PopED Results 

        2015-12-28 09:18:04

==============================================================================
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

Initial OFV = 47.5336

Efficiency criterion [usually defined as OFV^(1/npar)]  = 1.5358

Initial design expected parameter 
relative standard error (%RSE)
    Parameter    Values     RSE_0
      bpop[1]    1.8000    119.32
      bpop[2]   20.0000      2.27
      bpop[3]    2.0000    125.03
      bpop[4]   25.0000    862.24
      bpop[5]    5.0000   1366.14
       D[1,1]    0.0500     16.32
       D[2,2]    0.0500     15.08
   SIGMA[1,1]    0.0150      7.19
   SIGMA[2,2]    0.0015     27.36

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

OFV calculation for FIM: 4 
  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) = 47.5336
*******************************

RS - It. : 3   OFV : 47.5336

*******************************
RS Results
 OFV(mf) = 47.5336

Optimized 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

Optimized Covariates:
Group 1: 70
Group 2: 60
Group 3: 50
Group 4: 10

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

SG - It. : 1  OFV : 47.59   Diff. :     1
SG - It. : 2  OFV : 47.68   Diff. : 0.001796
SG - It. : 3  OFV : 47.79   Diff. : 0.002247

SG - Iteration 3 --------- FINAL -------------------------
Normalized gradient: Grad_xt(OFV)/OFV
-0.000111098 -0.000136499 -0.000163052 -0.000132685 -0.000105228 -2.96881e-05 
-0.000110947 -0.000154065 -0.000164234 -3.22414e-05 -5.60903e-05 -3.95374e-05 
-0.000669516 -0.000465525 -6.99176e-05 0.000313999 0.000701726 0.00144099 
-0.000915788 -0.000672935 -0.000187646 0.000662844 0.00215216 -8.17818e-10 
xt opt:
0.90049 1.90049 3.90049 5.90049 7.90049 23.9005 
0.90049 1.90049 3.90049 5.94849 7.90049 23.9245 
0.90049 1.90049 3.90049 6.09951 8.09951 24 
0.90049 1.90049 3.90049 6.09951 8.09951 23.9584 
Normalized gradient: Grad_a(OFV)/OFV
3.788830e-03
-3.071190e-03
-1.051118e-02
-2.253349e-03
aopt:
7.000000e+01
5.971391e+01
4.971391e+01
9.713908e+00
OFV(mf)    : 47.7855
diff       : 0.00224738
*************************************************************
*****************************
            Line Search

group 1 -- xt[5] changed from  7.90049 to  1e-05
     OFV(MF) changed from 47.7855 to 47.8184 
group 1 -- xt[4] changed from  5.90049 to  1e-05
     OFV(MF) changed from 47.8184 to 47.8253 
group 1 -- xt[3] changed from  3.90049 to  24
     OFV(MF) changed from 47.8253 to 47.8277 
group 1 -- xt[2] changed from  1.90049 to  1e-05
     OFV(MF) changed from 47.8277 to 47.8343 
group 1 -- xt[6] changed from  23.9005 to  24
     OFV(MF) changed from 47.8343 to 47.8359 
group 4 -- xt[6] changed from  23.9584 to  24
     OFV(MF) changed from 47.8359 to 47.8359 
group 4 -- xt[1] changed from  0.90049 to  1e-05
     OFV(MF) changed from 47.8359 to 47.8713 
group 4 -- xt[1] changed from  1e-05 to  16
     OFV(MF) changed from 47.8713 to 48.114 
group 4 -- xt[1] changed from  16 to  24
     OFV(MF) changed from 48.114 to 48.1141 
group 4 -- xt[3] changed from  3.90049 to  1e-05
     OFV(MF) changed from 48.1141 to 48.285 
group 4 -- xt[3] changed from  1e-05 to  16
     OFV(MF) changed from 48.285 to 48.3304 
group 4 -- xt[3] changed from  16 to  24
     OFV(MF) changed from 48.3304 to 48.3304 
group 4 -- xt[4] changed from  6.09951 to  1e-05
     OFV(MF) changed from 48.3304 to 48.5367 
group 4 -- xt[5] changed from  8.09951 to  8.00001
     OFV(MF) changed from 48.5367 to 48.5381 
group 4 -- xt[5] changed from  8.00001 to  16
     OFV(MF) changed from 48.5381 to 48.5862 
group 4 -- xt[5] changed from  16 to  24
     OFV(MF) changed from 48.5862 to 48.5868 
group 4 -- xt[2] changed from  1.90049 to  8.00001
     OFV(MF) changed from 48.5868 to 48.6299 
group 2 -- xt[6] changed from  23.9245 to  16
     OFV(MF) changed from 48.6299 to 48.6463 
group 2 -- xt[4] changed from  5.94849 to  1e-05
     OFV(MF) changed from 48.6463 to 48.673 
group 2 -- xt[5] changed from  7.90049 to  1e-05
     OFV(MF) changed from 48.673 to 48.6759 
group 2 -- xt[3] changed from  3.90049 to  8.00001
     OFV(MF) changed from 48.6759 to 48.6791 
group 2 -- xt[2] changed from  1.90049 to  1e-05
     OFV(MF) changed from 48.6791 to 48.6797 
group 3 -- xt[5] changed from  8.09951 to  16
     OFV(MF) changed from 48.6797 to 48.7312 
group 3 -- xt[5] changed from  16 to  24
     OFV(MF) changed from 48.7312 to 48.7369 
group 3 -- xt[1] changed from  0.90049 to  1e-05
     OFV(MF) changed from 48.7369 to 48.7389 
group 3 -- xt[2] changed from  1.90049 to  1e-05
     OFV(MF) changed from 48.7389 to 48.7398 
group 3 -- xt[2] changed from  1e-05 to  24
     OFV(MF) changed from 48.7398 to 48.7445 
group 3 -- xt[4] changed from  6.09951 to  1e-05
     OFV(MF) changed from 48.7445 to 48.7576 
group 3 -- xt[6] changed from  24 to  16
     OFV(MF) changed from 48.7576 to 48.7733 

Best value for OFV(MF) = 48.7733

Best value for xt:
Group 1 :  1e-05  1e-05  1e-05 0.9005     24     24
Group 2 :  1e-05  1e-05  1e-05 0.9005      8     16
Group 3 :  1e-05  1e-05    3.9     16     24     24
Group 4 :  1e-05      8     24     24     24     24

group 2 -- a[1] changed from  59.7139 to  1
     OFV(MF) changed from 48.7733 to 54.577 
group 2 -- a[1] changed from  1 to  24
     OFV(MF) changed from 54.577 to 59.2775 
group 3 -- a[1] changed from  49.7139 to  47
     OFV(MF) changed from 59.2775 to 59.7974 
Best value for OFV(MF) = 59.7974

Best value for a: 
Group 1: 70
Group 2: 24
Group 3: 47
Group 4: 9.71391


Line search run time: 5.611 seconds
***************************

===============================================================================
FINAL RESULTS
Optimized Sampling Schedule
Group 1 :  1e-05  1e-05  1e-05 0.9005     24     24
Group 2 :  1e-05  1e-05  1e-05 0.9005      8     16
Group 3 :  1e-05  1e-05    3.9     16     24     24
Group 4 :  1e-05      8     24     24     24     24

Optimized Covariates:
Group 1: 70
Group 2: 24
Group 3: 47
Group 4: 9.71391

 FIM: 
 5.582815e+02 -6.484947e+00  3.892266e+02 -1.322006e+01  3.690280e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-6.484947e+00  4.997406e+00 -4.248837e+00  1.066586e-01 -5.414264e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.892266e+02 -4.248837e+00  3.561765e+02 -6.843104e+00  6.402812e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-1.322006e+01  1.066586e-01 -6.843104e+00  1.095160e+00  1.445534e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.690280e+00 -5.414264e-02  6.402812e+00  1.445534e-01  3.380359e-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  1.490565e+04  2.680497e+02  9.182568e+03  5.328307e+03
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  2.680497e+02  1.822306e+04  4.937147e+03  5.789354e+02
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.182568e+03  4.937147e+03  6.373997e+05  3.986464e+05
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  5.328307e+03  5.789354e+02  3.986464e+05  2.774146e+07


Inverse(FIM):
 1.273345e-02  3.905708e-03 -1.582280e-02  3.515182e-02  1.462880e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.905708e-03  2.034429e-01 -2.056747e-03  1.130501e-02  2.407013e-02  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
-1.582280e-02 -2.056747e-03  2.654668e-02  1.980574e-02 -3.388905e-01  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 3.515182e-02  1.130501e-02  1.980574e-02  1.653344e+00 -1.464095e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
 1.462880e-01  2.407013e-02 -3.388905e-01 -1.464095e+00  8.410207e+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  6.769919e-05 -7.329839e-07 -9.702138e-07  9.543295e-10
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -7.329839e-07  5.499954e-05 -4.185860e-07  5.008107e-09
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -9.702138e-07 -4.185860e-07  1.600355e-06 -2.280211e-08
 0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  9.543295e-10  5.008107e-09 -2.280211e-08  3.637451e-08

OFV = 59.7974

Efficiency criterion [usually defined as OFV^(1/npar)]  = 1.57547

Efficiency [typically: (OFV_final/OFV_initial)^(1/npar)]: 1.02583

Expected parameter 
relative standard error (%RSE):
    Parameter    Values     RSE_0     RSE
      bpop[1]    1.8000    119.32    6.27
      bpop[2]   20.0000      2.27    2.26
      bpop[3]    2.0000    125.03    8.15
      bpop[4]   25.0000    862.24    5.14
      bpop[5]    5.0000   1366.14   58.00
       D[1,1]    0.0500     16.32   16.46
       D[2,2]    0.0500     15.08   14.83
   SIGMA[1,1]    0.0150      7.19    8.43
   SIGMA[2,2]    0.0015     27.36   12.71

Total running time: 15.395 seconds
