PopED Results 

        2014-11-19 11:14:07

==============================================================================
Model description : PopED model 

Model Sizes : 
Number of individual model parameters                  g[j]    : Ng    = 6
Number of population model fixed parameters            bpop[j] : Nbpop = 5
Number of population model random effects parameters   b[j]    : Nb    = 2

Typical Population Parameters:
bpop[1]:   1.8 
bpop[2]:    20 
bpop[3]:     2 
bpop[4]:    25 
bpop[5]:     5 

Between Subject Variability matrix D (variance units) 
0.05 0.00
0.00 0.05

Diagonal Elements of D [sqrt(param)]:
D[1,1]:  0.05 [0.2236] 
D[2,2]:  0.05 [0.2236] 

Residual Unexplained Variability matrix SIGMA (variance units) : 
0.0150 0.0000
0.0000 0.0015

Diagonal Elements of SIGMA [sqrt(param)]:
SIGMA[1,1]: 0.015 [0.1225] 
SIGMA[2,2]: 0.0015 [0.03873] 

==============================================================================
Experiment description (design and design space)

Numer of individuals: 110
Number of groups (individuals with same design): 4
Numer of individuals per group:
     Group 1: 50
     Group 2: 20
     Group 3: 20
     Group 4: 20
Numer of samples per group:
     Group 1: 6
     Group 2: 6
     Group 3: 6
     Group 4: 6
Number of discrete experimental variables: 0
Number of model covariates: 1

Initial Sampling Schedule
Group 1 :      1      2      4      6      8     24
Group 2 :      1      2      4      6      8     24
Group 3 :      1      2      4      6      8     24
Group 4 :      1      2      4      6      8     24

Minimum allowed sampling values
Group 1 :  1e-05  1e-05  1e-05  1e-05  1e-05  1e-05
Group 2 :  1e-05  1e-05  1e-05  1e-05  1e-05  1e-05
Group 3 :  1e-05  1e-05  1e-05  1e-05  1e-05  1e-05
Group 4 :  1e-05  1e-05  1e-05  1e-05  1e-05  1e-05

Maximum allowed sampling values
Group 1 :     24     24     24     24     24     24
Group 2 :     24     24     24     24     24     24
Group 3 :     24     24     24     24     24     24
Group 4 :     24     24     24     24     24     24

Covariates  (min, max):
Group 1: 70 (1, 70)
Group 2: 60 (1, 70)
Group 3: 50 (1, 70)
Group 4: 10 (1, 70)

===============================================================================
Initial design evaluation

OFV = 4.40113e+20

Efficiency criterion [usually defined as OFV^(1/npar)]  = 196.666

Initial design expected parameter variance 
and relative standard error (%RSE)
    Parameter    Values   Variance       RSE
      bpop[1]    1.8000   4.61e+00    119.32
      bpop[2]   20.0000   2.06e-01      2.27
      bpop[3]    2.0000   6.25e+00    125.03
      bpop[4]   25.0000   4.65e+04    862.24
      bpop[5]    5.0000   4.67e+03   1366.14
       D[1,1]    0.0500   6.66e-05     16.32
       D[2,2]    0.0500   5.69e-05     15.08
   SIGMA[1,1]    0.0150   1.16e-06      7.19
   SIGMA[2,2]    0.0015   1.68e-07     27.36

==============================================================================
Criterion Specification

OFV calculation for FIM: 1 
  1=Determinant of FIM,
  4=log determinant of FIM,
  6=determinant of interesting part of FIM (Ds)

Approximation method: 0
  0=FO, 
  1=FOCE, 
  2=FOCEI, 
  3=FOI

Fisher Information Matrix type: 1
  0=Full FIM,
  1=Reduced FIM,
  2=weighted models,
  3=Loc models,
  4=reduced FIM with derivative of SD of sigma as pfim,
  5=FULL FIM parameterized with A,B,C matrices & derivative of variance,
  6=Calculate one model switch at a time, good for large matrices,
  7=Reduced FIM parameterized with A,B,C matrices & derivative of variance

Design family: 1
  D-family design (1) or 
  ED-familty design (0) 
  (with or without parameter uncertainty)

==============================================================================
Optimization of design parameters

* Optimize Sampling Schedule
* Optimize Covariates


*******************************
Initial Value
 OFV(mf) = 4.40113e+20
*******************************

RS - It. : 3   OFV : 3.45531e+21

*******************************
RS Results
 OFV(mf) = 3.45531e+21

Optimized Sampling Schedule
Group 1 :  1e-05  4.068  4.769  7.276  10.08     24
Group 2 :  1e-05  1e-05  3.584  4.715  7.189     24
Group 3 :  1e-05  1.128  4.734   7.12  10.96     24
Group 4 :  1e-05  5.165  6.189  6.795  7.076  20.17

Optimized Covariates:
Group 1: 70
Group 2: 58.7482
Group 3: 47.6796
Group 4: 6.71271

*********************************

SG - It. : 1  OFV : 3.686e+21   Diff. :     1
SG - It. : 2  OFV : 4.026e+21   Diff. : 0.09231
SG - It. : 3  OFV : 4.462e+21   Diff. : 0.1083

SG - Iteration 3 --------- FINAL -------------------------
Normalized gradient: Grad_xt(OFV)/OFV
-0.00774768 -0.00906787 -0.00854762 -0.00739714 -0.00784279 -0.00218623 
0.000125787 0.000125815 -0.000902021 -0.000546318 0.00113247 -0.00466057 
-0.0117848 -0.0136561 -0.00549696 -0.00159097 0.00633858 0.0252649 
0.0741163 -0.0542747 0.0229163 0.04597 0.0314447 2.57335e-09 
xt opt:
3.96854 1e-05 4.6695 7.17683 9.98091 23.9005 
0.0415792 0.0415792 3.48457 7.15786 4.74623 23.9005 
1.02801 1e-05 4.63437 7.02062 11.057 24 
6.28806 1e-05 5.26418 6.89439 7.17529 20.2182 
Normalized gradient: Grad_a(OFV)/OFV
1.376445e-01
-1.075760e-01
-4.150399e-01
-1.745777e-01
aopt:
7.000000e+01
5.846212e+01
4.739349e+01
6.426619e+00
OFV(mf)    : 4.46186e+21
diff       : 0.108345
*************************************************************
*****************************
            Line Search

group 4 -- xt[4] changed from  6.89439 to  8.00001
     OFV(MF) changed from 4.46186e+21 to 4.55893e+21 
group 4 -- xt[4] changed from  8.00001 to  16
     OFV(MF) changed from 4.55893e+21 to 4.57697e+21 
group 4 -- xt[4] changed from  16 to  24
     OFV(MF) changed from 4.57697e+21 to 4.57697e+21 
group 4 -- xt[1] changed from  6.28806 to  1e-05
     OFV(MF) changed from 4.57697e+21 to 4.60205e+21 
group 4 -- xt[1] changed from  1e-05 to  8.00001
     OFV(MF) changed from 4.60205e+21 to 4.86297e+21 
group 4 -- xt[1] changed from  8.00001 to  16
     OFV(MF) changed from 4.86297e+21 to 4.88669e+21 
group 4 -- xt[1] changed from  16 to  24
     OFV(MF) changed from 4.88669e+21 to 4.88669e+21 
group 4 -- xt[5] changed from  7.17529 to  8.00001
     OFV(MF) changed from 4.88669e+21 to 4.96316e+21 
group 4 -- xt[5] changed from  8.00001 to  16
     OFV(MF) changed from 4.96316e+21 to 4.98998e+21 
group 4 -- xt[5] changed from  16 to  24
     OFV(MF) changed from 4.98998e+21 to 4.98998e+21 
group 4 -- xt[6] changed from  20.2182 to  24
     OFV(MF) changed from 4.98998e+21 to 4.98998e+21 
group 2 -- xt[1] changed from  0.0415792 to  1e-05
     OFV(MF) changed from 4.98998e+21 to 4.99015e+21 
group 2 -- xt[4] changed from  7.15786 to  24
     OFV(MF) changed from 4.99015e+21 to 5.03382e+21 
group 2 -- xt[3] changed from  3.48457 to  1e-05
     OFV(MF) changed from 5.03382e+21 to 5.06012e+21 
group 2 -- xt[2] changed from  0.0415792 to  1e-05
     OFV(MF) changed from 5.06012e+21 to 5.06019e+21 
group 2 -- xt[6] changed from  23.9005 to  24
     OFV(MF) changed from 5.06019e+21 to 5.06231e+21 
group 3 -- xt[1] changed from  1.02801 to  1e-05
     OFV(MF) changed from 5.06231e+21 to 5.12464e+21 
group 3 -- xt[4] changed from  7.02062 to  1e-05
     OFV(MF) changed from 5.12464e+21 to 5.20706e+21 
group 3 -- xt[4] changed from  1e-05 to  24
     OFV(MF) changed from 5.20706e+21 to 5.24086e+21 
group 3 -- xt[3] changed from  4.63437 to  1e-05
     OFV(MF) changed from 5.24086e+21 to 5.28859e+21 
group 3 -- xt[5] changed from  11.057 to  16
     OFV(MF) changed from 5.28859e+21 to 5.39471e+21 
group 1 -- xt[5] changed from  9.98091 to  1e-05
     OFV(MF) changed from 5.39471e+21 to 5.73316e+21 
group 1 -- xt[4] changed from  7.17683 to  1e-05
     OFV(MF) changed from 5.73316e+21 to 5.82339e+21 

Best value for OFV(MF) = 5.82339e+21

Best value for xt:
Group 1 :  1e-05  1e-05  1e-05  3.969   4.67   23.9
Group 2 :  1e-05  1e-05  1e-05  4.746     24     24
Group 3 :  1e-05  1e-05  1e-05     16     24     24
Group 4 :  1e-05  5.264     24     24     24     24

group 3 -- a[1] changed from  47.3935 to  24
     OFV(MF) changed from 5.82339e+21 to 8.87274e+24 
group 1 -- a[1] changed from  70 to  47
     OFV(MF) changed from 8.87274e+24 to 3.77989e+25 
group 2 -- a[1] changed from  58.4621 to  70
     OFV(MF) changed from 3.77989e+25 to 7.83506e+25 
Best value for OFV(MF) = 7.83506e+25

Best value for a: 
Group 1: 47
Group 2: 70
Group 3: 24
Group 4: 6.42662


Line search run time: 5.936 seconds
***************************

===============================================================================
FINAL RESULTS

Optimized Sampling Schedule
Group 1 :  1e-05  1e-05  1e-05  3.969   4.67   23.9
Group 2 :  1e-05  1e-05  1e-05  4.746     24     24
Group 3 :  1e-05  1e-05  1e-05     16     24     24
Group 4 :  1e-05  5.264     24     24     24     24

Optimized Covariates:
Group 1: 47
Group 2: 70
Group 3: 24
Group 4: 6.42662

 FIM: 
 5.271405e+02 -5.263077e+00  3.622028e+02 -1.288804e+01  1.047664e+01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-5.263077e+00  4.966972e+00 -2.921210e+00  1.190924e-01 -6.139217e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.622028e+02 -2.921210e+00  3.299827e+02 -7.742563e+00  1.133158e+01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-1.288804e+01  1.190924e-01 -7.742563e+00  9.465234e-01 -4.869208e-04  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 1.047664e+01 -6.139217e-02  1.133158e+01 -4.869208e-04  6.182296e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.329923e+04  1.957639e+02  9.159307e+03  2.788546e+04
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.957639e+02  1.799620e+04  5.277420e+03  3.090078e+03
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.159307e+03  5.277420e+03  6.287812e+05  3.253462e+05
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  2.788546e+04  3.090078e+03  3.253462e+05  3.038438e+07


Inverse(FIM):
 9.766194e-03  3.360928e-03 -1.068501e-02  4.516788e-02  3.071588e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.360928e-03  2.038141e-01 -8.538772e-04  1.312344e-02 -2.105445e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-1.068501e-02 -8.538772e-04  2.865094e-02  8.880596e-02 -3.440897e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 4.516788e-02  1.312344e-02  8.880596e-02  2.395065e+00 -2.389965e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.071588e-02 -2.105445e-02 -3.440897e-01 -2.389965e+00  7.399879e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  7.606126e-05 -5.025599e-07 -1.073604e-06 -5.825881e-08
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -5.025599e-07  5.570773e-05 -4.600959e-07 -2.776643e-10
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -1.073604e-06 -4.600959e-07  1.618311e-06 -1.629626e-08
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -5.825881e-08 -2.776643e-10 -1.629626e-08  3.313964e-08

det(FIM) = 7.83506e+25

Efficiency criterion [usually defined as OFV^(1/npar)]  = 753.556

Efficiency (final_design/initial_design): 3.83166

Expected parameter variance 
and relative standard error (%RSE):
    Parameter    Values   Variance     RSE   RSE_initial_design
      bpop[1]    1.8000   9.77e-03    5.49               119.32
      bpop[2]   20.0000   2.04e-01    2.26                 2.27
      bpop[3]    2.0000   2.87e-02    8.46               125.03
      bpop[4]   25.0000   2.40e+00    6.19               862.24
      bpop[5]    5.0000   7.40e+00   54.41              1366.14
       D[1,1]    0.0500   7.61e-05   17.44                16.32
       D[2,2]    0.0500   5.57e-05   14.93                15.08
   SIGMA[1,1]    0.0150   1.62e-06    8.48                 7.19
   SIGMA[2,2]    0.0015   3.31e-08   12.14                27.36

Total running time: 16.021 seconds
