Modeling biomarker data below the LOQ

From: [email protected] [mailto:[email protected]] On 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

-----Original Message----- From: Leonid Gibiansky [mailto:[email protected]] Sent: den 20 november 2009 04:01 To: Mats Karlsson Cc: 'Doshi, Sameer'; 'nmusers'; Martin Bergstrand Subject: Re: [NMusers] Modeling biomarker data below the LOQ 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:* [email protected] > [mailto:[email protected]] *On 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 > > > > > > > > >

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Leonid Gibiansky Sent: Friday, November 20, 2009 10:21 AM To: Martin Bergstrand Cc: 'Mats Karlsson'; 'Doshi, Sameer'; 'nmusers' Subject: Re: [NMusers] Modeling biomarker data below the LOQ Dear Martin, I wish I live in that bright future where "practical issues disappear as estimation methods and computational power improved"; at this time, many of my FOCEI models run for hours, even days, and this would make it difficult to use Laplacian on each and every model. If you look at the end of this discussion: http://cognigencorp.com/nonmem/nm/99oct041999.html you will find Lewis Sheiner description of LOQ/2 imputation 1. Delete all but the first in each continuous series of BQL observations 2. Set the remaining (first) one DV = QL/2 3. Use an additive plus proportional error model with the SD of the additive part >= QL/2. Step 3 (additive error with SD > QL/2) is really important. If you estimated SD for BQL observations without this restriction, this may invalidate your conclusions concerning this method. In my experience, this restriction makes a large difference in the results. The idea is to penalize the model for predictions above LOQ, but not below LOQ. Ideally, we would like to have a penalty function that is zero if IPRED < LOQ, and non-zero otherwise. Since we are restricted by normal residual error, BQL value is imputed as LOQ/2, and SD of the associated error is fixed at (LOQ/2)^2. Thus, the penalty for abs(IPRED-LOQ/2)< SD observations is small but increases as IPRED > LOQ. Note that ignoring observations is equivalent to assigning them a very large residual error. If you look on the plots in your paper, you will see that the direction of the bias for the method with ignored observations (infinite residual error associated with these observations) is the opposite relative to the bias for LOQ/2 imputation (presumably, with small associated additive error). It could be that if you fix an optimal value of the residual error, the bias would get smaller or disappear completely. As to the value of the bias, 10% bias is rarely important in real-life examples: you rarely see parameters estimated with less than 10% (RSE=0.1) precision (confidence intervals on the parameter estimates are approximately VALUE*(1 +/- 2*RSE). With that, I completely agree that if you can use the best method (M3) you should do it. Thanks Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Martin Bergstrand wrote: > Dear Leonid, > > The extra error term for the BQL observations was estimated. This extra > error term was only added for Model A. In the other examples there was > already an additive part in the residual error that sufficiently relaxed the > assumption of the imputation. > > I am not a big fan of imputations of BQL samples and think that they should > be avoided in favor of the M3 or M4 method as often as possible. However if > practical issues (probably disappearing as estimation methods and > computational power are improving) hinder you from using the likelihood > based methods I suggest to do a small sensitivity analysis regarding what > imputation to chose. There are no possibility to make general > recommendations on what imputations (LOQ/2 etc.) that will result in > unbiased estimates. > > The first thing you should do is to evaluate the simulation properties of > the obtained model parameters. In the article that you refer to we have > described how we think that VPC are best done for datasets with censored > observations such as BQL. If a certain imputation is chosen and the final > model demonstrate good simulation properties both for the contentious > observations (above LOQ) and for the fraction of BQL samples this is a good > indication that the obtained parameter estimates are likely to be fairly > unbiased. > > I have also thought of more elaborate approaches with simulation and > re-estimation with different imputations of BQL observations to evaluate the > possible biased introduced by substitution the BQL samples with an assumed > value (similar principle as the Back step method described by Kjellsson MC > et.al. (1)). However this is nothing that I have tested or think is an > attractive solution for many cases. > > (1) Kjellsson MC, Jönsson S, Karlsson MO. The back-step method--method for > obtaining unbiased population parameter estimates for ordered categorical > data. AAPS J. 2004 Aug 11;6(3):e19. > > By the way I don't agree with your conclusion that LOQ/2 substitution > provides reasonable results in the indirect response model example (C). It > induces a non negligible amount of bias in both the concentration effect > parameter (SLOP) and Kout (5-15%). In my opinion substitution with LOQ/2 are > just as bad as omitting the BQL data (just bad in another way) for that very > example. > > Kind regards, > > Martin Bergstrand, MSc, PhD student > ----------------------------------------------- > Pharmacometrics Research Group, > Department of Pharmaceutical Biosciences, > Uppsala University > ----------------------------------------------- > P.O. Box 591 > SE-751 24 Uppsala > Sweden > ----------------------------------------------- > [email protected] > ----------------------------------------------- > Work: +46 18 471 4639 > Mobile: +46 709 994 396 > Fax: +46 18 471 4003 > > > -----Original Message----- > From: Leonid Gibiansky [mailto:[email protected]] > Sent: den 20 november 2009 04:01 > To: Mats Karlsson > Cc: 'Doshi, Sameer'; 'nmusers'; Martin Bergstrand > Subject: Re: [NMusers] Modeling biomarker data below the LOQ > > 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:* [email protected] >> [mailto:[email protected]] *On 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 >> >> >> >> >> >> >> >> >> > >