 1 BBA B 109.626

26 2 BBA B 80.252

27 2 ABB B 33.349

27 3 ABB B 124.874

28 1 BBA B 29.083

28 2 BBA B 23.024

29 2 ABB B 34.671

29 3 ABB B 23.049

30 1 BAB B 2.782

30 3 BAB B 2.249

31 1 BBA B 57.630

31 2 BBA B -

32 2 ABB B 24.816

32 3 ABB B 39.266

33 1 BAB B 68.419

33 3 BAB B 85.845

34 1 BBA B 51.760

34 2 BBA B 54.845

35 1 BAB B 30.751

35 3 BAB B 2.921

36 2 ABB B 70.271

36 3 ABB B 38.989

37 1 BAB B 114.890

37 3 BAB B 54.372

38 1 BBA B 98.310

38 2 BBA B 147.839

39 2 ABB B 534.900

39 3 ABB B 16.465

40 1 BBA B 176.916

40 2 BBA B 105.915

Thanks
John

Helmut
★★★

Vienna, Austria,
2013-04-23 00:10
(4379 d 21:54 ago)

@ jag009
Posting: # 10466
Views: 25,206

SAS vs. PHX

Post reply

Hi John,

❝ My SAS SCABE for this parameter is

❝ Theta Bound y (S2wr) (sWR) (T/R) Pt Est 95% Upper Crit

❝ 0.79669 -0.22198 0.41135 0.64137 89.8994 -0.18423

No need to post Theta (a constant in RSABE). ;-)

My PHX6.3 code gives for RSABE …

boundy     S²wr     Swr       PE       95% upper

-0.221998  0.41138  0.64139  89.8990  -0.18424336

❝ I ran Unscaled Avg BE (Progesterone guidance SAS code)

❝ T/R Ratio 90% CI

❝ 101.021 80.7739 - 126.343

… and for ABE

  PE          90% CI

104.782  69.7855 – 157.328

But: PHX’ LME kicked my ass with “Warning 11094: Negative final variance component. Consider omitting this VC structure.” Nice. Old story with partial replicates – overspecified model since T is not repeated. We have seen in the past that SAS and PHX give different results in such a case. BTW, did you get “Convergence criteria met but final hessian is not positive definite.” or somefink sⁱm_il^a_r in Sas?

If I go with the ABE-module I got:
“ERROR 11070: Error in Satterthwaite DF. Try using Residual DF option.”
… which I tried, only to get:
“ERROR 11070: Error in Satterthwaite DF. Try using Residual DF option.”
That’s funny! Same if I exclude subjects #14 and #31 (no results for T). What the heck?

Running PHX’ PBE/IBE module I first obtained …

Warning 11121: Subject 31 had incomplete design and was discarded.

Warning 11121: Subject 14 had incomplete design and was discarded.

Warning 11121: Subject 8 had incomplete design and was discarded.

Warning 11121: Subject 17 had incomplete design and was discarded.

… and a PE which is exactly like in RSABE 89.899043.

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

The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Shuanghe
★★

Spain,
2013-04-23 13:45
(4379 d 08:18 ago)

@ Helmut
Posting: # 10471
Views: 25,073

SAS vs. PHX

Post reply

Hi Helmut,

❝ My PHX6.3 code gives for RSABE …

❝ boundy S²wr Swr PE 95% upper

❝ -0.221998 0.41138 0.64139 89.8990 -0.18424336

Just out of curiosity I tried my SAS macro and it only gives Swr, PE, 95% upper. They are the same as yours, which is slightly different from John's.

❝ ❝ I ran Unscaled Avg BE (Progesterone guidance SAS code)

❝ ❝ T/R Ratio 90% CI

❝ ❝ 101.021 80.7739 - 126.343

❝

❝ … and for ABE

❝ PE 90% CI

❝ 104.782 69.7855 – 157.328

Now, my average BE gives:
PE: 1.01021, same as John's :yes:

90% CI: 80.7733 - 126.3450, different from both of yours. :no:

Weird.

❝ But: PHX’ LME kicked my ass with “Warning 11094: Negative final variance component. Consider omitting this VC structure.” Nice. Old story with partial replicates – overspecified model since T is not repeated. We have seen in the past that SAS and PHX give different results in such a case. BTW, did you get “Convergence criteria met but final hessian is not positive definite.” or somefink sⁱm_il^a_r in Sas?

SAS did give me warning of " Convergence criteria met but final hessian is not positive definite".

❝ That’s funny! Same if I exclude subjects #14 and #31 (no results for T). What the heck?

after delete subject 14 and 31, same result for SABE but for ABE:
PE: 98.04322%
90% CI: 78.61817 - 122.26784.
Man, I never doubted the macro before. should I worry about it now? :confused:

Shall we compare the result from EMA's data set?

Edit:
Just tried EMA's 3-period data set, using "logdata" directly from the dataset.
SABE gives:

Swr=0.11397

PE=1.02264

95% upper= -0.00397289

ABE gives the same result as in the EMA's Q&A. 102.264 (97.05-107.76)

delete subject 5 and 8 (don't ask why those subjects)

SABE gives:

Swr=0.11803

PE=1.01341

95% upper= -0.00510258

ABE gives:

PE=101.218

90% CI= 95.7687 - 106.978

Can anyone check it?

—
All the best,
Shuanghe

d_labes
★★★

Berlin, Germany,
2013-04-23 18:50
(4379 d 03:13 ago)

@ Shuanghe
Posting: # 10475
Views: 25,059

SAS vs. SAS

Post reply

Hi Shuanghe,

❝ Now, my average BE gives:

❝ PE: 1.01021, same as John's :yes:

❝ 90% CI: 80.7733 - 126.3450, different from both of yours. :no:

❝ Weird.

don't worry. My results (using Johns code for ABE as given above at start of the thread) under SAS9.2 are:

  point est.  90% confidence interval

  101.0213%     80.7733   126.3450

  s2wR = 0.4210 -> CVwR = 72.35%

Deleting the 4 subjects with missings (same happens in the intra-subject contrast calculations) gives

  point est.  90% confidence interval

  90.5032%     73.5627   111.3449

  s2wR = 0.4001 -> CVwR = 70.14%

very similar to the numbers used for the RSABE criterion :cool:

.

But I don't believe in this numbers anyway. I think the optimizer stops here arbitrarily as almost ever for a partial replicate design in which the intra-individual variability for T is not identifiable.
Any modification to the code, f.i. fitting a model with no subject-by-treatment interaction via the CS covariance structure crashes with infinite likelihood and an estimate of s2wT=0!

I always wondered why the FDA insists on the Proc MIXED code, especially for that design.
On the other hand in the context of RSABE linearized criterion the point estimator and its 90% CI are calculated via intra-subject contrast T-R.
Why not use these results for ABE also :confused:

.

To increase the confusion here the results of the mighty oracle EMA code (same Proc GLM as for a 2x2 crossover for the PE and CI, s2wR from analysis of data for R (B) only):

  point est.  90% confidence interval

  98.4476%     78.6492   123.2298

  s2wR = 0.39824522 -> CVwR = 69.94%

So much numbers to choose between :-D

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2019-11-12 14:01
(1985 d 07:02 ago)

@ d_labes
Posting: # 20788
Views: 11,176

SAS vs. SAS vs. Phoenix

Post reply

Hi to all victims of the partial replicate with incomplete data,

following extensive off-list discussions with PharmCat (who is working on a Julia-library; see here and there) I checked again what we got with the FDA’s covariance structure, Satterthwaite’s df (PE, 90% CI).
Not the slightest idea how I arrived at the results given above. Sorry for the confusion caused.

John’s first dataset.
- John (SAS, v?)
  101.021 80.7739 – 126.343
- Shuanghe (SAS, v?)
  101.021 80.7733 – 126.3450
- Detlew (SAS, v9.2)
  101.0213 80.7733 – 126.3450
- Myself (Phoenix v6.3 and v8.1)
  No convergence with the default setup.
  However, when I lowered the convergence criterion to 1E-11:
  101.0213 80.7733 – 126.3450
John’s second dataset (ln AUCi).
- John (SAS, v?)
  No convergence.
- Myself (Phoenix v6.3 and v8.1)
  Convergence with warning, tweaking the setup doesn’t help.
  95.2967 88.4014 – 102.7298
  Compound symmetry (as suggested by Detlew)
  95.2967 88.4014 – 102.7298
- Detlew (SAS, v9.2, CS)
  95.30 88.23 – 102.82

In all cases simplifying the covariance structure (in SAS-lingo FA0(1) instead of the FA0(2) in the guidance): Convergence without warning.

—
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,
2013-04-23 17:56
(4379 d 04:07 ago)

@ Helmut
Posting: # 10473
Views: 24,638

SAS vs. PHX

Post reply

Hi Helmut and shanghue,

❝ That’s funny! Same if I exclude subjects #14 and #31 (no results for T). What the heck?

Yes but Proc Mixed takes into account the missing data correct?

Great, I opened up a Pandora's Box...
Let me investigate further and let you guys know.

Calling for Detlew the SAS guru (heheh, one of the gurus to be politically correct) :-D

. He might have some idea on this...

Thanks
John

jag009
★★★

NJ,
2013-04-23 19:07
(4379 d 02:57 ago)

@ jag009
Posting: # 10476
Views: 25,716

SAS Warning (Note) on Proc Mixed

Post reply

Thanks guys (and girls),

Here are the notes from my SAS Log on Proc Mixed.

NOTE: 6 observations are not included because of missing values.

NOTE: Convergence criteria met but final hessian is not positive definite.

NOTE: Asymptotic variance matrix of covariance parameter estimates has been found to be singular and a generalized inverse was used. Covariance parameters with zero variance do not contribute to degrees of freedom computed by DDFM=SATTERTH.

I think this is problematic... One runs a dataset and SCABE criteria for Swr not met so he/she resorts to the ABE routine. Tada!

Thanks
John

jag009
★★★

NJ,
2013-04-30 23:09
(4371 d 22:55 ago)

@ jag009
Posting: # 10515
Views: 25,149

Nut Job..

Post reply

Hi everyone,

Continuing the sage... I now have full dataset and I included AUCt as well.

Once again using the ABE procedure with Proc Mixed from FDA progesterone guidance. I was fine with ln AUCt but did get a message in the SAS log:

NOTE: Convergence criteria met but final hessian is not positive definite.
NOTE: Asymptotic variance matrix of covariance parameter estimates has been found to be singular and a generalized inverse was used. Covariance parameters with zero variance do not contribute to degrees of freedom computed by DDFM=SATTERTH.

For AUCt
Ratio: 94.7377; 90% CI: 87.4898-102.586

However, Proc Mixed failed to compute the above for ln AUCi and gave me a warning message in SAS log:

WARNING: Did not converge. :confused:

WARNING: Output 'Estimates' was not created....

The last output from Proc Mixed on ln AUCi was:

Covariance Parameter Values At Last Iteration

Cov Parm   Subject   Group          Estimate

FA(1,1)    subject                  0.3722

FA(2,1)    subject                  0.3975

FA(2,2)    subject                  0.2362

Residual   subject formulation Ref  0.06248

Residual   subject formulation Test 0.01460

I used the same ABE SAS Code posted in the first message in this thread (and the codes are the same for AUCt and AUCi).

The Dataset:
Subject, Sequence, Period, Treatment, ln AUCt, ln AUCi.
Sequence: ABB = 1, BAB = 2, BBA = 3

1 BBA 3 A 7.392949199 7.966255738

2 ABB 1 A 7.486969192 7.642465619

3 BAB 2 A 7.795040591 7.900675886

4 ABB 1 A 7.704527971 7.810454463

5 BBA 3 A 7.74341453 7.813019037

6 BAB 2 A 8.862899236 8.887092743

7 BBA 3 A 7.474575339 7.520470843

8 ABB 1 A 6.649783454 6.786800469

9 BAB 2 A 7.900081068 7.917934089

10 BAB 2 A 8.498478152 8.537308319

11 BBA 3 A 7.687297563 7.764432727

12 ABB 1 A 7.854077711 8.056187995

14 BAB 2 A 6.834931866 7.311990298

15 BBA 3 A 8.004066923 8.015037211

17 ABB 1 A 7.954169654 8.081352274

18 BAB 2 A 8.813960369 8.878784152

19 ABB 1 A 7.936215453 8.005634299

20 BAB 2 A 7.585678156 7.624085152

21 BBA 3 A 7.882511503 7.908029742

23 BAB 2 A 7.252320394 7.329537863

25 BAB 2 A 7.460390761 7.612326456

26 BBA 3 A 7.519507463 7.544075461

27 ABB 1 A 7.842873653 7.906903707

28 BBA 3 A 7.974813947 8.117347067

29 ABB 1 A 7.952082082 8.030115018

30 BAB 2 A 6.969401496 7.626733448

31 BBA 3 A 7.375110404 7.425354311

32 ABB 1 A 7.854046269 7.909554125

33 BAB 2 A 8.180100682 8.240037917

34 BBA 3 A 8.498685373 8.50785008

35 BAB 2 A 7.689511601 7.753216597

36 ABB 1 A 7.697065912 7.731297188

37 BAB 2 A 7.743985836 7.768691851

38 BBA 3 A 8.860378559 8.90071176

39 ABB 1 A 7.649143902 7.760258994

40 BBA 3 A 8.178085044 8.269703924

42 ABB 1 A 7.699680257 8.477479957

44 ABB 1 A 8.469052606 8.546889654

45 BBA 3 A 8.734765894 8.773995092

46 ABB 1 A 7.438072894 7.502691878

47 BBA 3 A 7.70220194 7.870368371

48 BAB 2 A 8.326805753 8.371119472

49 BAB 2 A 8.23649812 8.251025744

51 ABB 1 A 8.89042446 8.926528534

52 BBA 3 A 8.319488803 8.645876426

53 ABB 1 A 8.254585577 8.26745589

54 BAB 2 A 8.774547697 8.830803941

55 BBA 3 A 7.695208954 7.75602795

56 BAB 2 A 8.088395381 8.173364805

57 ABB 1 A 7.721135381 7.754655632

59 BAB 2 A 7.624704432 7.649123891

1 BBA 1 B 7.918112873 7.956429845

1 BBA 2 B 8.165388938 8.236181092

2 ABB 2 B 7.648429922 7.840311803

2 ABB 3 B 7.767760063 7.99990909

3 BAB 1 B 7.84509492 7.903718188

3 BAB 3 B 7.004410917 7.201138817

4 ABB 2 B 8.273957131 8.299682496

4 ABB 3 B 7.893447812 7.922782677

5 BBA 1 B 7.873074242 7.993014477

5 BBA 2 B 7.928661129 7.973013452

6 BAB 1 B 8.953187117 9.070644877

6 BAB 3 B 8.620163052 8.635798822

7 BBA 1 B 7.733732169 7.925830821

7 BBA 2 B 7.883843938 7.915115941

8 ABB 2 B 7.040298183 7.138905094

8 ABB 3 B 6.455060189 6.919911097

9 BAB 1 B 8.246138252 8.302636666

9 BAB 3 B 8.369926761 8.407009731

10 BAB 1 B 8.854970576 8.867276941

10 BAB 3 B 8.985634977 9.003601402

11 BBA 1 B 8.178239438 8.255348312

11 BBA 2 B 8.286612805 8.339918637

12 ABB 2 B 8.240486403 8.305583617

12 ABB 3 B 7.800706552 7.826649818

14 BAB 1 B 7.553067914 7.897693791

14 BAB 3 B 7.105642559 7.345723072

15 BBA 1 B 8.238080695 8.313684606

15 BBA 2 B 8.446723945 8.453986902

17 ABB 2 B 6.918289598 8.123267843

17 ABB 3 B 7.238486783 7.484658489

18 BAB 1 B 8.00908587 8.197899082

18 BAB 3 B 7.76105637 7.935726911

19 ABB 2 B 8.102567049 8.141680789

19 ABB 3 B 7.693701307 7.710909115

20 BAB 1 B 8.263957891 8.29405139

20 BAB 3 B 8.174826537 8.190936874

21 BBA 1 B 8.120727864 8.167847324

21 BBA 2 B 7.93456468 8.013054162

23 BAB 1 B 7.358441651 7.473058861

23 BAB 3 B 7.48803103 7.535879021

25 BAB 1 B 7.602494691 7.697937968

25 BAB 3 B 7.387379977 7.469852557

26 BBA 1 B 8.329193303 8.344287565

26 BBA 2 B 8.037593588 8.060771153

27 ABB 2 B 7.905330655 7.935414562

27 ABB 3 B 8.082943041 8.29080137

28 BBA 1 B 7.738586593 7.774590185

28 BBA 2 B 7.859365663 7.889316764

29 ABB 2 B 7.888838125 8.04080281

29 ABB 3 B 7.779364076 7.821842385

30 BAB 1 B 6.982335711 7.543216142

30 BAB 3 B 6.697153994 6.829441243

31 BBA 1 B 7.747856304 7.809290887

31 BBA 2 B 7.560504854 7.797942664

32 ABB 2 B 7.759783505 7.817275946

32 ABB 3 B 7.356405667 7.515982167

33 BAB 1 B 8.36886463 8.379766221

33 BAB 3 B 8.216466676 8.276196466

34 BBA 1 B 8.258608715 8.287758895

34 BBA 2 B 7.998750632 8.069192434

35 BAB 1 B 7.574446055 7.644724111

35 BAB 3 B 7.149663272 7.258526933

36 ABB 2 B 8.2490222 8.258958847

36 ABB 3 B 7.327066091 7.5359057

37 BAB 1 B 8.139238284 8.195958196

37 BAB 3 B 7.634118159 7.675717682

38 BBA 1 B 8.444112046 8.468275809

38 BBA 2 B 8.725257703 8.835573174

39 ABB 2 B 7.265019149 7.428235744

39 ABB 3 B 7.08341721 7.144682596

40 BBA 1 B 8.089394434 8.723463832

40 BBA 2 B 8.21551415 8.256136432

42 ABB 2 B 7.876135868 8.032802077

42 ABB 3 B 7.828881103 7.976931205

44 ABB 2 B 8.410692915 8.428963108

44 ABB 3 B 8.589966402 8.605777165

45 BBA 1 B 8.525890857 8.539325065

45 BBA 2 B 8.458267051 8.472018404

46 ABB 2 B 7.296383438 7.439829543

46 ABB 3 B 7.502625684 8.280353272

47 BBA 1 B 8.195452589 8.244132241

47 BBA 2 B 8.349083368 8.362756337

48 BAB 1 B 8.176094027 8.20568553

48 BAB 3 B 7.815589152 7.870187719

49 BAB 1 B 8.186195741 8.24090015

49 BAB 3 B 8.046571451 8.140032993

51 ABB 2 B 9.073040287 9.097873779

51 ABB 3 B 9.039707436 9.101568489

52 BBA 1 B 7.856079031 7.917417221

52 BBA 2 B 8.921983405 8.936348427

53 ABB 2 B 8.04764098 8.076713878

53 ABB 3 B 8.439900183 8.497614983

54 BAB 1 B 8.082637012 8.110054083

54 BAB 3 B 8.632410093 8.658085799

55 BBA 1 B 8.226321237 8.316787172

55 BBA 2 B 8.105905766 8.171993299

56 BAB 1 B 8.215087328 8.369842175

56 BAB 3 B 7.985378156 8.083406692

57 ABB 2 B 7.86516185 7.899924985

57 ABB 3 B 7.706186822 7.809824158

59 BAB 1 B 7.77147021 7.842954906

59 BAB 3 B 7.423932557 7.452101942

Any idea?

Thanks
John

Helmut
★★★

Vienna, Austria,
2013-05-01 18:21
(4371 d 03:42 ago)

@ jag009
Posting: # 10517
Views: 24,986

Second opinion (PHX 6.3)

Post reply

Hi John,

❝ For AUCt

❝ Ratio: 94.7377; 90% CI: 87.4898-102.586

PHX tells me:
Ratio: 94.7377; 90% CI: 87.4898–102.586 [image]

Warning 11091: Newton's algorithm converged with modified Hessian. Output is suspect.

Model may be over-specified. A simpler model could be tried.

PHX after 6 iterations:

Final variance parameter estimates: lambda(1,1)_11 0.44268399 lambda(1,2)_11 0.42362946 lambda(2,2)_11 0.16237525 Var(Period*Formulation*Subject)_21 0.053010265 Var(Period*Formulation*Subject)_22 0.061648310

❝ However, Proc Mixed failed to compute the above for ln AUCi

Contrary to SAS PHX ‘succeeded’ for AUCi as well …

Ratio: 95.2967; 90% CI: 88.4014–102.730

… but throws the same warning as above.

❝ The last output from Proc Mixed on ln AUCi was:

❝ Covariance Parameter Values At Last Iteration

❝ Cov Parm Subject Group Estimate

❝ FA(1,1) subject 0.3722

❝ FA(2,1) subject 0.3975

❝ FA(2,2) subject 0.2362

❝ Residual subject formulation Ref 0.06248

❝ Residual subject formulation Test 0.01460

PHX after 6 iterations:

Final variance parameter estimates: lambda(1,1)_11 0.37216022 lambda(1,2)_11 0.39747315 lambda(2,2)_11 0.15492894 Var(Period*Formulation*Subject)_21 0.0624828 Var(Period*Formulation*Subject)_22 0.0463781

Except for the subject-by-formulation interaction and s²_wT quite similar. We have seen with other data sets that SAS and PHX disagree here. Can you post your variances for AUCt as well? I bet we will see differences.

❝ Any idea?

Nope. Let’s wait for the SAS-guru Detlew. :-D

IMHO, since a partial replicate according to FDA’s model is always (!) over-specified there is no guarantee that the LME-engine will converge. Don’t blame SAS and PHX; they warn us… Stupid design. If you want to have only three periods maybe it is better to run a fully replicated design (TRT|RTR) in the future.

P.S.: You are not alone. Last week a colleague posted at Pharsight’s Extranet an example where a replicate design failed to converge for C_max (but not for AUC_t and AUC_∞). Pharsight suggested to change the variance structure to Heterogeneous Compound Symmetry (instead of FDA’s Banded No-Diagonal Factor Analytic [f=2]). In my experience this rarely helps…
BTW, does anybody know the rationale behind FDA’s partial replicate? Higher precision of the estimate of CV_wR (see this post and followings)?

—
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,
2013-05-01 19:16
(4371 d 02:47 ago)

@ Helmut
Posting: # 10518
Views: 24,679

Second opinion (PHX 6.3)

Post reply

Thank you Helmut!

Detlew, need help! :-)

Here is the covariance output from SAS on ln AUCt

Covariance Parameter Estimates

Cov Parm  Subject       Group         Estimate

FA(1,1)   subject                     0.4427

FA(2,1)   subject                     0.4236

FA(2,2)   subject                     0.2481

Residual  subject   formulation Ref   0.05301

Residual  subject   formulation Test  0.02648

Question, what does the residual "formulation Test" represent? Is it the residual attributed to both test and ref, while residual "formulation ref" is attributed to the ref (since it was given 2x)? which one would one use to compute the 90% geometric CI then?

❝ IMHO, since a partial replicate according to FDA’s model is always (!) overspecified there is no guarantee that the LME-engines will converge. Don’t blame SAS and PHX; they warn us… Stupid design. If you want to have only three periods maybe it is better to run a fully replicated design (TRT|RTR) in the future.

Any hint on the stat approach?

Thanks
John

ElMaestro
★★★

Denmark,
2013-05-01 20:48
(4371 d 01:16 ago)

@ jag009
Posting: # 10519
Views: 24,497

Second opinion (PHX 6.3)

Post reply

Hi John,

❝ Question, what does the residual "formulation Test" represent? Is it the residual attributed to both test and ref, while residual "formulation ref" is attributed to the ref (since it was given 2x)? which one would one use to compute the 90% geometric CI then?

Can you ask SAS to spit out the covariance matrix? I mean the one corresponding to ZGZ^T+R? Then I think you can definitely interpret the variabilities in the context of the model specification.

—
Pass or fail!
ElMaestro

Helmut
★★★

Vienna, Austria,
2013-05-01 21:16
(4371 d 00:48 ago)

@ jag009
Posting: # 10520
Views: 25,060

In praise of a full replicate

Post reply

Hi John!

❝ Here is the covariance output from SAS on ln AUCt

❝

❝ Covariance Parameter Estimates

❝ Cov Parm Subject Group Estimate

❝ FA(1,1) subject 0.4427

❝ FA(2,1) subject 0.4236

❝ FA(2,2) subject 0.2481

❝ Residual subject formulation Ref 0.05301

❝ Residual subject formulation Test 0.02648

OK, similar again (except for the usual suspects).

❝ Question, what does the residual "formulation Test" represent?

Nothing. Only a desperate attempt of the algo to estimate something based on too little information. Think about a parallel design. Intra-subject variability is there, but we cannot extract it (only the total/pooled). We need a cross-over. Same here. s²_wT exists, but we have only one observation of T / subject.

❝ Is it the residual attributed to both test and ref, …

Cough.

❝ … while residual "formulation ref" is attributed to the ref (since it was given 2x)?

Correct.

❝ which one would one use to compute the 90% geometric CI then?

None of them directly. PHX spits out a standard error of the difference T–R of 0.0474839 (too lazy to dig out the reference on how it is composed from the other variances).

❝ ❝ IMHO, since a partial replicate according to FDA’s model is always (!) overspecified there is no guarantee that the LME-engines will converge. :blahblah:

❝

❝ Any hint on the stat approach?

No idea.

I took the opportunity and massaged you data. I kept all subjects in sequence RTR, and recoded a little bit. Of course I had to change some Rs to Ts… I got:

Subject Sequence Period Treatment lAUCt lAUCi

1 RTR 1 R 7.918112873 7.956429845

1 RTR 2 T 7.392949199 7.966255738

1 RTR 3 R 8.165388938 8.236181092

2 RTR 1 R 7.648429922 7.840311803

2 RTR 2 T 7.486969192 7.642465619

2 RTR 3 R 7.767760063 7.999909090

3 RTR 1 R 7.845094920 7.903718188

3 RTR 2 T 7.795040591 7.900675886

3 RTR 3 R 7.004410917 7.201138817

4 RTR 1 R 8.273957131 8.299682496

4 RTR 2 T 7.704527971 7.810454463

4 RTR 3 R 7.893447812 7.922782677

5 RTR 1 R 7.873074242 7.993014477

5 RTR 2 T 7.743414530 7.813019037

5 RTR 3 R 7.928661129 7.973013452

6 RTR 1 R 8.953187117 9.070644877

6 RTR 2 T 8.862899236 8.887092743

6 RTR 3 R 8.620163052 8.635798822

7 RTR 1 R 7.733732169 7.925830821

7 RTR 2 T 7.474575339 7.520470843

7 RTR 3 R 7.883843938 7.915115941

8 RTR 1 R 7.040298183 7.138905094

8 RTR 2 T 6.649783454 6.786800469

8 RTR 3 R 6.455060189 6.919911097

9 RTR 1 R 8.246138252 8.302636666

9 RTR 2 T 7.900081068 7.917934089

9 RTR 3 R 8.369926761 8.407009731

10 RTR 1 R 8.854970576 8.867276941

10 RTR 2 T 8.498478152 8.537308319

10 RTR 3 R 8.985634977 9.003601402

11 TRT 1 T 8.178239438 8.255348312

11 TRT 2 R 8.286612805 8.339918637

11 TRT 3 T 7.687297563 7.764432727

12 RTR 1 R 8.240486403 8.305583617

12 RTR 2 T 7.854077711 8.056187995

12 RTR 3 R 7.800706552 7.826649818

14 RTR 1 R 7.553067914 7.897693791

14 RTR 2 T 6.834931866 7.311990298

14 RTR 3 R 7.105642559 7.345723072

15 TRT 1 T 8.238080695 8.313684606

15 TRT 2 R 8.446723945 8.453986902

15 TRT 3 T 8.004066923 8.015037211

17 TRT 1 T 7.954169654 8.081352274

17 TRT 2 R 6.918289598 8.123267843

17 TRT 3 T 7.238486783 7.484658489

18 RTR 1 R 8.009085870 8.197899082

18 RTR 2 T 8.813960369 8.878784152

18 RTR 3 R 7.761056370 7.935726911

19 TRT 1 T 7.936215453 8.005634299

19 TRT 2 R 8.102567049 8.141680789

19 TRT 3 T 7.693701307 7.710909115

20 RTR 1 R 8.263957891 8.294051390

20 RTR 2 T 7.585678156 7.624085152

20 RTR 3 R 8.174826537 8.190936874

21 TRT 1 T 8.120727864 8.167847324

21 TRT 2 R 7.934564680 8.013054162

21 TRT 3 T 7.882511503 7.908029742

23 RTR 1 R 7.358441651 7.473058861

23 RTR 2 T 7.252320394 7.329537863

23 RTR 3 R 7.488031030 7.535879021

25 RTR 1 R 7.602494691 7.697937968

25 RTR 2 T 7.460390761 7.612326456

25 RTR 3 R 7.387379977 7.469852557

26 TRT 1 T 8.329193303 8.344287565

26 TRT 2 R 8.037593588 8.060771153

26 TRT 3 T 7.519507463 7.544075461

27 TRT 1 T 7.842873653 7.906903707

27 TRT 2 R 7.905330655 7.935414562

27 TRT 3 T 8.082943041 8.290801370

28 TRT 1 T 7.738586593 7.774590185

28 TRT 2 R 7.859365663 7.889316764

28 TRT 3 T 7.974813947 8.117347067

29 TRT 1 T 7.952082082 8.030115018

29 TRT 2 R 7.888838125 8.040802810

29 TRT 3 T 7.779364076 7.821842385

30 RTR 1 R 6.982335711 7.543216142

30 RTR 2 T 6.969401496 7.626733448

30 RTR 3 R 6.697153994 6.829441243

31 TRT 1 T 7.747856304 7.809290887

31 TRT 2 R 7.560504854 7.797942664

31 TRT 3 T 7.375110404 7.425354311

32 TRT 1 T 7.854046269 7.909554125

32 TRT 2 R 7.759783505 7.817275946

32 TRT 3 T 7.356405667 7.515982167

33 RTR 1 R 8.368864630 8.379766221

33 RTR 2 T 8.180100682 8.240037917

33 RTR 3 R 8.216466676 8.276196466

34 TRT 1 T 8.258608715 8.287758895

34 TRT 2 R 7.998750632 8.069192434

34 TRT 3 T 8.498685373 8.507850080

35 RTR 1 R 7.574446055 7.644724111

35 RTR 2 T 7.689511601 7.753216597

35 RTR 3 R 7.149663272 7.258526933

36 TRT 1 T 7.697065912 7.731297188

36 TRT 2 R 8.249022200 8.258958847

36 TRT 3 T 7.327066091 7.535905700

37 RTR 1 R 8.139238284 8.195958196

37 RTR 2 T 7.743985836 7.768691851

37 RTR 3 R 7.634118159 7.675717682

38 TRT 1 T 8.444112046 8.468275809

38 TRT 2 R 8.725257703 8.835573174

38 TRT 3 T 8.860378559 8.90071176

39 TRT 1 T 7.649143902 7.760258994

39 TRT 2 R 7.265019149 7.428235744

39 TRT 3 T 7.083417210 7.144682596

40 TRT 1 T 8.089394434 8.723463832

40 TRT 2 R 8.215514150 8.256136432

40 TRT 3 T 8.178085044 8.269703924

42 TRT 1 T 7.699680257 8.477479957

42 TRT 2 R 7.876135868 8.032802077

42 TRT 3 T 7.828881103 7.976931205

44 TRT 1 T 8.469052606 8.546889654

44 TRT 2 R 8.410692915 8.428963108

44 TRT 3 T 8.589966402 8.605777165

45 TRT 1 T 8.525890857 8.539325065

45 TRT 2 R 8.458267051 8.472018404

45 TRT 3 T 8.734765894 8.773995092

46 TRT 1 T 7.438072894 7.502691878

46 TRT 2 R 7.296383438 7.439829543

46 TRT 3 T 7.502625684 8.280353272

47 TRT 1 T 8.195452589 8.244132241

47 TRT 2 R 8.349083368 8.362756337

47 TRT 3 T 7.702201940 7.870368371

48 RTR 1 R 8.176094027 8.205685530

48 RTR 2 T 8.326805753 8.371119472

48 RTR 3 R 7.815589152 7.870187719

49 RTR 1 R 8.186195741 8.240900150

49 RTR 2 T 8.236498120 8.251025744

49 RTR 3 R 8.046571451 8.140032993

51 TRT 1 T 8.890424460 8.926528534

51 TRT 2 R 9.073040287 9.097873779

51 TRT 3 T 9.039707436 9.101568489

52 TRT 1 T 7.856079031 7.917417221

52 TRT 2 R 8.921983405 8.936348427

52 TRT 3 T 8.319488803 8.645876426

53 TRT 1 T 8.254585577 8.267455890

53 TRT 2 R 8.047640980 8.076713878

53 TRT 3 T 8.439900183 8.497614983

54 RTR 1 R 8.082637012 8.110054083

54 RTR 2 T 8.774547697 8.830803941

54 RTR 3 R 8.632410093 8.658085799

55 TRT 1 T 8.226321237 8.316787172

55 TRT 2 R 8.105905766 8.171993299

55 TRT 3 T 7.695208954 7.756027950

56 RTR 1 R 8.215087328 8.369842175

56 RTR 2 T 8.088395381 8.173364805

56 RTR 3 R 7.985378156 8.083406692

57 TRT 1 T 7.721135381 7.754655632

57 TRT 2 R 7.865161850 7.899924985

57 TRT 3 T 7.706186822 7.809824158

59 RTR 1 R 7.771470210 7.842954906

59 RTR 2 T 7.624704432 7.649123891

59 RTR 3 R 7.423932557 7.452101942

Now I had a fully replicated design (TRT|RTR). No warnings, no problems with convergence. Unless some genius comes up with a model for the partial replicate which shows no problems with convergence I would avoid it in the future. Alternative: Send your data to [email protected]. :-D

—
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,
2013-05-02 14:00
(4370 d 08:04 ago)

@ jag009
Posting: # 10522
Views: 24,775

Third opinion

Post reply

Hi John,

❝ Detlew, need help! :-)

Here I am! But don't know if I can help anyway. The whole story "Use Proc MIXED code for Partial replicate design" is mysterious to me.

❝ Here is the covariance output from SAS on ln AUCt

❝

❝ Covariance Parameter Estimates

❝ Cov Parm Subject Group Estimate

❝ FA(1,1) subject 0.4427

❝ FA(2,1) subject 0.4236

❝ FA(2,2) subject 0.2481

❝ Residual subject formulation Ref 0.05301

❝ Residual subject formulation Test 0.02648

❝

❝ Question, what does the residual "formulation Test" represent? Is it the residual attributed to both test and ref

No.
As Helmut already pointed out: an ambiguous attempt of the REML algo to obtain the within-subject variance of the Test formulation. But IMHO the model is over-specified (s2D + s2wT not separable, see below) and therefore there is no guarantee that the value obtained is reasonable.

❝ while residual "formulation ref" is attributed to the ref (since it was given 2x)?

Correct. Unambiguously identifiable.

❝ which one would one use to compute the 90% geometric CI then?

Not clear to me what a 90% geometric CI is :confused:

.

The difference µT-µR has as standard error associated with it for the partial replicate design

sd = sqrt((s2D + s2wT + s2wR/2)*sum(1/ni)/seq^2)
where s2D is the variance of the subject-by-formulation interaction, ni are the number of subjects in the sequence groups, seq is the number of sequences.

s2D can be obtained from the G-matrix according to
s2D = g₁₁+g₂₂-2*g₁₂
(see for more details this post).

Since the model seems over-specified try to use a simple model, f.i. neglect s2D which in turn results in a CS variance-covariance structure for the random part. Sometimes this helps.
See also this thread for another even simpler model specification.

BTW: @Helmut, asking the FDA seems a very good idea!

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2013-05-02 16:41
(4370 d 05:23 ago)

@ d_labes
Posting: # 10524
Views: 24,925

Compound Symmetry

Post reply

Hi Detlew & John,

❝ […] try to use a simple model, f.i. neglect s2D which in turn results in a CS variance-covariance structure for the random part. Sometimes this helps.

Nice – no warnings in PHX any more (only two iterations with the default settings).

log AUCt

PE: 94.7377 (90% CI: 87.4898 – 102.586) Final variance parameter estimates: csDiag_11 0.00843516 csBlock_11 0.187534 Var(Period*Formulation*Subject)_21 0.0530102 Var(Period*Formulation*Subject)_22 0.0715068

log AUCi

PE: 95.2967 (90% CI: 88.4014 – 102.730) Final variance parameter estimates: csDiag_11 -0.00942047 csBlock_11 0.147924 Var(Period*Formulation*Subject)_21 0.0624828 Var(Period*Formulation*Subject)_22 0.0898627

What do you SASians get?

—
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,
2013-05-02 18:26
(4370 d 03:37 ago)

@ Helmut
Posting: # 10529
Views: 25,222

Compound Symmetry - SASian (1)

Post reply

Dear Helmut,

❝ What do you SASians get?

Aye, aye Sir, here I am :-D

.

log AUCt

     90% CI

     PE=94.74%  [ 87.49% ... 102.59%] 



    Covariance Parameter Estimates



  Cov Parm     Subject    Group    Estimate



  Variance     subject              0.008436

  CS           subject              0.1875

  Residual     subject    tmt A     0.07150

  Residual     subject    tmt B     0.05300



NOTE: Convergence criteria met.

log AUCinf

     90% CI

     PE=95.30%  [ 88.32% ... 102.82%]  



    Covariance Parameter Estimates



  Cov Parm     Subject    Group    Estimate



  Variance     subject                    0 (!)

  CS           subject              0.1441

  Residual     subject    tmt A     0.07465

  Residual     subject    tmt B     0.06088



NOTE: Convergence criteria met.

NOTE: Estimated G matrix is not positive definite.

NOTE: Asymptotic variance matrix of covariance parameter estimates has been found to be singular and a generalized inverse was used. Covariance parameters with zero variance do not contribute to degrees of freedom computed by DDFM=SATTERTH.

Please note the 'Variance' parameter in case of AUCinf.
CS Covariance matrix parameterized in Proc MIXED as:

( CS+var  CS

  CS      CS+var)

See this post to notice that we really need 'Variance'=0 in our model (Type CS is only an approximation to that end, hoping the 'Variance' parameter is fitted with a value near zero).
So we eventually have the optimizer to tell that for AUCt. Couldn't figure out in a hurry at moment how to do that.

—
Regards,

Detlew

Helmut
★★★

Vienna, Austria,
2013-05-03 18:07
(4369 d 03:56 ago)

@ d_labes
Posting: # 10535
Views: 24,912

Variance=0

Post reply

Dear Detlew!

❝ Please note the 'Variance' parameter in case of AUCinf.

… and the negative one obtained in PHX. Seems that SAS’ RLME-engine forces negative values to zero.

❝ See this post to notice that we really need 'Variance'=0 in our model (Type CS is only an approximation to that end, hoping the 'Variance' parameter is fitted with a value near zero).

Ooh – that one. :-D

❝ So we eventually have the optimizer to tell that for AUCt.

I’m not very optimistic whether this is possible in PHX at all; I will ask Pharsight. In PHX for linear mixed effects models the initial estimates are derived by the method of moments:
log AUCt

Starting estimates of variance parameters: csDiag_11 0.00881650 csBlock_11 0.188267 Var(Period*Formulation*Subject)_21 0.0519883 Var(Period*Formulation*Subject)_22 0.0703479

log AUCi

Starting estimates of variance parameters: csDiag_11 -0.00961080 csBlock_11 0.148549 Var(Period*Formulation*Subject)_21 0.0620715 Var(Period*Formulation*Subject)_22 0.0894799

Alternatively one can state initial variances. If I set csDiag_11 (PHX’ terminology) to zero (whilst keeping the others), the optimizer iterates happily around (four iterations instead of two) – only to end up with the same final estimates…

—
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