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Re: Modeling biomarker data below the LOQ

From: Leonid Gibiansky <LGibiansky>
Date: Thu, 19 Nov 2009 22:01:29 -0500

Mats, Martin,
In the paper, you mentioned that "an extra additive error
model term was added for samples substituted with LOQ/2". Was it fixed
or estimated? If fixed, how? Have you tried to vary this level?

In many of your examples, LOQ/2 imputations and exclusion of BQL samples
seen to lead to bias in opposite directions; if so, it could be an
optimal value (relative to LOQ) of the fixed extra error term that
provides the least biased parameters.

Laplacian method is often not feasible for receptor (target) models
since they are strongly nonlinear (thus requiring differential
equations) and stiff. Based on the the indirect-response model
simulations considered in your paper, LOQ/2 substitution seems to
provide reasonable results if Laplacian (and thus M2-M3-M4) cannot be used.

Thanks
Leonid

--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566




Mats Karlsson wrote:
> 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
> [mailto:owner-nmusers
> *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 Thu Nov 19 2009 - 22:01:29 EST

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