From:  "Emily"  
Subject:  [NMusers] Error message.. 
Date:  Thu, March 7, 2002 6:04 am   


Dear NONMEM users: 
Is ther anyone can give me advice? 
What should I do if I got following error messages? 
  
0MINIMIZATION SUCCESSFUL
 NO. OF FUNCTION EVALUATIONS USED:  354
 NO. OF SIG. DIGITS IN FINAL EST.:  3.3
0R MATRIX ALGORITHMICALLY SINGULAR
0COVARIANCE MATRIX UNOBTAINABLE 
  
and the results content a "T Matrix". 
What is "T Matrix" ? 
  
Thaks a lot !!  
 

*******

From:"Sam Liao"   
Subject:RE: [NMusers] Error message..  
Date:Thu, March 7, 2002 7:53 am  


Hi Emily: 
  
Could you please show your control stream and some brief description
of what kind of data you have to give us more clue? 


Best regards,



Sam Liao, Ph.D.
PharMax Research
270 Kerry Lane,
Blue Bell, PA 19422
phone: 215-6541151
efax: 1-720-2946783

*******


From:"Kowalski, Ken"   
Subject:RE: [NMusers] Error message..  
Date:Thu, March 7, 2002 8:22 am  


Emily, 
  
The R matrix singular condition is an indication that your
model is over-parameterized, i.e., an infinite set of parameter values
in Theta, Omega and Sigma can result in the same value of the Objective Function.
I suggest that you re-check the coding of your model to verify that it is
correct and what you intended.  If that is fine, you may have to reduce your model.
If you can provide the control stream as Sam suggests I'm sure
one or more NMUSERs will be happy to provide you
some suggestions on modifying your model. 
  
Regarding the T matrix I could not find any description of it in
the NONMEM user's guides.  Does anyone out there know?
I believe it is only reported when the R matrix singular condition
arises and presumably is a diagnostic that can help determine
the nature of the singularity. 
  
Ken  
 



*******

From:"Amir A. Tahami"   
Subject:Re: [NMusers] Error message..  
Date:Thu, March 7, 2002 11:31 am  


Dear Emily,

        The variance-covariance matrix (the precision of the parameter
estimates) is computed from the R and  S  matrices [$covariance].  Error
messages from the covariance step indicating that these matrices are not
positive definite or are singular indicate that the minimization routine
may not have found a true minimum.  When the S matrix is singular,
NONMEM attempts to  compute  and  display  a related matrix, the T
matrix. This matrix in turn can be used to define a confidence region of
the parameter space.
Ref.: please see "covariance matrix of estimate" in nmhelp.

        T matrix helps the geometric transformation, can avoid unwanted
translation introduced when we scale or rotate an object not centered at
origin.

Best regards,
Amir A. Tahami


*******


From:"Ludden, Thomas"   
Subject:[NMusers] T Matrix  
Date:Thu, March 7, 2002 2:02 pm


Dear nmusers,

The following is provided by Dr. Stuart Beal in response to the inquiry
about the T matrix.

Tom Ludden

_________________________________________________________________
_________________________________________________________________




On occasion, people want a little more information about the T matrix
that sometimes appears in output from the Covariance Step.
Here is an updated help item from the current NONMEM Version VI (under
development).  It notes that the T matrix can be output when
either the R or S matrix is singular.  In such a case, in order to obtain
information about just where the singularity is located, one should
examine the R or S matrix itself.

Stuart Beal

 -------------------------------------------------------------------
 |                                                                 |
 |                    COVARIANCE MATRIX OF ESTIMATE                |
 |                                                                 |
 ------------------------------------------------------------------

 MEANING: NONMEM's estimate of the precision of its parameter estimates
 CONTEXT: NONMEM output

 DISCUSSION:
 From asymptotic statistical theory, the distribution of the  parameter
 estimates  is  multivariate  normal, with a variance-covariance matrix
 that can be estimated from the data.  NONMEM supplies such an estimate
 of  the variance-covariance matrix.  This matrix is not to be confused
 with either SIGMA, the covariance matrix for the second  level  random
 effects, or with OMEGA, the covariance matrix for the first level ran-
 dom effects.  These two matrices estimate the variability of  epsilons
 or  etas,  respectively,  about  their means.  The variance-covariance
 matrix of the parameter estimates, on the  other  hand,  measures  the
 variability  under the assumed model of the parameter estimates across
 (imagined) replicated data sets, using the design  of  the  real  data
 set.   The  following  is  an  example of the NONMEM output giving the
 estimate of the variance-covariance matrix.

 **************** COVARIANCE MATRIX OF ESTIMATE  ********************
             TH 1      TH 2      OM11      OM12      OM22      SG11

  TH 1    3.94E+01
  TH 2   -6.89E+00  3.67E+02
  OM11   -4.31E-02  3.17E-02  -2.92E-04
  OM12   ......... ......... ......... .........
  OM22    8.65E-02 -5.05E-01  2.71E-04 .........  1.26E-02
  SG11   -1.01E-02 -1.85E-02 -2.11E-05 ......... -3.10E-04  3.10E-05

 The matrix (which is symmetric) is given in lower triangular form.  In
 this  example,  the 2x2 matrix, OMEGA, was constrained to be diagonal;
 the omitted entries  above  (.........)  indicate  that  OM12  is  not
 estimated,  and  consequently  has  no corresponding row/column in the
 variance-covariance matrix.  When the size of the array exceeds 75x75,
 a  compressed form is printed in which the omitted entries (.........)
 are not printed.  The compressed form may also be requested for arrays
 smaller than 75x75 (See $covariance).

 The (estimated) variance-covariance matrix is computed from the R  and
 S  matrices;  it  is  Rinv*S*Rinv,  where Rinv is the inverse of the R
 matrix.  The R matrix is the Hessian matrix of the objective function,
 evaluated  at  the  parameter  estimates.  The S matrix is obtained by
 adding the cross-product gradient vectors of the  objective  function,
 evaluated at the parameter estimates, across the individual records of
 the data set.

 The  inverse  variance-covariance  matrix  R*Sinv*R  is  also   output
 (labeled  as the Inverse Covariance Matrix), where Sinv is the inverse
 of the S matrix. This matrix can be used to develop a joint confidence
 region  for  the complete set of population parameters.  As we usually
 develop a confidence region for  a  very  limited  set  of  population
 parameters,  this  use  of  the  inverse variance-covariance matrix is
 somewhat limited.

 An error message from the Covariance Step stating that the R matrix is
 not  positive  semidefinite  indicates that the parameter estimates do
 not correspond to a true (local) minimum and are not  to  be  trusted.
 An  error  message stating that the R matrix is positive semidefinite,
 but singular, indicates that the  objective  function  is  flat  in  a
 neighborhood  of  the  parameter  estimate,  and so the minimum is not
 really unique, and there is  probably  some  overparameterization.  An
 error  message  stating that the S matrix is singular indicates strong
 overparameterization.

 When the S matrix is judged to be singular, but the R matrix is  posi-
 tive  definite,  the  T  matrix,  R*Spinv*R,  where Spinv is a pseudo-
 inverse of  the  S  matrix,  is  output.  Just  as  with  the  inverse
 variance-covariance  matrix,  T  can be used to develop a joint confi-
 dence region for the complete set of population parameters.

 When the R matrix is judged to be singular, but S is nonsingular,  the
 T  matrix,  R*Sinv*R,  is  output.  (This cannot be called the inverse
 covariance matrix, as the covariance matrix does not exist.)  Just  as
 with  the inverse variance-covariance matrix, T can be used to develop
 a joint confidence region for the complete set of  population  parame-
 ters.

 There are options that allow the variance-covariance matrix to be com-
 puted  as either Rinv or Sinv.  Asymptotic statistical theory suggests
 that these matrices are appropriate under  the  additional  assumption
 that the objective function is indeed additively proportional to minus
 twice the likelihood function for the data.

 (See standard error of estimate, correlation matrix of estimate).

 REFERENCES: Guide I, section C.3.5.2 (p. 20)
 REFERENCES: Guide II, section D.2.5 (p. 21)
 REFERENCES: Guide V, section 5.4 (p. 43), 13.3 (p. 145)

*******

From:"Emily"   
Subject:[NMusers] Error message (continued..)  
Date:Fri, March 8, 2002 2:41 am  


Dear nmusers: 
Thanks for everyone trying help me !! 
Here is my control files: 
  
$PROB 1
$INPUT ID AGE SEX HT WT DATE=DROP EVID TIME AMT SS II DV MDV CBZ VAL
$DATA data
$SUBR ADVAN6 TOL=3 
  
$MODEL COMP=(DEPOT, DEFDOS), COMP=(CENTRAL, DEFOBS) 
  
$PK
 TVVM=THETA(1)
 TVKM=THETA(2)
 VM=TVVM*(1+ETA(1))
 KM=TVKM*(1+ETA(2))
 K12=THETA(3)
 V2=THETA(4) 
  
$DES
 C2=A(2)/V2
 DADT(1)=-K12*A(1)
 DADT(2)=K12*A(1)-VM*C2/(KM+C2) 
  
$ERROR
 Y=F+ERR(1) 
  
$THETA
 (0,400);  1 VM
 (0,4);     2 KM
 (0,0.0023);   3 K12
 (0,80);  4  V2 
  
$OMEGA 0.01, 0.01 
  
$SIGMA 40 
  
$EST NOABORT PRINT=1 
  
$TABLE ID AMT DV 
  
$COVARIANCE 
  
$SCATTER PRED VS DV UNIT
$SCATTER RES VS WT 
  

So, what can I do to improve it ? 
  
Thanks a lot !!  
 


*******

From:Nick Holford   
Subject:Re: [NMusers] Error message (continued..)  
Date:Fri, March 8, 2002 3:18 am 



Emily,

Looks like a reasonable model for oral phenytoin. I am guessing this is the primary
drug of interest because you have carbamazepine and valproate as covariates and your
inital estimate of Vmax=400 mg/d, Km=4 mg/L and V of 80L would be reasonable for
phenytoin. However, because the default units for TIME when you use DATE=DROP and
TIME with PREDPP are hours the initial estimate of Vmax would be 24 times too big.

However, irrespective of my guess for the drug I have difficulty with K12 (or Ka in
more usual terminology). You have an initial estimate of 0.0023 ie. an absorption
half-life of 301 h. I don't know of any oral formulation that would be described
reasonably by such a long half-life.

So my suggestion to you is first of all to think hard about the time units you are
using here. I very much doubt you can get any reasonable solution with these initial
estimate values.

Nick
 
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/