NONMEM Users Network Archive

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Modeling biomarker data below the LOQ

From: Doshi, Sameer <sdoshi>
Date: Wed, 18 Nov 2009 09:53:17 -0800

Hello,
We are attempting to model suppression of a biomarker, where a number of sa=
mples (40-60%) are below the quantification limit of the assay and where 2 =
different assays (with different quantification limits) were used. We are =
trying to model these BQL data using the M3 and M4 methods proposed by Ahn =
et al (2008).

I would like to know if anyone has any comments or experience implementing =
the M3 or M4 methods for biomarker data, where levels are observed at basel=
ine, are supressed below the LOQ for a given duration, and then return to b=
aseline.

Also please advise if there are other methods to try and incorporate these =
BQL data into the model.

I have included the relevant pieces of the control file (for both M3 and M4=
) and data from a single subject.

Thanks for your review/suggestions.

Sameer

DATA:
#ID TIME AMT DV CMT EVID TYPE ASSY
1 0 0 65.71 0 0 0 1
1 0 120 0 3 1 0 1
1 168 0 10 0 0 1 1
1 336 0 10 0 0 1 1
1 336 120 0 3 1 0 1
1 504 0 12.21 0 0 0 1
1 672 120 0 3 1 0 1
1 1008 0 10 0 0 1 1
1 1008 120 0 3 1 0 1
1 1344 0 10 0 0 1 1
1 1344 120 0 3 1 0 1
1 1680 0 10 0 0 1 1
1 1680 120 0 3 1 0 1
1 2016 0 10 0 0 0 1
1 2352 0 25.64 0 0 0 1
1 2688 0 59.48 0 0 0 1

MODEL M3:
$DATA data.csv IGNORE=#
$SUB ADVAN8 TRANS1 TOL=6
$MODEL
  COMP(central)
  COMP(peri)
  COMP(depot,DEFDOSE)
  COMP(effect)

$DES
DADT(1) = KA*A(3) - K10*A(1) - K12*A(1) + K21*A(2)
DADT(2) = K12*A(1) - K21*A(2)
DADT(3) = -KA*A(3)
CONC = A(1)/V1
DADT(4) = KEO*(CONC-A(4))

$ERROR
CALLFL = 0

LOQ1=10
LOQ2=20

EFF = BL* (1 - IMAX*A(4)**HILL/ (IC50**HILL+A(4)**HILL))
IPRED=EFF
SIGA=THETA(7)
STD=SIGA
IF(TYPE.EQ.0) THEN ; GREATER THAN LOQ
  F_FLAG=0
  Y=IPRED+SIGA*EPS(1)
  IRES =DV-IPRED
  IWRES=IRES/STD
ENDIF
IF(TYPE.EQ.1.AND.ASSY.EQ.1) THEN ; BELOW LOQ1
  DUM1=(LOQ1-IPRED)/STD
  CUM1=PHI(DUM1)
  F_FLAG=1
  Y=CUM1
  IRES = 0
  IWRES=0
ENDIF
IF(TYPE.EQ.1.AND.ASSY.EQ.2) THEN ; BELOW LOQ2
  DUM2=(LOQ2-IPRED)/STD
  CUM2=PHI(DUM2)
  F_FLAG=1
  Y=CUM2
  IRES = 0
  IWRES=0
ENDIF

$SIGMA 1 FIX

$ESTIMATION MAXEVAL=9990 NOABORT SIGDIG=3 METHOD=1 INTER LAPLACIAN
  POSTHOC PRINT=2 SLOW NUMERICAL
$COVARIANCE PRINT=E SLOW

MODEL M4:
$DATA data.csv IGNORE=#
$SUB ADVAN8 TRANS1 TOL=6
$MODEL
  COMP(central)
  COMP(peri)
  COMP(depot,DEFDOSE)
  COMP(effect)

$DES
DADT(1) = KA*A(3) - K10*A(1) - K12*A(1) + K21*A(2)
DADT(2) = K12*A(1) - K21*A(2)
DADT(3) = -KA*A(3)
CONC = A(1)/V1DADT(4) = KEO*(CONC-A(4))

$ERROR
CALLFL = 0

LOQ1=10
LOQ2=20

EFF = BL* (1 - IMX*A(4)**HILL/ (IC50**HILL+A(4)**HILL))
IPRED=EFF
SIGA=THETA(7)
STD=SIGA
IF(TYPE.EQ.0) THEN ; GREATER THAN LOQ
  F_FLAG=0
  YLO=0
  Y=IPRED+SIGA*EPS(1)
  IRES =DV-IPRED
  IWRES=IRES/STD
ENDIF
IF(TYPE.EQ.1.AND.ASSY.EQ.1) THEN
  DUM1=(LOQ1-IPRED)/STD
  CUM1=PHI(DUM1)
  DUM0=-IPRED/STD
  CUMD0=PHI(DUM0)
  CCUMD1=(CUM1-CUMD0)/(1-CUMD0)
  F_FLAG=1
  Y=CCUMD1
  IRES = 0
  IWRES=0
ENDIF
IF(TYPE.EQ.1.AND.ASSY.EQ.2) THEN
  DUM2=(LOQ2-IPRED)/STD
  CUM2=PHI(DUM2)
  DUM0=-IPRED/STD
  CUMD0=PHI(DUM0)
  CCUMD2=(CUM2-CUMD0)/(1-CUMD0)
  F_FLAG=1
  Y=CCUMD2
  IRES = 0
  IWRES=0
ENDIF

$SIGMA 1 FIX

$ESTIMATION MAXEVAL=9990 NOABORT SIGDIG=3 METHOD=1 INTER LAPLACIAN
  POSTHOC PRINT=2 SLOW NUMERICAL
$COVARIANCE PRINT=E SLOW




Sameer Doshi
Pharmacokinetics and Drug Metabolism, Amgen Inc.
(805) 447-6941





Received on Wed Nov 18 2009 - 12:53:17 EST

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