NONLINEAR MIXED EFFECTS MODEL PROGRAM (NONMEM) VERSION 7.4.1
ORIGINALLY DEVELOPED BY STUART BEAL, LEWIS SHEINER, AND ALISON BOECKMANN
CURRENT DEVELOPERS ARE ROBERT BAUER, ICON DEVELOPMENT SOLUTIONS,
AND ALISON BOECKMANN. IMPLEMENTATION, EFFICIENCY, AND STANDARDIZATION
PERFORMED BY NOUS INFOSYSTEMS.

PROBLEM NO.:         1
THEOPHYLLINE ORAL

DATA CHECKOUT RUN:              NO
DATA SET LOCATED ON UNIT NO.:    2
THIS UNIT TO BE REWOUND:        NO
NO. OF DATA RECS IN DATA SET:      132
NO. OF DATA ITEMS IN DATA SET:   4
ID DATA ITEM IS DATA ITEM NO.:   1
DEP VARIABLE IS DATA ITEM NO.:   3

LABELS FOR DATA ITEMS:
ID TIME DV BWT

FORMAT FOR DATA:
(4E6.0)

TOT. NO. OF OBS RECS:      132
TOT. NO. OF INDIVIDUALS:       12

LENGTH OF THETA:   3

DEFAULT THETA BOUNDARY TEST OMITTED:    NO

OMEGA HAS BLOCK FORM:
 1
 1  1
 1  1  1

DEFAULT OMEGA BOUNDARY TEST OMITTED:    NO

SIGMA HAS SIMPLE DIAGONAL FORM WITH DIMENSION:   2

DEFAULT SIGMA BOUNDARY TEST OMITTED:    NO

INITIAL ESTIMATE OF THETA:
LOWER BOUND    INITIAL EST    UPPER BOUND
 0.0000E+00     0.2000E+01     0.1000E+07
 0.0000E+00     0.5000E+02     0.1000E+07
 0.0000E+00     0.1000E+00     0.1000E+07

INITIAL ESTIMATE OF OMEGA:
BLOCK SET NO.   BLOCK                                                                    FIXED
       1                                                                                   NO
                 0.2000E+00
                 0.1000E+00   0.2000E+00
                 0.1000E+00   0.1000E+00   0.2000E+00

INITIAL ESTIMATE OF SIGMA:
0.1000E+00
0.0000E+00   0.1000E+00

COVARIANCE STEP OMITTED:        NO
R MATRIX PRINTED:              YES
S MATRIX PRINTED:              YES
EIGENVLS. PRINTED:             YES
SPECIAL COMPUTATION:            NO
COMPRESSED FORMAT:              NO
GRADIENT METHOD USED:       SLOW
SIGDIGITS ETAHAT (SIGLO):                  -1
SIGDIGITS GRADIENTS (SIGL):                -1
EXCLUDE COV FOR FOCE (NOFCOV):              NO
TURN OFF Cholesky Transposition of R Matrix (CHOLROFF): NO
KNUTHSUMOFF:                                -1
RESUME COV ANALYSIS (RESUME):               NO
SIR SAMPLE SIZE (SIRSAMPLE):              -1
NON-LINEARLY TRANSFORM THETAS DURING COV (THBND): 1
PRECONDTIONING CYCLES (PRECOND):        0
PRECONDTIONING TYPES (PRECONDS):        TOS
FORCED PRECONDTIONING CYCLES (PFCOND):0
PRECONDTIONING TYPE (PRETYPE):        0
FORCED POS. DEFINITE SETTING: (FPOSDEF):0

TABLES STEP OMITTED:    NO
NO. OF TABLES:           1
SEED NUMBER (SEED):    11456
RANMETHOD:             3U
MC SAMPLES (ESAMPLE):    300
WRES SQUARE ROOT TYPE (WRESCHOL): EIGENVALUE

-- TABLE   1 --

RECORDS ONLY:    FIRSTONLY

4 COLUMNS APPENDED:    NO
PRINTED:               YES
FORMAT:                S1PE11.4
LFORMAT:
RFORMAT:
FIXED_EFFECT_ETAS:

USER-CHOSEN ITEMS:
ID ETA1 ETA2 ETA3



#TBLN:      1
#METH: Laplacian Conditional Estimation with Interaction

ESTIMATION STEP OMITTED:                 NO
ANALYSIS TYPE:                           POPULATION
NUMBER OF SADDLE POINT RESET ITERATIONS:      0
GRADIENT METHOD USED:               SLOW
CONDITIONAL ESTIMATES USED:              YES
CENTERED ETA:                            NO
EPS-ETA INTERACTION:                     YES
LAPLACIAN OBJ. FUNC.:                    YES
NUMERICAL 2ND DERIVATIVES:               YES
NO. OF FUNCT. EVALS. ALLOWED:            9999
NO. OF SIG. FIGURES REQUIRED:            3
INTERMEDIATE PRINTOUT:                   YES
ESTIMATE OUTPUT TO MSF:                  NO
IND. OBJ. FUNC. VALUES SORTED:           NO
NUMERICAL DERIVATIVE
      FILE REQUEST (NUMDER):               NONE
MAP (ETAHAT) ESTIMATION METHOD (OPTMAP):   0
ETA HESSIAN EVALUATION METHOD (ETADER):    0
INITIAL ETA FOR MAP ESTIMATION (MCETA):    0
SIGDIGITS FOR MAP ESTIMATION (SIGLO):      100
GRADIENT SIGDIGITS OF
      FIXED EFFECTS PARAMETERS (SIGL):     100
NOPRIOR SETTING (NOPRIOR):                 OFF
NOCOV SETTING (NOCOV):                     OFF
DERCONT SETTING (DERCONT):                 OFF
FINAL ETA RE-EVALUATION (FNLETA):          ON
EXCLUDE NON-INFLUENTIAL (NON-INFL.) ETAS
      IN SHRINKAGE (ETASTYPE):             NO
NON-INFL. ETA CORRECTION (NONINFETA):      OFF
RAW OUTPUT FILE (FILE): THEO-LAPLI.ext
EXCLUDE TITLE (NOTITLE):                   NO
EXCLUDE COLUMN LABELS (NOLABEL):           NO
FORMAT FOR ADDITIONAL FILES (FORMAT):      S1PE12.5
PARAMETER ORDER FOR OUTPUTS (ORDER):       TSOL
WISHART PRIOR DF INTERPRETATION (WISHTYPE):0
KNUTHSUMOFF:                               0
INCLUDE LNTWOPI:                           NO
INCLUDE CONSTANT TERM TO PRIOR (PRIORC):   NO
INCLUDE CONSTANT TERM TO OMEGA (ETA) (OLNTWOPI):NO
ADDITIONAL CONVERGENCE TEST (CTYPE=4)?:    NO
EM OR BAYESIAN METHOD USED:                 NONE


THE FOLLOWING LABELS ARE EQUIVALENT
PRED=PREDI
RES=RESI
WRES=WRESI
IWRS=IWRESI
IPRD=IPREDI
IRS=IRESI

MONITORING OF SEARCH:



ITERATION NO.:    0    OBJECTIVE VALUE:   194.101735812272        NO. OF FUNC. EVALS.:  12
CUMULATIVE NO. OF FUNC. EVALS.:       12
NPARAMETR:  2.0000E+00  5.0000E+01  1.0000E-01  2.0000E-01  1.0000E-01  1.0000E-01  2.0000E-01  1.0000E-01  2.0000E-01  1.0000E-01
            1.0000E-01
PARAMETER:  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01  1.0000E-01
            1.0000E-01
GRADIENT:   2.6107E+00  3.1419E+01  1.0573E+01 -5.4831E+00  1.1147E+01  2.4197E+01  8.1076E+00 -6.9286E+00  1.1212E+01  1.1203E+02
            1.9184E+01


ITERATION NO.:   27    OBJECTIVE VALUE:   93.5587038455012        NO. OF FUNC. EVALS.: 374
CUMULATIVE NO. OF FUNC. EVALS.:      386
NPARAMETR:  1.5052E+00  3.2295E+01  8.7304E-02  4.3732E-01  5.6344E-02 -4.6835E-03  1.8685E-02  1.2644E-02  1.9830E-02  1.7716E-02
            7.5581E-02
PARAMETER: -1.8423E-01 -3.3711E-01 -3.5773E-02  4.9118E-01  3.8103E-02 -3.1673E-03 -1.1874E+00  9.6000E-02 -1.6034E+00 -7.6535E-01
           -3.9983E-02
GRADIENT:  -3.2056E-03  6.6289E-03  1.8981E-02 -2.1097E-04 -1.0645E-02  9.9893E-03 -1.8771E-04  1.4852E-03  2.4916E-04 -2.0151E-03
           -3.1343E-04

#TERM:

MINIMIZATION SUCCESSFUL
NO. OF FUNCTION EVALUATIONS USED:      386
NO. OF SIG. DIGITS IN FINAL EST.:  3.4

ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES,
AND THE P-VALUE IS GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0.

ETABAR:        -2.6231E-02 -1.3601E-04  5.0887E-03
SE:             1.8001E-01  3.7369E-02  3.7639E-02
N:                      12          12          12

P VAL.:         8.8414E-01  9.9710E-01  8.9246E-01

ETASHRINKSD(%)  1.5137E+00  1.0879E+00  3.2920E+00
ETASHRINKVR(%)  3.0044E+00  2.1639E+00  6.4756E+00
EBVSHRINKSD(%)  3.1146E+00  4.7110E+00  7.3754E+00
EBVSHRINKVR(%)  6.1321E+00  9.2000E+00  1.4207E+01
EPSSHRINKSD(%)  7.9965E+00  8.7624E+00
EPSSHRINKVR(%)  1.5354E+01  1.6757E+01


TOTAL DATA POINTS NORMALLY DISTRIBUTED (N):          132
N*LOG(2PI) CONSTANT TO OBJECTIVE FUNCTION:    242.59977276603360
OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT:    93.558703845501213
OBJECTIVE FUNCTION VALUE WITH CONSTANT:       336.15847661153481
REPORTED OBJECTIVE FUNCTION DOES NOT CONTAIN CONSTANT

TOTAL EFFECTIVE ETAS (NIND*NETA):                            36

#TERE:
Elapsed estimation  time in seconds:     0.81
Elapsed covariance  time in seconds:     0.53
Elapsed postprocess time in seconds:     0.00





















************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
#OBJT:**************                       MINIMUM VALUE OF OBJECTIVE FUNCTION                      ********************
********************                                                                                ********************
************************************************************************************************************************






#OBJV:********************************************       93.559       **************************************************

************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                             FINAL PARAMETER ESTIMATE                           ********************
********************                                                                                ********************
************************************************************************************************************************



THETA - VECTOR OF FIXED EFFECTS PARAMETERS   *********


        TH 1      TH 2      TH 3

        1.51E+00  3.23E+01  8.73E-02



OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS  ********


        ETA1      ETA2      ETA3

ETA1    4.37E-01

ETA2    5.63E-02  1.87E-02

ETA3   -4.68E-03  1.26E-02  1.98E-02



SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS  ****


        EPS1      EPS2

EPS1    1.77E-02

EPS2    0.00E+00  7.56E-02




OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS  *******


        ETA1      ETA2      ETA3

ETA1    6.61E-01

ETA2    6.23E-01  1.37E-01

ETA3   -5.03E-02  6.57E-01  1.41E-01



SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS  ***


        EPS1      EPS2

EPS1    1.33E-01

EPS2    0.00E+00  2.75E-01


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                            STANDARD ERROR OF ESTIMATE                          ********************
********************                                                                                ********************
************************************************************************************************************************



THETA - VECTOR OF FIXED EFFECTS PARAMETERS   *********


        TH 1      TH 2      TH 3

        2.92E-01  1.57E+00  3.98E-03



OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS  ********


        ETA1      ETA2      ETA3

ETA1    2.19E-01

ETA2    3.58E-02  9.34E-03

ETA3    2.14E-02  9.08E-03  1.79E-02



SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS  ****


        EPS1      EPS2

EPS1    8.72E-03

EPS2   .........  7.08E-02




OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS  *******


        ETA1      ETA2      ETA3

ETA1    1.66E-01

ETA2    2.58E-01  3.41E-02

ETA3    2.26E-01  3.84E-01  6.35E-02



SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS  ***


        EPS1      EPS2

EPS1    3.27E-02

EPS2   .........  1.29E-01


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                          COVARIANCE MATRIX OF ESTIMATE                         ********************
********************                                                                                ********************
************************************************************************************************************************


           TH 1      TH 2      TH 3      OM11      OM12      OM13      OM22      OM23      OM33      SG11      SG12      SG22


TH 1    8.52E-02

TH 2    2.26E-01  2.46E+00

TH 3   -2.31E-04  8.75E-04  1.58E-05

OM11    3.91E-02  1.04E-01  1.30E-04  4.80E-02

OM12    5.29E-03 -7.13E-03  2.08E-05  6.48E-03  1.28E-03

OM13    4.43E-04  2.01E-03 -2.42E-05 -1.26E-03 -6.88E-05  4.59E-04

OM22   -4.17E-04  5.12E-04  1.97E-05  6.42E-04  1.42E-04 -1.53E-05  8.71E-05

OM23    2.52E-04  6.87E-04 -3.03E-05 -5.49E-04 -1.22E-04  8.40E-05 -4.77E-05  8.25E-05

OM33    7.12E-04 -6.48E-03 -5.52E-05 -7.17E-04 -1.13E-04 -2.41E-05 -9.89E-05  1.28E-04  3.20E-04

SG11   -5.63E-04  4.89E-04  1.97E-05 -4.25E-04 -5.89E-05  1.35E-05  1.86E-05 -4.22E-05 -1.05E-04  7.60E-05

SG12   ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

SG22    2.30E-03 -3.15E-02 -2.17E-04 -2.24E-03 -2.90E-04 -1.55E-04 -3.98E-04  4.70E-04  1.24E-03 -4.75E-04 .........  5.02E-03


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                          CORRELATION MATRIX OF ESTIMATE                        ********************
********************                                                                                ********************
************************************************************************************************************************


           TH 1      TH 2      TH 3      OM11      OM12      OM13      OM22      OM23      OM33      SG11      SG12      SG22


TH 1    2.92E-01

TH 2    4.94E-01  1.57E+00

TH 3   -1.99E-01  1.40E-01  3.98E-03

OM11    6.12E-01  3.01E-01  1.50E-01  2.19E-01

OM12    5.06E-01 -1.27E-01  1.46E-01  8.25E-01  3.58E-02

OM13    7.09E-02  5.98E-02 -2.84E-01 -2.69E-01 -8.97E-02  2.14E-02

OM22   -1.53E-01  3.50E-02  5.32E-01  3.14E-01  4.25E-01 -7.67E-02  9.34E-03

OM23    9.52E-02  4.82E-02 -8.38E-01 -2.76E-01 -3.75E-01  4.32E-01 -5.63E-01  9.08E-03

OM33    1.36E-01 -2.31E-01 -7.76E-01 -1.83E-01 -1.76E-01 -6.28E-02 -5.92E-01  7.85E-01  1.79E-02

SG11   -2.21E-01  3.58E-02  5.68E-01 -2.22E-01 -1.88E-01  7.24E-02  2.28E-01 -5.34E-01 -6.71E-01  8.72E-03

SG12   ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

SG22    1.11E-01 -2.83E-01 -7.71E-01 -1.45E-01 -1.14E-01 -1.02E-01 -6.02E-01  7.30E-01  9.77E-01 -7.70E-01 .........  7.08E-02


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                      INVERSE COVARIANCE MATRIX OF ESTIMATE                     ********************
********************                                                                                ********************
************************************************************************************************************************


           TH 1      TH 2      TH 3      OM11      OM12      OM13      OM22      OM23      OM33      SG11      SG12      SG22


TH 1    6.04E+02

TH 2   -7.23E+01  1.12E+01

TH 3    3.05E+04 -3.33E+03  1.99E+06

OM11    1.18E+03 -1.76E+02  5.90E+04  4.04E+03

OM12   -1.01E+04  1.47E+03 -4.92E+05 -3.12E+04  2.47E+05

OM13    5.07E+03 -8.37E+02  2.46E+05  2.23E+04 -1.68E+05  1.39E+05

OM22    2.45E+04 -2.87E+03  1.33E+06  5.92E+04 -4.80E+05  2.87E+05  1.16E+06

OM23    5.82E+03  3.09E+02  5.66E+05 -2.78E+04  1.80E+05 -2.66E+05  7.25E+04  1.29E+06

OM33   -4.70E+04  4.75E+03 -2.74E+06 -9.09E+04  7.56E+05 -3.69E+05 -2.13E+06 -8.84E+05  4.52E+06

SG11    3.18E+04 -3.29E+03  1.87E+06  7.31E+04 -5.85E+05  3.37E+05  1.55E+06  3.36E+05 -3.08E+06  2.24E+06

SG12   ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

SG22    1.67E+04 -1.80E+03  9.62E+05  3.83E+04 -3.09E+05  1.78E+05  7.94E+05  1.49E+05 -1.57E+06  1.12E+06 .........  5.69E+05






















************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                      EIGENVALUES OF COR MATRIX OF ESTIMATE                     ********************
********************                                                                                ********************
************************************************************************************************************************


            1         2         3         4         5         6         7         8         9        10        11

        2.02E-04  2.86E-03  2.65E-02  1.49E-01  2.14E-01  2.75E-01  6.49E-01  1.05E+00  1.54E+00  2.54E+00  4.55E+00


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                                     R MATRIX                                   ********************
********************                                                                                ********************
************************************************************************************************************************


           TH 1      TH 2      TH 3      OM11      OM12      OM13      OM22      OM23      OM33      SG11      SG12      SG22


TH 1    1.94E+01

TH 2   -2.30E+00  7.15E-01

TH 3    2.10E+02 -4.05E+01  4.59E+04

OM11   -3.77E-01 -5.48E-01  1.82E+02  6.88E+01

OM12   -1.27E+01  6.73E+00 -1.71E+03 -3.68E+02  3.40E+03

OM13    4.76E+00 -3.19E+00  7.36E+02  1.09E+02 -6.82E+02  1.42E+03

OM22    1.96E+01 -1.08E+01  2.53E+03  4.20E+02 -5.70E+03  7.62E+02  1.96E+04

OM23    6.54E+00  2.87E+00 -5.53E+02 -2.59E+02  2.71E+03 -3.97E+03 -6.29E+03  2.51E+04

OM33   -1.17E+01  2.84E+00 -8.57E+02  7.24E+01 -7.01E+02  1.40E+03  1.62E+03 -5.88E+03  6.45E+03

SG11    8.71E+01 -2.44E+01  3.49E+03  1.99E+02 -2.16E+03  1.25E+03  7.43E+03 -8.91E+03  3.67E+03  8.97E+04

SG12   ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

SG22   -1.21E+01  5.31E-02 -1.02E+02  4.90E+01 -5.20E+02  3.34E+02  1.68E+03 -2.33E+03  7.84E+02  6.61E+03 .........  1.41E+03


************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                                     S MATRIX                                   ********************
********************                                                                                ********************
************************************************************************************************************************


           TH 1      TH 2      TH 3      OM11      OM12      OM13      OM22      OM23      OM33      SG11      SG12      SG22


TH 1    1.89E+01

TH 2   -2.33E+00  7.18E-01

TH 3    2.38E+02 -4.10E+01  4.48E+04

OM11   -5.01E+00  3.21E+00  2.79E+02  4.44E+01

OM12    1.47E+02 -2.55E+01 -2.56E+03 -2.10E+02  2.86E+03

OM13    2.04E+01 -5.40E+00 -6.68E+02 -5.25E+01  3.69E+02  1.49E+02

OM22   -3.17E+02  2.70E+01  9.94E+03  2.86E+02 -6.61E+03 -6.15E+02  2.06E+04

OM23   -5.71E+01  4.18E+01 -6.41E+03  2.46E+02  9.65E+01 -3.19E+02 -4.67E+03  8.27E+03

OM33   -5.02E+01 -4.26E+00 -1.65E+04 -2.34E+02  1.07E+03  6.60E+02 -2.62E+03 -1.58E+03  1.01E+04

SG11    3.47E+02 -1.76E+02  3.97E+04 -8.13E+02 -5.85E+03  1.65E+03  2.18E+04 -2.60E+04 -9.82E+02  2.76E+05

SG12   ......... ......... ......... ......... ......... ......... ......... ......... ......... ......... .........

SG22   -3.98E+01 -9.11E+00 -7.05E+03 -1.54E+02  1.38E+02  3.44E+02  6.85E+01 -2.25E+03  5.28E+03  1.05E+04 .........  3.34E+03






















************************************************************************************************************************
********************                                                                                ********************
********************                LAPLACIAN CONDITIONAL ESTIMATION WITH INTERACTION               ********************
********************                          TABLES OF DATA AND PREDICTIONS                        ********************
********************                                                                                ********************
************************************************************************************************************************

TABLE NO.  1



LINE NO.ID        ETA1      ETA2      ETA3

   1    1.00E+00 -1.28E-01 -1.96E-01 -2.71E-01

   2    2.00E+00  3.23E-01  6.17E-02  4.51E-02

   3    3.00E+00  3.97E-01  4.59E-02 -7.58E-03

   4    4.00E+00 -3.57E-01 -3.85E-02  1.81E-02

   5    5.00E+00 -3.67E-02 -1.01E-01 -9.84E-02

   6    6.00E+00 -4.97E-01  1.34E-01  2.41E-01

   7    7.00E+00 -8.78E-01  3.23E-03  1.51E-01

   8    8.00E+00 -8.33E-02  6.90E-02  8.62E-02

   9    9.00E+00  1.32E+00  1.77E-01 -4.50E-03

  10    1.00E+01 -7.23E-01 -2.10E-01 -1.48E-01

  11    1.10E+01  8.51E-01  1.77E-01  8.45E-02

  12    1.20E+01 -5.02E-01 -1.24E-01 -3.46E-02

Elapsed finaloutput time in seconds:     0.02
#CPUT: Total CPU Time in Seconds,        1.328
