PopED Results 

        2015-03-20 12:44:30

==============================================================================
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:
 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 : 5.34591e+23

*******************************
RS Results
 OFV(mf) = 5.34591e+23

Optimized Sampling Schedule
Group 1 : 0.1551  3.178  3.514  6.686  7.479     24
Group 2 :  4.383  5.036  6.326  6.618   10.2  23.32
Group 3 :  2.627  3.816  5.284  5.537  8.569     24
Group 4 :  1.543  3.982  7.197    8.6  9.208  19.84

Optimized Covariates:
Group 1: 68.6881
Group 2: 49.6547
Group 3: 37.5071
Group 4: 5.99079

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

SG - It. : 1  OFV : 5.657e+23   Diff. :     1
SG - It. : 2  OFV : 6.123e+23   Diff. : 0.08227
SG - It. : 3  OFV : 6.742e+23   Diff. : 0.1011

SG - Iteration 3 --------- FINAL -------------------------
Normalized gradient: Grad_xt(OFV)/OFV
-0.00700433 -0.006792 -0.00623429 -0.00658604 -0.00629645 -0.00332984 
-0.0308372 0.00937355 -0.0356624 -0.0208963 -0.01901 -0.00850495 
-0.0481447 -0.0674892 -0.0246374 0.0295664 -0.0207368 0.00282961 
0.00132813 -0.194145 0.0363615 0.0178786 0.000415308 -6.56945e-10 
xt opt:
0.0556215 3.07807 6.58688 3.41463 7.37995 23.9005 
4.93672 10.2951 4.28365 6.22633 6.51854 23.218 
3.71671 2.52737 5.18464 8.66828 5.43738 24 
8.69989 1.44313 4.08178 7.29663 9.30771 19.8592 
Normalized gradient: Grad_a(OFV)/OFV
5.804896e-02
-8.743386e-02
-3.830463e-01
-4.752833e-03
aopt:
6.897423e+01
4.936857e+01
3.722103e+01
6.037861e+00
OFV(mf)    : 6.74209e+23
diff       : 0.101146
*************************************************************
*****************************
            Line Search

group 4 -- xt[2] changed from  1.44313 to  1e-05
     OFV(MF) changed from 6.74209e+23 to 8.27671e+23 
group 4 -- xt[5] changed from  9.30771 to  16
     OFV(MF) changed from 8.27671e+23 to 8.27861e+23 
group 4 -- xt[5] changed from  16 to  24
     OFV(MF) changed from 8.27861e+23 to 8.27861e+23 
group 4 -- xt[4] changed from  7.29663 to  8.00001
     OFV(MF) changed from 8.27861e+23 to 8.33881e+23 
group 4 -- xt[4] changed from  8.00001 to  16
     OFV(MF) changed from 8.33881e+23 to 8.36222e+23 
group 4 -- xt[4] changed from  16 to  24
     OFV(MF) changed from 8.36222e+23 to 8.36222e+23 
group 4 -- xt[6] changed from  19.8592 to  24
     OFV(MF) changed from 8.36222e+23 to 8.36222e+23 
group 4 -- xt[1] changed from  8.69989 to  16
     OFV(MF) changed from 8.36222e+23 to 8.36863e+23 
group 4 -- xt[1] changed from  16 to  24
     OFV(MF) changed from 8.36863e+23 to 8.36863e+23 
group 2 -- xt[2] changed from  10.2951 to  1e-05
     OFV(MF) changed from 8.36863e+23 to 9.8875e+23 
group 2 -- xt[6] changed from  23.218 to  1e-05
     OFV(MF) changed from 9.8875e+23 to 1.04382e+24 
group 2 -- xt[5] changed from  6.51854 to  8.00001
     OFV(MF) changed from 1.04382e+24 to 1.05106e+24 
group 2 -- xt[5] changed from  8.00001 to  16
     OFV(MF) changed from 1.05106e+24 to 1.05517e+24 
group 2 -- xt[4] changed from  6.22633 to  1e-05
     OFV(MF) changed from 1.05517e+24 to 1.07529e+24 
group 2 -- xt[4] changed from  1e-05 to  24
     OFV(MF) changed from 1.07529e+24 to 1.08391e+24 
group 2 -- xt[1] changed from  4.93672 to  1e-05
     OFV(MF) changed from 1.08391e+24 to 1.10099e+24 
group 2 -- xt[3] changed from  4.28365 to  1e-05
     OFV(MF) changed from 1.10099e+24 to 1.10244e+24 
group 3 -- xt[6] changed from  24 to  1e-05
     OFV(MF) changed from 1.10244e+24 to 1.19824e+24 
group 3 -- xt[1] changed from  3.71671 to  1e-05
     OFV(MF) changed from 1.19824e+24 to 1.25876e+24 
group 3 -- xt[1] changed from  1e-05 to  24
     OFV(MF) changed from 1.25876e+24 to 1.29807e+24 
group 3 -- xt[5] changed from  5.43738 to  1e-05
     OFV(MF) changed from 1.29807e+24 to 1.3794e+24 
group 3 -- xt[3] changed from  5.18464 to  24
     OFV(MF) changed from 1.3794e+24 to 1.42681e+24 
group 1 -- xt[5] changed from  7.37995 to  1e-05
     OFV(MF) changed from 1.42681e+24 to 1.47288e+24 
group 1 -- xt[3] changed from  6.58688 to  1e-05
     OFV(MF) changed from 1.47288e+24 to 1.48545e+24 

Best value for OFV(MF) = 1.48545e+24

Best value for xt:
Group 1 :  1e-05  1e-05 0.05562  3.078  3.415   23.9
Group 2 :  1e-05  1e-05  1e-05  1e-05     16     24
Group 3 :  1e-05  1e-05  2.527  8.668     24     24
Group 4 :  1e-05  4.082     24     24     24     24

group 1 -- a[1] changed from  68.9742 to  24
     OFV(MF) changed from 1.48545e+24 to 2.06431e+26 
group 2 -- a[1] changed from  49.3686 to  70
     OFV(MF) changed from 2.06431e+26 to 5.02488e+26 
Best value for OFV(MF) = 5.02488e+26

Best value for a: 
Group 1: 24
Group 2: 70
Group 3: 37.221
Group 4: 6.03786


Line search run time: 6.94 seconds
***************************

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

Optimized Sampling Schedule
Group 1 :  1e-05  1e-05 0.05562  3.078  3.415   23.9
Group 2 :  1e-05  1e-05  1e-05  1e-05     16     24
Group 3 :  1e-05  1e-05  2.527  8.668     24     24
Group 4 :  1e-05  4.082     24     24     24     24

Optimized Covariates:
Group 1: 24
Group 2: 70
Group 3: 37.221
Group 4: 6.03786

 FIM: 
 5.587835e+02 -4.459415e+00  2.998337e+02 -2.950618e+01  3.959686e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-4.459415e+00  4.915125e+00 -2.248438e+00  1.167588e-01 -8.732000e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 2.998337e+02 -2.248438e+00  2.260683e+02 -1.512605e+01  6.049369e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-2.950618e+01  1.167588e-01 -1.512605e+01  2.662317e+00  1.605762e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.959686e+00 -8.732000e-02  6.049369e+00  1.605762e-01  8.043448e-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  1.491247e+04  1.701472e+02  9.944289e+03  1.289317e+03
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.701472e+02  1.761950e+04  6.207334e+03  2.883115e+02
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.944289e+03  6.207334e+03  6.060485e+05  7.004923e+04
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  1.289317e+03  2.883115e+02  7.004923e+04  3.726316e+07


Inverse(FIM):
 9.528826e-03  3.309496e-03 -9.830965e-03  4.853942e-02  1.769725e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.309496e-03  2.055844e-01 -1.455344e-03  1.859434e-02  1.325945e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-9.830965e-03 -1.455344e-03  2.279721e-02  2.840522e-02 -1.288869e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 4.853942e-02  1.859434e-02  2.840522e-02  1.114738e+00 -6.731085e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 1.769725e-02  1.325945e-02 -1.288869e-01 -6.731085e-01  2.261284e+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  6.780104e-05 -2.637609e-07 -1.109776e-06 -2.576824e-10
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -2.637609e-07  5.696187e-05 -5.791689e-07  6.571543e-10
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -1.109776e-06 -5.791689e-07  1.674533e-06 -3.104995e-09
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -2.576824e-10  6.571543e-10 -3.104995e-09  2.684199e-08

det(FIM) = 5.02488e+26

Efficiency criterion [usually defined as OFV^(1/npar)]  = 926.385

Efficiency (final_design/initial_design): 4.71045

Expected parameter variance 
and relative standard error (%RSE):
    Parameter    Values   Variance     RSE   RSE_initial_design
      bpop[1]    1.8000   9.53e-03    5.42               119.32
      bpop[2]   20.0000   2.06e-01    2.27                 2.27
      bpop[3]    2.0000   2.28e-02    7.55               125.03
      bpop[4]   25.0000   1.11e+00    4.22               862.24
      bpop[5]    5.0000   2.26e+00   30.08              1366.14
       D[1,1]    0.0500   6.78e-05   16.47                16.32
       D[2,2]    0.0500   5.70e-05   15.09                15.08
   SIGMA[1,1]    0.0150   1.67e-06    8.63                 7.19
   SIGMA[2,2]    0.0015   2.68e-08   10.92                27.36

Total running time: 19.24 seconds
