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/