Bioequivalence and Bioavailability Forum • Convergence problem in PROC MIXED

dixit
★

India,
2010-03-21 11:19
(5512 d 10:14 ago)

Posting: # 4948
Views: 13,169

Convergence problem in PROC MIXED [Software]

Dear All,

when i am trying to analyze the data by using PROC MIXED in iteration history i got the following warning and stop the iterations. Can any body helps me how can i solve this problem.

Iteration History



 Iteration    Evaluations    -2 Res Log Like       Criterion



         0              1       330.71136792

         1              3       350.25410318     14.15354052

         2              1       335.12518114     20.11197330

         3              1       328.32075414     21.32435138

         4              1       326.56585294      2.27665204

         5              1       325.80212668      1.12958114

         6              1       325.42477726      0.87109278

         7              1       325.23746886      0.77448400

         8              1       325.14418551      0.73204830

         9              1       325.09764019      0.71209596

        10              1       325.07439206      0.70241455

        11              1       325.06277419      0.69764831

        12              1       325.05696683      0.69525806

        13              1       325.05406348      0.69433841

        14              1       325.05261221      0.69689548

        15              1       325.05258960      0.68939848

        16              1       325.05187275      0.72275886





WARNING: Stopped because of infinite likelihood.





 Covariance Parameter Values At Last Iteration



Cov Parm     Subject    Group          Estimate



FA(1,1)      Subject                     0.3033

FA(2,1)      Subject                     0.8739

FA(2,2)      Subject                     0.1540

Residual     Subject    Treatment R      0.9181

Residual     Subject    Treatment T     4.8E-22

Thanks in advance for your suggestions.

Regards

ambati

ElMaestro ★★★ Denmark, 2010-03-21 12:35 (5512 d 08:57 ago) @ dixit Posting: # 4949 Views: 11,216	Convergence problem in PROC MIXED Post reply
	Hi Dixit, Please describe your design and please paste the entire SAS-coding you have used to run the mixed model. Best regards EM.

dixit
★

India,
2010-03-22 07:26
(5511 d 14:07 ago)

@ ElMaestro
Posting: # 4951
Views: 11,208

Convergence problem in PROC MIXED

Post reply

thanks for your reply and the my study design was two-treatment, three-period and three-sequence partial replicate, and the SAS code which i used was

Proc mixed data=pkpd;

class treatment period sequence subject;

model LogCMAX= sequence period treatment/ddfm = satterth;

random treatment/type = FA0(2) subject=subject G;

repeated/grp= treatment subject = subject;

lsmeans treatment;

estimate "t Vs r" treatment -1 1/cl alpha = 0.1;

run;

thanks in advance

regards

dixit

ElMaestro
★★★

Denmark,
2010-03-22 09:21
(5511 d 12:12 ago)

@ dixit
Posting: # 4954
Views: 11,337

Convergence problem in PROC MIXED

Post reply

Hi dixit,

I am not a SAS-user myself, so the following is said on basis of very little insight.

Your code seems to be a direct translation of the FDA code, and as such I would expect it to give a result.

Have you worked with and got meaningful results from exactly this code before?

You specify "random treatment/type = FA0(2) subject=subject G;", where a direct translation from the FDA's proposal would be "..SUB=SUBJECT G" - I am not sure this makes a difference though, but the change can be tried. Same in the other line.

Also note this page; "It will always occur if you have code which includes a REPEATED statement AND you have named an effect on the REPEATED statement AND there are two or more observations from one subject which have identical effect values." - a check of your data listing may be necessary.

It could also be that your code and data are ok, but that the optimiser does not converge. When the optimisation is done the program 'guesses' a set of initial values in the covariance matrix and then changes each of the N values (s₁, s₂, s₃ ... s_N) one by one until the likelihood of the matrix is maximised. The way these changes are done is complex, and if the functional surface of likelihood (s₁, s₂, s₃ ... s_N) is not nice and smooth, the optimiser may not converge with automated settings (pardon my French). In this case it will be necessary to manually seed the initial values, possibly even take control over how each optimisation step is done. I do not know how to do that in SAS (or in R for that matter).

Best regards
EM.

dixit ★ India, 2010-03-23 20:15 (5510 d 01:18 ago) @ ElMaestro Posting: # 4964 Views: 11,142	Convergence problem in PROC MIXED Post reply
	"there are two or more observations from one subject which have identical effect values" and for my concern how can I ensure the above one when I analyzed my data by using the earlier mentioned code and found that there is no issue in LogAuclast and LogAucinf but the problem faced on LogCmax only. Thanks in advance Regards dixit

ElMaestro
★★★

Denmark,
2010-03-23 21:29
(5510 d 00:03 ago)

@ dixit
Posting: # 4966
Views: 11,115

Convergence problem in PROC MIXED

Post reply

Hi dixit,

❝ and for my concern how can I ensure the above one when I analyzed my data by using the earlier mentioned code and found that there is no issue in LogAuclast and LogAucinf but the problem faced on LogCmax only.

I am not sure I t understand what you write here. Can it be rephrased?
But even if I did understand, I might not be able to help you. As usual, d_labes is ahead of everybody else here - please read his post. He pointed out there is something with the model specification and the partial replication of your study.
If you have RRT, RTR, TRR as sequences then there is not point trying to fit a within-T variance estimate. The restricted max likelihood optimises the likelihood of ZGZ^t+R, and there cannot be a within-T sigma anywhere in it due to your study design. I do not know which syntax forces a within-R but no within-T into the covar matrix.

Did SAS converge with a result when you did the AUC-analysis using the same code lines? If so, then that would be really weird (there's still no within-T in your design). Please post the output, including the within-T variance estimate and the likelihood.

Best regards
EM.

dixit
★

India,
2010-03-24 16:09
(5509 d 05:23 ago)

@ ElMaestro
Posting: # 4968
Views: 11,094

Convergence problem in PROC MIXED

Post reply

thank u
and this is the output when i analyzed the logauclast by using the same code


The Mixed Procedure



                  Model Information

Data Set                     WORK.PKPD1

Dependent Variable           logauclast

Covariance Structures        Factor Analytic, Variance

                             Components

Subject Effects              subject, subject

Group Effect                 treatment

Estimation Method            REML

Residual Variance Method     None

Fixed Effects SE Method      Model-Based

Degrees of Freedom Method    Satterthwaite



               Class Level Information



Class        Levels    Values

treatment         2    R T

period            3    1 2 3

sequence          3    RRT RTR TRR

subject          58    1 2 4 5 6 7 8 9 10 12 13 14 15

                       16 17 18 19 20 21 22 23 24 25

                       26 27 28 29 30 31 32 33 34 35

                       36 37 38 39 40 41 42 43 44 45

                       46 47 48 49 50 51 52 53 54 55

                       56 57 58 59 60



                         Dimensions

Covariance Parameters             5

Columns in X                      9

Columns in Z Per Subject          2

Subjects                         58

Max Obs Per Subject               3

Observations Used               174

Observations Not Used             0

Total Observations              174

Iteration History



Iteration    Evaluations    -2 Res Log Like       Criterion



        0              1       485.12566720

        1              2       451.59833387      1.20878767

        2              1       444.40184343      0.03925632

        3              1       442.68719482      0.00074042

        4              1       442.63682114      0.00049434

        5              1       442.63665059      0.00000005

        6              1       442.63664695      0.00000000



                 Convergence criteria met.





                                          Estimated G Matrix



Row    Effect       treatment    subject        Col1        Col2

  1    treatment    R             1           0.4529      0.4233

  2    treatment    T             1           0.4233      0.5232





        Covariance Parameter Estimates



Cov Parm     Subject    Group          Estimate

FA(1,1)      subject                     0.6729

FA(2,1)      subject                     0.6291

FA(2,2)      subject                     0.3571

Residual     subject    treatment R      0.6289

Residual     subject    treatment T     0.09081



Fit Statistics



-2 Res Log Likelihood           442.6

AIC (smaller is better)         452.6

AICC (smaller is better)        453.0

BIC (smaller is better)         462.9





Null Model Likelihood Ratio Test



  DF    Chi-Square      Pr > ChiSq

   4         42.49          <.0001





        Type 3 Tests of Fixed Effects



              Num     Den

Effect         DF      DF    F Value    Pr > F

treatment       1    53.9       .31    0.5820

sequence        2    57.2       1.91    0.1576

period          2     104       1.92    0.1520



Estimates



Label  Estimate    Standard     DF    t Value      Pr > |t|     Alpha   lower         Upper

                   Error

t Vs r 0.05318     0.09603    53.9       0.55      0.5820       0.1     -0.1075      0.2139



                             Least Squares Means



                                      Standard

Effect       treatment    Estimate       Error      DF    t Value    Pr > |t|



treatment    R              7.9762      0.1150    54.5      69.33      <.0001

treatment    T              8.0294      0.1029    54.8      78.02      <.0001

Regard

dixit

ElMaestro
★★★

Denmark,
2010-03-25 08:44
(5508 d 12:48 ago)

@ dixit
Posting: # 4969
Views: 10,991

Convergence problem in PROC MIXED

Post reply

Hi dixit,

looks to me like it fits an intra-T sigma component, which makes no sense.
My guess is accordingly that the model is mis-specified in that. I do not know how the power's Al Gore Rhythms work, but in the case of the intra-T it will (should!) make no difference on the likelihood to fiddle with it, which I am sure would be caught with a warning before spitting out a result.

Sorry, I am of not help (Should actually make that a standard sentence in my signature).

EM.

d_labes
★★★

Berlin, Germany,
2010-03-25 10:15
(5508 d 11:18 ago)

@ dixit
Posting: # 4970
Views: 11,180

Bogus PROC MIXED/FDA

Post reply

Dear dixit,

I fully agree with EM.

IMHO Proc MIXED stops here with arbitrary values for the inter-inividual variance parameters and also with arbitrary intra-individual variability for Test. An indication is:

❝ Estimated G Matrix

❝

❝ Row Effect treatment subject Col1 Col2


❝   1    treatment    R             1           0.4529      0.4233   CV_inter=75.7%

❝   2    treatment    T             1           0.4233      0.5232   CV_inter=82.9%

❝                                                                    

❝         Covariance Parameter Estimates
❝ 
❝ Cov Parm     Subject    Group          Estimate
❝ ...
❝ Residual     subject    treatment R      0.6289  CV_intra=93.6%
❝ Residual     subject    treatment T     0.09081  CV_intra=30.8%

❝

Do you really believe that your Test preparation has such a very lower intra-individual variability? If it is the same drug I can't imagine that at all :no:

.

Once again said, the FDA model is over-specified for the partial replicate design. And therefore the model fit with Proc MIXED is not reliable.
We had this phenomenon already here were SAS Proc MIXED and WINNONLIN gave totally different values for the covariance parameters.

What to the rescue?

Within a model formulation in Proc MIXED I don't know, as I already said. I have the strong believe (but believe is not The power to know :-D

) that it is impossible to get a solution within that because we have a confounding between the subject-by-formulation interaction (an inter-individual term) and the intra-individual variability of the Reference in the design used here.

I would suggest you to go with the so called "Methods of moments".
See

^[1]R.J. McNally
Tests for Individual and Population Bioequivalence Using 3-Period Crossover Designs

which can be found here for the necessary statistics within a partial replicate design.
They can be used also in the framework of ABE and scaled ABE. Your intention I guess?

Or neglect any subject-by-formulation interaction and go with the classical model (same as for a 2x2 cross-over) to obtain the ABE 90% confidence intervals and estimate independently the intra-individual variability of the Reference using the intra-subject contrasts (R-R')/sqrt(2).

Good luck.
BTW: Seems no m on your keyboard :-)

—
Regards,

Detlew

ElMaestro
★★★

Denmark,
2010-03-25 11:42
(5508 d 09:51 ago)

@ d_labes
Posting: # 4971
Views: 11,028

Bogus PROC MIXED/FDA

Post reply

Hi dixit and migthy oracle,

❝ What to the rescue?

Imho, what we need is at least a covariance matrix which has a common error sigma squared on the diagonal, zero's elsewhere, and where a sigmaR squared is added on all of the elements corresponding to a (the, one) same person receiving R. Can be souped up with a within-subject-but-between-treatments-sigma squared, too, depending on other preferences.
But how :ponder:

?

Best regards
EM.

d_labes
★★★

Berlin, Germany,
2010-03-26 10:45
(5507 d 10:48 ago)

@ ElMaestro
Posting: # 4975
Views: 11,132

Bogus PROC MIXED/FDA

Post reply

Grosser Meister!

❝ But how :ponder: ?

Thats the question!
Just to cite myself: "I have the strong believe ...". See above.

Without really understanding the AlGore rhythms for REML as a "statistical amateur" (stolen from Helmut :cool:

) the overall variance matrix, which is part of the likelihood, which is maximised or equivalently -log likelihood is minimised ... :blahblah:

is

V= Z*G*Z^t + R

where the intra-individual variance parameter go into R matrix and the inter-individual go into G. There is no possibility within Proc MIXED, and I suppose also in other real mixed model software, to parameterize a interdependence between both. And such an interdependence we have.

Just a short outline (according to McNally's paper, citation above):
From the values of Test -> total variability of T = var(between-T)+var(within-T)
From the subject mean values of Ref -> total variability of R = var(between-R)+var(within-R)/2
From R-R -> within variability of R = var(within-R)
From T-R -> var(diff) = var(SxF) + var(within-T) + 0.5*var(within-R)

red: not separable between and within terms because of
var(SxF)=var(between-T)+var(between-R)-2*cov(between-T,between-R)

Thats the basis of my strong believe.

—
Regards,

Detlew

shri ☆ 2010-04-05 10:01 (5497 d 12:32 ago) @ dixit Posting: # 5017 Views: 10,898	Convergence problem in PROC MIXED Post reply
	❝ "there are two or more observations from one subject which have identical effect values" its sound like u got two or more same values of Cmax for same subject. if that is the case then u have to take first cmax value. then run your proc mixed again. — shri

d_labes
★★★

Berlin, Germany,
2010-03-22 10:50
(5511 d 10:43 ago)

@ dixit
Posting: # 4955
Views: 11,127

partial replicate?

Post reply

Dear dixit, ambati?,

I guess your design is eventually a partially replicate design (only Reference replicated, RTR/TRR/RRT)?

In that design one would expect sigma²_T not identifiable because Test was not administered replicated.
Then using the FDA code results in over-specifying the model. See this thread.
One hint for this is the result for residual Test in your output above.

But don't ask me for an other implementation in SAS for that design. I was up to now not able to figure it out and had also not been successful in finding a reference. Sorry :crying:

—
Regards,

Detlew