NONMEM Users Network Archive

Hosted by Cognigen

RE: [NMusers] Ordinal data model: Incorporation of variability & assessment of predictive performance

From: Mats Karlsson <Mats.Karlsson_at_farmbio.uu.se>
Date: Wed, 6 Feb 2019 03:09:35 +0000

Hi Eduard,

If you want to have a minimalistic model, with respect to both fixed effect=
s and random effects, but still incorporate all 4 categories as well as the=
 Markov element, you can try the minimal Continuous-Time Markov Model (mCTM=
M) described in "A Minimal Continuous-Time Markov Pharmacometric Model. Sch=
indler E, Karlsson MO. AAPS J. 2017 Sep;19(5):1424-1435"

Best regards,
Mats

From: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> On Behalf=
 Of Eduard Schmulenson
Sent: den 5 februari 2019 11:04
To: nmusers_at_globomaxnm.com
Subject: [NMusers] Ordinal data model: Incorporation of variability & asses=
sment of predictive performance

Dear all,

I am currently trying to model the transitions between four adverse event g=
rades (0-3) using a continuous-time Markov modeling approach. I have includ=
ed a dose effect as well as a time effect on the transition constants. Over=
all, 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 approache=
s 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 blo=
ck structure (see Lacroix BD et al. CPT PSP 2014), also with rounding error=
s and c) with two OMEGA BLOCK(3) structures which solely include "forward" =
and "backward" transition constants, respectively (also with rounding error=
s).

- Two different etas: One mutual eta on "forward" and "backward" t=
ransition 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 o=
f model? Or is it solely a data-dependent issue? You can find the control s=
tream (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 g=
rade 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 predict=
ion error appropriate for this type of data? And what kind of error would y=
ou 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

[cid:image004.png_at_01D3092E.080FB8B0][unnamed]
_____________________
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.schmulenson_at_uni-bonn.de<mailto:e.schmulenson_at_uni-bonn.de>









När du har kontakt med oss på Uppsala universitet med e-post så inneb=
är det att vi behandlar dina personuppgifter. För att läsa mer om hur=
 vi gör det kan du läsa här: http://www.uu.se/om-uu/dataskydd-personu=
ppgifter/

E-mailing Uppsala University means that we will process your personal data.=
 For more information on how this is performed, please read here: http://ww=
w.uu.se/en/about-uu/data-protection-policy





image001.png
(image/png attachment: image001.png)

image002.gif
(image/gif attachment: image002.gif)

Received on Tue Feb 05 2019 - 22:09:35 EST

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to: nmusers-request@iconplc.com. Once subscribed, you may contribute to the discussion by emailing: nmusers@globomaxnm.com.