Dear Baysian modellers
We have generated a nine compartment model from extremely rich imaging data
using MCMC Baysian analysis (and also SAEM during burn-in). For model
evaluation we skip single or multiple compartments and compare the numerical
outcomes such as the conditional weighted residuals, the Bayes trend or
caterpillar plots and the objective function value (OFV).
Let's now assume we want to compare
model 1 ($PRIOR NWPRI NTHETA=14, NETA=14, NTHP=0, NETP=14)
with
model 2 ($PRIOR NWPRI NTHETA=18, NETA=18, NTHP=0, NETP=18)
More details on the models can be found below (sorry for the many lines of text)
For model 1, two peripheral compartments were omitted from model 2. Thus, model
1 has 8 model parameters less than model 2 (as can be seen from NTHETA and
NETA).
CONCERN and QUESTION:
Giving the fact that we estimate the full covariance matrix, I am not quite
certain if I am allowed to compare the OFV values from these two model using
the F-Test. Could anyone give an advise or comment on this?
Many thanks for your help
Andreas
______________________________________________________
MODEL 1
$PK
MU_1 = THETA(1)
MU_2 = THETA(2)
MU_3 = THETA(3)
MU_4 = THETA(4)
MU_5 = THETA(5)
MU_6 = THETA(6)
MU_7 = THETA(7)
MU_8 = THETA(8)
MU_9 = THETA(9)
MU_10 = THETA(10)
MU_11 = THETA(11)
MU_12 = THETA(12)
MU_13 = THETA(13)
MU_14 = THETA(14)
MU_15 = THETA(15)
MU_16 = THETA(16)
MU_17 = THETA(17)
MU_18 = THETA(18)
; CENTRAL
CL = 0.04
VC = EXP(MU_1+ETA(1))
S2 = VC
S3 = VC
S5 = VC
; C
K10 = CL/VC
; M
K19 = EXP(MU_2+ETA(2))
K91 = EXP(MU_3+ETA(3))
K92 = EXP(MU_4+ETA(4))
K29 = EXP(MU_5+ETA(5))
K24 = EXP(MU_6+ETA(6))
K42 = EXP(MU_7+ETA(7))
; TL
K16 = EXP(MU_8+ETA(8))
K61 = EXP(MU_9+ETA(9))
; T
K63 = EXP(MU_10+ETA(10))
K36 = EXP(MU_11+ETA(11))
K37 = EXP(MU_12+ETA(12))
K73 = EXP(MU_13+ETA(13))
; L
K65 = EXP(MU_14+ETA(14))
K56 = EXP(MU_15+ETA(15))
K58 = EXP(MU_16+ETA(16))
K85 = EXP(MU_17+ETA(17))
ALAG1 = EXP(MU_18+ETA(18))
$ERROR
Y=F+F*ERR(2)+ERR(1)
IPRED = F
IRES = DV-IPRED ; INDIVIDUAL-SPECIFIC RESIDUAL
IWRES = IRES ; INDIVIDUAL-SPECIFIC WEIGHTED RESIDUAL
$THETA
1.3 ; VC
-1.4 ; K19
-4.4 ; K91
0.8 ; K92
5.2 ; K29
-1.8 ; K24
-6.3 ; K42
1.0 ; K16
-0.5 ; K61
-3 ; K63
-1.25 ; K36
1.2 ; K37
-0.37 ; K73
-5.2; K65
-5.0 ; K56
-3.2 ; K58
-10. ; K85
2.35 ; ALAG1
$OMEGA BLOCK(17)
0.1 ; VC
0.01 0.1 ; K19
0.01 0.01 0.1 ; K91
0.01 0.01 0.01 0.1 ; K92
0.01 0.01 0.01 0.01 0.1 ; K29
0.01 0.01 0.01 0.01 0.01 0.1 ; K24
0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K42
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K16
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K61
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K63
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K36
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K37
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K73
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K65
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K56
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1
; K58
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
0.1 ; K85
$OMEGA
0.04 ; ALAG1
$SIGMA 5.5E-05 0.0068
$OMEGA BLOCK(17)
0.1 FIX
0 0.1
0 0 0.1
0 0 0 0.1
0 0 0 0 0.1
0 0 0 0 0 0.1
0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.1
$OMEGA
0.1 FIX ; ALAG1
$THETA (17.0 FIXED) (1 FIXED)
_______________________________________________
MODEL 2
$PK
MU_1 = THETA(1)
MU_2 = THETA(2)
MU_3 = THETA(3)
MU_4 = THETA(4)
MU_5 = THETA(5)
MU_6 = THETA(6)
MU_7 = THETA(7)
MU_8 = THETA(8)
MU_9 = THETA(9)
MU_10 = THETA(10)
MU_11 = THETA(11)
MU_12 = THETA(12)
MU_13 = THETA(13)
MU_14 = THETA(14)
; CENTRAL
CL = 0.04
VC = EXP(MU_1+ETA(1))
S2 = VC
S3 = VC
S5 = VC
; C
K10 = CL/VC
; M
K17 = EXP(MU_2+ETA(2))
K71 = EXP(MU_3+ETA(3))
K72 = EXP(MU_4+ETA(4))
K27 = EXP(MU_5+ETA(5))
K24 = EXP(MU_6+ETA(6))
K42 = EXP(MU_7+ETA(7))
; TL
K16 = EXP(MU_8+ETA(8))
K61 = EXP(MU_9+ETA(9))
; T
K63 = EXP(MU_10+ETA(10))
K36 = EXP(MU_11+ETA(11))
; L
K65 = EXP(MU_12+ETA(12))
K56 = EXP(MU_13+ETA(13))
ALAG1 = EXP(MU_14+ETA(14))
$ERROR
Y=F+F*ERR(2)+ERR(1)
IPRED = F
IRES = DV-IPRED ; INDIVIDUAL-SPECIFIC RESIDUAL
IWRES = IRES ; INDIVIDUAL-SPECIFIC WEIGHTED RESIDUAL
$THETA
1.3 ; VC
-1.4 ; K17
-4.4 ; K71
0.8 ; K72
5.2 ; K27
-1.8 ; K24
-6.3 ; K42
1.0 ; K16
-0.5 ; K61
-3 ; K63
-1.25 ; K36
-5.2; K65
-5.0 ; K56
2.35 ; ALAG1
$OMEGA BLOCK(13)
0.1 ; VC
0.01 0.1 ; K17
0.01 0.01 0.1 ; K71
0.01 0.01 0.01 0.1 ; K72
0.01 0.01 0.01 0.01 0.1 ; K27
0.01 0.01 0.01 0.01 0.01 0.1 ; K24
0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K42
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K16
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K61
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K63
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K36
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K65
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.1 ; K56
$OMEGA
0.04 ; ALAG1
$SIGMA 5.5E-05 0.0068
$OMEGA BLOCK(13)
0.1 FIX
0 0.1
0 0 0.1
0 0 0 0.1
0 0 0 0 0.1
0 0 0 0 0 0.1
0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0.1
$OMEGA
0.1 FIX ; ALAG1
$THETA (13.0 FIXED) (1 FIXED)
$EST PRINT=1 METHOD=SAEM INTERACTION NBURN=100 NITER=20 FILE=SAEM.EXT NOPRIOR=1
$EST METHOD=BAYES FILE=BAYES.EXT NBURN = 4000 NSIG = 3 NITER= 3000 NOPRIOR=0
$COV MATRIX=R PRINT=E UNCONDITIONAL SIGL=12
----------------------------------------------------------------------------------------------------------------------------------------
Andreas Steingötter, PhD
Division for Gastroenterology and Hepatology
Institut for Biomedical Engineering
Department of Internal Medicine
Divisions of Bioimaging and MRI Technology
University Hospital Zurich
University and ETH Zurich
Rämistrasse 100
Gloriastrasse 35
CH - 8091 Zurich
CH - 8092 Zurich
Tel. +41 44 255 5684
Tel. +41 44 255 5684
Fax +41 44 255 4591
Fax +41 44 632 1193
Email [email protected]
Email [email protected]
