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Model estimation and results#

Pharmpy can both estimate a model and retrieve results from a NONMEM run (including runs that were not started by Pharmpy).

Fitting a model#

You can fit a model using the pharmpy.tools.fit() function:

from pharmpy.modeling import load_example_model
from pharmpy.tools import fit

model = load_example_model('pheno')
results = fit(model)

It is also possible to specify which estimation tool:

results = fit(model, tool='nlmixr')

Note

In order to esimate using any of the supported softwares (NONMEM, nlmixr2, rxode2) you need to have a configuration file set up with a path to NONMEM, instructions can be found here.

Modelfit results#

To read in the results (if not fitted in Pharmpy), you can use the pharmpy.tools.read_modelfit_results() function.

from pharmpy.tools import read_modelfit_results

results = read_modelfit_results('tests/testdata/nonmem/pheno_real.mod')

Final OFV#

The final OFV is available in the ofv-attribute:

results.ofv

586.2760562818805

Parameter estimates#

The parameter_estimates series contains the final estimates of all estimated parameters.

results.parameter_estimates

PTVCL        0.004696
PTVV         0.984258
THETA_3      0.158920
IVCL         0.029351
IVV          0.027906
SIGMA_1_1    0.013241
Name: estimates, dtype: float64

It is also possible to get the parameters with all variability parameters as standard deviations or correlations.

results.parameter_estimates_sdcorr

PTVCL        0.004696
PTVV         0.984258
THETA_3      0.158920
IVCL         0.171321
IVV          0.167051
SIGMA_1_1    0.115069
Name: estimates, dtype: float64

Standard errors of parameter estimates#

The standard errors of the parameter estimates are in the standard_errors series.

results.standard_errors

PTVCL        0.000210
PTVV         0.026895
THETA_3      0.083762
IVCL         0.013415
IVV          0.007477
SIGMA_1_1    0.002279
Name: SE, dtype: float64

Or in standard_errors_sdcorr with variability parameters as standard deviations or correlations.

results.standard_errors_sdcorr

PTVCL        0.000210
PTVV         0.026895
THETA_3      0.083762
IVCL         0.039153
IVV          0.022378
SIGMA_1_1    0.009904
Name: SE, dtype: float64

Relative standard errors of parameter estimates#

The relative standard errors of the parameter estimates

results.relative_standard_errors

PTVCL        0.044731
PTVV         0.027325
THETA_3      0.527072
IVCL         0.457068
IVV          0.267918
SIGMA_1_1    0.172147
Name: RSE, dtype: float64

Covariance matrix#

The covariance matrix for all estimated parameters

results.covariance_matrix
PTVCL PTVV THETA_3 IVCL IVV SIGMA_1_1
PTVCL 4.411510e-08 4.010000e-08 -0.000002 -0.000001 1.538630e-07 8.178090e-08
PTVV 4.010000e-08 7.233530e-04 -0.000804 0.000050 7.171840e-05 1.461760e-05
THETA_3 -1.665010e-06 -8.040250e-04 0.007016 -0.000108 -3.944800e-05 2.932950e-05
IVCL -1.093430e-06 4.981380e-05 -0.000108 0.000180 -1.856650e-05 4.867230e-06
IVV 1.538630e-07 7.171840e-05 -0.000039 -0.000019 5.589820e-05 -4.685650e-07
SIGMA_1_1 8.178090e-08 1.461760e-05 0.000029 0.000005 -4.685650e-07 5.195640e-06

Correlation Matrix#

The correlation matrix for all estimated parameters.

Note

Note to NONMEM users. This is a proper correlation matrix meaning that diagonal elements are 1. Standard errors can be retrieved from standard_errors.

results.correlation_matrix
PTVCL PTVV THETA_3 IVCL IVV SIGMA_1_1
PTVCL 1.000000 0.007099 -0.094640 -0.388058 0.097981 0.170820
PTVV 0.007099 1.000000 -0.356900 0.138062 0.356662 0.238442
THETA_3 -0.094640 -0.356900 1.000000 -0.096516 -0.062991 0.153616
IVCL -0.388058 0.138062 -0.096516 1.000000 -0.185111 0.159170
IVV 0.097981 0.356662 -0.062991 -0.185111 1.000000 -0.027495
SIGMA_1_1 0.170820 0.238442 0.153616 0.159170 -0.027495 1.000000

Precision Matrix#

The precision matrix for all estimated parameters. This is the inverse of the covariance matrix.

results.precision_matrix
PTVCL PTVV THETA_3 IVCL IVV SIGMA_1_1
PTVCL 29955600.0 22660.100 16057.800 203511.000 -39474.400 -820116.00
PTVV 22660.1 2129.910 260.177 -375.267 -2800.820 -7718.80
THETA_3 16057.8 260.177 187.039 177.207 -205.809 -2225.15
IVCL 203511.0 -375.267 177.207 7527.520 2462.980 -9977.45
IVV -39474.4 -2800.820 -205.809 2462.980 22343.200 9370.81
SIGMA_1_1 -820116.0 -7718.800 -2225.150 -9977.450 9370.810 249847.00

Indiviudal OFV#

The OFV for each individual or iOFV is in the individual_ofv series.

results.individual_ofv

ID
1      5.947352
2     12.970591
3      9.982342
4      8.457091
5     10.839437
6     13.257230
7      8.098338
8     11.538621
9     14.647969
10     8.394643
11     9.480164
12     9.650233
13     7.991406
14    15.378880
15     5.739902
16    10.328800
17    10.113284
18    21.212096
19     9.334047
20     9.327778
21     8.821533
22     5.631281
23    11.861669
24    12.915261
25    27.988977
26     7.279273
27     9.733181
28     2.830053
29     2.851724
30     5.212095
31     3.774791
32    12.352283
33     6.172643
34     7.427376
35    11.381444
36    10.624014
37     5.970627
38    14.177028
39    10.206540
40     4.955029
41     8.982447
42    15.051499
43     4.424503
44     7.734342
45     7.018477
46     2.810285
47     3.279258
48    28.168486
49    10.190508
50    16.749134
51    14.598565
52    14.237467
53     8.568934
54    15.800062
55     5.098025
56     2.586253
57     5.663948
58     9.850993
59    10.605845
Name: iOFV, dtype: float64

Predictions#

Different predictions can be found in predictions

results.predictions
PRED IPRED
ID TIME
1 0.0 18.143 18.045
2.0 17.971 17.881
12.5 19.633 19.575
24.5 21.080 21.063
37.0 22.400 22.427
... ... ... ...
59 108.3 32.616 35.668
120.5 33.543 36.662
132.3 34.478 37.667
144.8 35.253 38.495
146.8 34.918 38.123

744 rows × 2 columns

Residuals#

Different residual metrics can be found in residuals

results.residuals
RES CWRES
ID TIME
1 2.0 -0.67071 -0.401100
112.5 2.35080 0.587770
2 2.0 -0.36360 -1.278800
63.5 6.19730 1.670700
135.5 7.21710 1.352600
... ... ... ...
58 47.5 4.86050 1.067200
131.8 1.35060 -0.059269
59 1.8 1.72100 -0.036754
73.8 5.10860 0.814140
146.8 5.28180 0.699410

155 rows × 2 columns

Individual estimates#

Individual estimates (or EBEs)

results.individual_estimates
ETA_1 ETA_2
ID
1 -0.043861 0.005430
2 -0.166321 -0.131833
3 0.095934 0.130868
4 -0.009154 0.017388
5 0.102019 0.283500
6 -0.019417 0.099839
7 0.045946 0.059072
8 -0.024270 -0.189351
9 -0.248536 -0.091872
10 0.009545 0.012052
11 0.066151 0.293685
12 -0.030236 0.074789
13 -0.094502 -0.147433
14 0.076820 -0.105604
15 0.020051 0.066265
16 -0.086035 0.023260
17 -0.067138 -0.030859
18 0.337255 0.035532
19 0.032579 -0.028410
20 0.003589 -0.080613
21 -0.060233 -0.052854
22 -0.004469 -0.057344
23 0.051992 -0.212941
24 0.137510 -0.004111
25 0.023282 0.302636
26 -0.039069 -0.119442
27 -0.044956 -0.263320
28 0.000776 0.083231
29 0.003150 0.012752
30 0.049654 0.080932
31 -0.000555 -0.099614
32 0.061864 0.332738
33 -0.038156 -0.067641
34 -0.038017 -0.184137
35 -0.156617 -0.208753
36 0.114558 -0.053036
37 -0.008405 0.026004
38 0.144920 0.081646
39 0.083320 -0.015380
40 0.000392 0.078062
41 0.018966 0.112030
42 0.112715 0.383786
43 -0.001730 -0.167583
44 0.042068 0.066598
45 0.012052 0.037600
46 0.000093 0.010662
47 -0.009775 -0.058306
48 -0.229005 0.033958
49 0.008959 0.092312
50 -0.050987 -0.192569
51 -0.002727 0.225657
52 0.115824 -0.204269
53 -0.054792 -0.066334
54 -0.123689 -0.239678
55 0.047215 0.186615
56 -0.000949 -0.010812
57 0.015929 -0.017213
58 -0.005234 -0.122552
59 -0.076677 -0.095696

Uncertainty for the individual estimates can be found in individual_estimates_covariance, which is a series of covariance matrices for each individual.

results.individual_estimates_covariance[1]
ETA_1 ETA_2
ETA_1 0.024883 -0.002999
ETA_2 -0.002999 0.007157
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