From: Eduard Schmulenson <*e.schmulenson*>

Date: Tue, 5 Feb 2019 11:04:22 +0100

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

cid:image004.png

_____________________

Eduard Schmulenson, M.Sc.

Apotheker/Pharmacist

Klinische Pharmazie

Pharmazeutisches Institut

Universität Bonn

An der Immenburg 4

D-53121 Bonn

Tel.: +49 228 73-5242

<mailto:e.schmulenson

Received on Tue Feb 05 2019 - 05:04:22 EST

Date: Tue, 5 Feb 2019 11:04:22 +0100

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

cid:image004.png

_____________________

Eduard Schmulenson, M.Sc.

Apotheker/Pharmacist

Klinische Pharmazie

Pharmazeutisches Institut

Universität Bonn

An der Immenburg 4

D-53121 Bonn

Tel.: +49 228 73-5242

<mailto:e.schmulenson

(image/png attachment: image001.png)

(image/gif attachment: image002.gif)