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RE: Modeling biomarker data below the LOQ

From: Mats Karlsson <mats.karlsson>
Date: Wed, 18 Nov 2009 23:27:49 +0100

Dear Sameer,

 

We've had this problem with biomarker data and published experiences in
terms of a methodological paper (below). Maybe it can give you some ideas.

 

Handling data below the limit of quantification in mixed effect models.

Bergstrand M, Karlsson MO.

AAPS J. 2009 Jun;11(2):371-80. Epub 2009 May 19.

 

Best regards,

Mats

 

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

 

From: owner-nmusers
Behalf Of Doshi, Sameer
Sent: Wednesday, November 18, 2009 6:53 PM
To: nmusers
Subject: [NMusers] Modeling biomarker data below the LOQ

 

Hello,

We are attempting to model suppression of a biomarker, where a number of
samples (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
baseline, are supressed below the LOQ for a given duration, and then return
to baseline.

 

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 - 17:27:49 EST

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