Background and Objectives Methods and Materials Results Conclusions References Increased computing...
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Background and Objectives Methods and Materials Results Conclusions References M odel1 M odel2 M odel3 M odel4 M odel5 Absolute runtim e reduction (m inutes) -100000 -10000 -1000 -100 -10 0 M odel1 M odel2 M odel3 M odel4 M odel5 R elative runtim e reduction -100% -80% -60% -40% -20% 0 Increased computing power gives us the possibility of building more complex models that more adequately describes the sometimes complex mechanisms of diseases and drug effects. Even with the modern computers of today these models may require quite substantial amount of computing time, and for a model to be widely useful long runtimes are not practical. Models with long runtimes are often defined as differential equations ($DES in NONMEM). In this work we aimed to explore if updating parts of the functions dependent on compartment amounts in the differential equations at pre-specified intervals could shorten model runtimes without loosing model fit. In NONMEM VI there is the possibility to update the system at non-event times using a function called MTIME. Different parts of the differential equations in nine fairly complex models based on differential equations [1-8] were moved from $DES to $PK and MTIME was used to update $PK at given intervals. The intervals were increased to give as short runtimes as possible but the intervals were kept short enough to retain roughly the same fit (OFV). • Moving parts of or whole equations from differential to difference equations using MTIME can shorten runtimes substantially. • Model fit and parameter estimates are similar. • This approach may for example be useful in covariate modeling and in exploring the random effects model (e.g. IIV, IOV and semi- parametric distributions [9]). • The mean absolute error for the fixed effects parameters in the faster models were between 1.5% and 8.0% and between 2.2% and 19.8% for the variance parameters • The difference in OFV compared to the original models ranged between -14.4 and 1.7 units. The small differences in OFV suggests similar prediction properties and this can also be seen in fig. 3. Transforming Parts of a Differential Equations System to Difference Equations as a Method for Run-time Savings in NONMEM VI Klas JF Petersson, Lena E Friberg, Mats O Karlsson Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden • For five [1,4,6-8] of the nine models we were able to shorten the runtimes to a pronounced degree (59-96% reduction), see fig. 1. • For the prolactin model [7] (Model 3) which had a runtime of over one month using FOCE the runtime dropped to 24 h. Figure 1. Absolute and relative changes in runtimes for five models where the runtimes could be shortened by transforming whole or parts of the differential equation system into difference equations. • The fixed effects parameter estimates for four of the models which could be expedited were within 12% from the estimates of the original model. • For the last of the improved models [1] fixed effect parameter bias was slightly higher; one parameter differed by 23% and one by 13%, see fig. 2. Figure 2. Relative bias in parameter estimates for models using difference equations compared to differential equations. Figure 3. Population and individual predictions for models using differntial equations vs using difference equations. [1] Troconiz, I. F. et al Clin Pharmacol Ther 1998;64(1):106-16 [2] Friberg, LE. et al. J Clin Oncol 2002;20(24):4713-21 [3] Hamrén, B. et al Clin Pharmacol Ther. 2008 Mar 19. [Epub ahead of print] [4] Lönnebo, A. et al. Br J Clin Pharmacol. 2007;64(2):125-32 [5] Ribbing, J. et al. PAGE 2008; presentation [6] Silber, HE. et al. J Clin Pharmacol. 2007;47(9):1159-71. [7] Friberg, L.E. et al. PAGE 2006; poster [8] Hamrén, B. Doctoral Thesis, 2008 Uppsala University. [9] Petersson, K. et al. PAGE 2007; poster IF(TIME.EQ.0) STEP=0 STEP=STEP+0.1 MTIME(1)=STEP MTDIFF=1 Type ofparam eter R elative estim ation error -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fixed R andom M odel 1 [4] Fixed R andom M odel 2 [6] Fixed R andom M odel 3 [7] Fixed R andom M odel 4 [8] Fixed R andom M odel 5 [1] $PK Predictions,D ifference equations Predictions,D ifferentialequations 1 2 3 4 5 1 2 3 4 5 M odel 3 -5 0 5 -5 0 5 M odel 4 30 40 50 60 70 30 40 50 60 70 M odel 5 0 200 400 600 800 0 200 400 600 800 M odel 1 1 2 3 4 5 6 1 2 3 4 5 6 M odel 2 Ipred Pred [ 4 ] [ 6 ] [ 7 ] [ 8 ] [ 1 ] [4] [6] [7] [8] [1] [4] [6] [7] [8] [1]
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Transcript of Background and Objectives Methods and Materials Results Conclusions References Increased computing...
Background and Objectives
Methods and Materials
Results
Conclusions
References
Model 1 Model 2 Model 3 Model 4 Model 5
Abs
olut
e ru
ntim
e re
duct
ion
(min
utes
)
-100
000
-100
00-1
000
-100
-10
0
Model 1 Model 2 Model 3 Model 4 Model 5
Rel
ativ
e ru
ntim
e re
duct
ion
-100
%-8
0%-6
0%-4
0%-2
0%0
Increased computing power gives us the possibility of building more complex models that more adequately describes the sometimes complex mechanisms of diseases and drug effects. Even with the modern computers of today these models may require quite substantial amount of computing time, and for a model to be widely useful long runtimes are not practical. Models with long runtimes are often defined as differential equations ($DES in NONMEM). In this work we aimed to explore if updating parts of the functions dependent on compartment amounts in the differential equations at pre-specified intervals could shorten model runtimes without loosing model fit.
In NONMEM VI there is the possibility to update the system at non-event times using a function called MTIME. Different parts of the differential equations in nine fairly complex models based on differential equations [1-8] were moved from $DES to $PK and MTIME was used to update $PK at given intervals. The intervals were increased to give as short runtimes as possible but the intervals were kept short enough to retain roughly the same fit (OFV).
•Moving parts of or whole equations from differential to difference equations using MTIME can shorten runtimes substantially.
•Model fit and parameter estimates are similar.
•This approach may for example be useful in covariate modeling and in exploring the random effects model (e.g. IIV, IOV and semi-parametric distributions [9]).
•The mean absolute error for the fixed effects parameters in the faster models were between 1.5% and 8.0% and between 2.2% and 19.8% for the variance parameters
•The difference in OFV compared to the original models ranged between -14.4 and 1.7 units. The small differences in OFV suggests similar prediction properties and this can also be seen in fig. 3.
Transforming Parts of a Differential Equations System to Difference Equations as a Method for Run-time Savings in NONMEM VI
Klas JF Petersson, Lena E Friberg, Mats O Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
•For five [1,4,6-8] of the nine models we were able to shorten the runtimes to a pronounced degree (59-96% reduction), see fig. 1.
•For the prolactin model [7] (Model 3) which had a runtime of over one month using FOCE the runtime dropped to 24 h.
Figure 1. Absolute and relative changes in runtimes for five models where the runtimes could be shortened by transforming whole or parts of the differential equation system into difference equations.
•The fixed effects parameter estimates for four of the models which could be expedited were within 12% from the estimates of the original model.
• For the last of the improved models [1] fixed effect parameter bias was slightly higher; one parameter differed by 23% and one by 13%, see fig. 2.
Figure 2. Relative bias in parameter estimates for models using difference equations compared to differential equations.
Figure 3. Population and individual predictions for models using differntial equations vs using difference equations.
[1] Troconiz, I. F. et al Clin Pharmacol Ther 1998;64(1):106-16[2] Friberg, LE. et al. J Clin Oncol 2002;20(24):4713-21[3] Hamrén, B. et al Clin Pharmacol Ther. 2008 Mar 19. [Epub ahead of print][4] Lönnebo, A. et al. Br J Clin Pharmacol. 2007;64(2):125-32[5] Ribbing, J. et al. PAGE 2008; presentation[6] Silber, HE. et al. J Clin Pharmacol. 2007;47(9):1159-71.[7] Friberg, L.E. et al. PAGE 2006; poster[8] Hamrén, B. Doctoral Thesis, 2008 Uppsala University.[9] Petersson, K. et al. PAGE 2007; poster
IF(TIME.EQ.0) STEP=0STEP=STEP+0.1
MTIME(1)=STEPMTDIFF=1
Type of parameter
Re
lativ
e e
stim
atio
n e
rro
r-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fixed Random
Model 1 [4]
Fixed Random
Model 2 [6]
Fixed Random
Model 3 [7]
Fixed Random
Model 4 [8]
Fixed Random
Model 5 [1]
$PK
Predictions
Predictions, Difference equations
Pre
dic
tion
s, D
iffe
ren
tial e
qu
atio
ns
12
34
5
1 2 3 4 5
Model 3
-50
5
-5 0 5
Model 4
30
40
50
60
70
30 40 50 60 70
Model 5
02
00
40
06
00
80
0
0 200 400 600 800
Model 1
12
34
56
1 2 3 4 5 6
Model 2
IpredPred
[4] [6]
[7] [8] [1]
[4] [6] [7] [8] [1] [4] [6] [7] [8] [1]
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