Dear Eduard,
Have you tried SAEM or IMP methods to estimate the variability ?
Also did you check how good are your population predictions when compared to
individual observations? I'm curious to see whether your model with the
Markovian and time components would not be capturing all the variability,
conditional on the data.
Kind regards,
Pascal Girard
Le mardi 5 février 2019 à 11:13:36 UTC+1, Eduard Schmulenson
<e.schmulen...@uni-bonn.de> a écrit :
Dear all,
I am currently trying to model the transitions between four adverse event
grades (0-3) using a continuous-time Markov modeling approach. I have included
a dose effect as well as a time effect on the transition constants. Overall,
the parameters are well estimated and the VPC looks also quite good.
However, the model does not have any IIV or other variability incorporated, so
no individual predictions can be made. I have tried different approaches to
include variability:
- Six different etas: a) One eta per transition constant without a
block structure (this has resulted in rounding errors), b) with a full block
structure (see Lacroix BD et al. CPT PSP 2014), also with rounding errors and
c) with two OMEGA BLOCK(3) structures which solely include “forward” and
“backward” transition constants, respectively (also with rounding errors).
- Two different etas: One mutual eta on “forward” and “backward”
transition constants (shrinkage values of ~ 40 and 60%, respectively, which do
not lower after including the dose effect. The impact of time cannot be
estimated anymore)
- Just one eta on every transition constant (shrinkage value of 46%
which slightly increases after including the dose and time effect.
The etas were added as exponential variables.
Other tested covariates were not significant or resulted in run errors when a
bootstrap was performed.
Are there any other possibilities to incorporate variability in this type of
model? Or is it solely a data-dependent issue? You can find the control stream
(without any IIV) below.
My second question is about the assessment of predictive performance in the
same model. One can compare the observed proportions of an adverse event grade
vs. the simulated probability or the observed vs. simulated grade. Is there a
meaningful error which I can calculate in order to assess bias and precision?
Would be a median prediction error and a median absolute prediction error
appropriate for this type of data? And what kind of error would you suggest
when one has to calculate a relative error which would include a division by 0?
Thank you very much in advance.
Best regards,
Eduard
##########################################
$ABB COMRES = 1
$SUBROUTINES ADVAN6 TOL = 4
$MODEL
NCOMP = 4
COMP = (G0) ; No AE
COMP = (G1) ; Mild AE
COMP = (G2) ; Moderate AE
COMP = (G3) ; Severe AE
$PK
IF(NEWIND.NE.2) THEN
PSDV = 0
COM(1) = 0
ENDIF
PRSP = PSDV ; Previous DV
IF(PRSP.EQ.1) COM(1) = 0
IF(PRSP.EQ.2) COM(1) = 1
IF(PRSP.EQ.3) COM(1) = 2
IF(PRSP.EQ.4) COM(1) = 3
F1 = 0
F2 = 0
F3 = 0
F4 = 0
IF(COM(1).EQ.0) F1 = 1
IF(COM(1).EQ.1) F2 = 1
IF(COM(1).EQ.2) F3 = 1
IF(COM(1).EQ.3) F4 = 1
TVK01 = THETA(1)
K01 = TVK01*EXP(ETA(1))
TVK12 = THETA(2)
K12 = TVK12
TVK23 = THETA(3)
K23 = TVK23
TVK10 = THETA(4)
K10 = TVK10
TVK21 = THETA(5)
K21 = TVK21
TVK32 = THETA(6)
K32 = TVK32
TVKT = THETA(8)
KT = TVKT
$DES
K01F = K01*EXP(KT*T) ; Time effect
K12F = K12*EXP(KT*T)
K23F = K23*EXP(KT*T)
K10B = K10*EXP(THETA(7)*(DOSEDAY-3000)) ; Dose effect
K21B = K21*EXP(THETA(7)*(DOSEDAY-3000))
K32B = K32*EXP(THETA(7)*(DOSEDAY-3000))
DADT(1) = K10B*A(2) - K01F*A(1) ; Grade 0
DADT(2) = K01F*A(1) + K21B*A(3) - A(2)*(K10B + K12F) ; Grade 1
DADT(3) = K12F*A(2) + K32B*A(4) - A(3)*(K21B + K23F) ; Grade 2
DADT(4) = K23F*A(3) - K32B*A(4) ;
Grade 3
$ERROR
Y = 1
IF(DV.EQ.1.AND.CMT.EQ.0) Y = A(1)
IF(DV.EQ.2.AND.CMT.EQ.0) Y = A(2)
IF(DV.EQ.3.AND.CMT.EQ.0) Y = A(3)
IF(DV.EQ.4.AND.CMT.EQ.0) Y = A(4)
P0 = A(1)
P1 = A(2)
P2 = A(3)
P3 = A(4)
; Cumulative probabilities
CUP0 = P0
CUP1 = P0 + P1
CUP2 = P0 + P1 + P2
CUP3 = P0 + P1 + P2 + P3
; Start of simulation block
IF(ICALL.EQ.4) THEN
IF(CMT.EQ.0) THEN
CALL RANDOM (2,R)
IF(R.LE.CUP0) DV = 1
IF(R.GT.CUP0.AND.R.LE.CUP1) DV = 2
IF(R.GT.CUP1.AND.R.LE.CUP2) DV = 3
IF(R.GT.CUP2) DV = 4
ENDIF
ENDIF
; End of simulation block
PSDV=DV
$THETA
…
$OMEGA
0 FIX
$COV PRINT=E
;$SIM (7776) (8877 UNIFORM) ONLYSIM NOPREDICTION
$EST METHOD=1 LAPLACIAN LIKE SIG=2 PRINT=1 MAX=9999 NOABORT
_____________________
Eduard Schmulenson, M.Sc.
Apotheker/Pharmacist
Klinische Pharmazie
Pharmazeutisches Institut
Universität Bonn
An der Immenburg 4
D-53121 Bonn
Tel.: +49 228 73-5242
e.schmulen...@uni-bonn.de
