From: Leonid Gibiansky <*LGibiansky*>

Date: Wed, 18 Nov 2009 14:42:36 -0500

Hi Sameer,

Several comments:

--------------------

You did not provide the entire code, but if BL is the observed baseline,

it should not be included in the dataset. If you have

BL=THETA(*)*EXP(ETA(*)) then the data are fine

--------------------

Additive error is assumed. I would rather use combined error (my guess

is that assay STD at DV=65 is larger than STD at DV < LLOQ).

---------------------

M2 method can be implemented using YLO option (BQL observations are

included with MDV=1). PRB will give you a model-based probability of

DV > YLO (see YLO EXAMPLE in help).

$ERROR

YLO = LOG1

IF(ASSY.EQ.2) YLO=LOG2

PRB = PR_Y

$EST METH=1 LAPLACIAN SLOW NOABORT

--------------------

I would increase TOL to 9 (if possible). It does not look like a stiff

system, so ADVAN6 can be tried

------------------

You have not described the problem: how well these M3 - M4 methods

describe your data? If you are not satisfied, could you describe the

deficiencies if there are any; these can help to resolve them.

Thanks

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Doshi, Sameer wrote:

*> 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 - 14:42:36 EST

Date: Wed, 18 Nov 2009 14:42:36 -0500

Hi Sameer,

Several comments:

--------------------

You did not provide the entire code, but if BL is the observed baseline,

it should not be included in the dataset. If you have

BL=THETA(*)*EXP(ETA(*)) then the data are fine

--------------------

Additive error is assumed. I would rather use combined error (my guess

is that assay STD at DV=65 is larger than STD at DV < LLOQ).

---------------------

M2 method can be implemented using YLO option (BQL observations are

included with MDV=1). PRB will give you a model-based probability of

DV > YLO (see YLO EXAMPLE in help).

$ERROR

YLO = LOG1

IF(ASSY.EQ.2) YLO=LOG2

PRB = PR_Y

$EST METH=1 LAPLACIAN SLOW NOABORT

--------------------

I would increase TOL to 9 (if possible). It does not look like a stiff

system, so ADVAN6 can be tried

------------------

You have not described the problem: how well these M3 - M4 methods

describe your data? If you are not satisfied, could you describe the

deficiencies if there are any; these can help to resolve them.

Thanks

Leonid

--------------------------------------

Leonid Gibiansky, Ph.D.

President, QuantPharm LLC

web: www.quantpharm.com

e-mail: LGibiansky at quantpharm.com

tel: (301) 767 5566

Doshi, Sameer wrote:

Received on Wed Nov 18 2009 - 14:42:36 EST