Re: batches with different half-life - linear PK

I am resending my response to this email. What I sent earlier was too complicated. The attachment "remarks.txt" contains the explanation. On Thu, 19 Apr 2007 14:54:11 +0000 (GMT), [EMAIL PROTECTED] said: > Hello NONMEM Users, > > Sometimes the same subjects receive the same drug from different batches. > Potentially, half-life can be different accross batches. Theoretically, > it is easy to model if PKis linear because NONMEM superimposes > single-dose processes to obtain predicted concentrations for multiple > doses. Does enyone know how to implement it in NONMEM? Are there any > classes or publications which can help? > > Thanks! > Pavel -- Alison Boeckmann [EMAIL PROTECTED] $PROB batch1 $DATA dat1.txt IGNORE=# $INPUT ID TIME AMT RATE CMT DV $SUBR ADVAN1 $PK F1=1 D1=1 ALAG1=1 K=1 S1=1+ETA(1) $ERROR Y=F+ERR(1) $OMEGA 1 $SIGMA 1 $TABLE TIME CMT FILE=tab1.txt $PROB batch2 $DATA dat1.txt IGNORE=# $INPUT ID TIME AMT RATE CMT DV $SUBR ADVAN1 $PK F1=.5 D1=.5 ALAG1=.5 K=1 S1=1+ETA(1) $ERROR Y=F+ERR(1) $OMEGA 1 $SIGMA 1 $TABLE TIME CMT FILE=tab2.txt $PROB batch1+batch2 $DATA dat3.txt IGNORE=# $INPUT ID TIME AMT RATE BAT CMT DV $BIND - - - - DOSE $SUBR ADVAN1 $PK (NONEVENT) IF (BAT.EQ.1) THEN F1=1 D1=1 ALAG1=1 ENDIF IF (BAT.EQ.2) THEN F1=.5 D1=.5 ALAG1=.5 ENDIF K=1 S1=1+ETA(1) $ERROR Y=F+ERR(1) $OMEGA 1 $SIGMA 1 $TABLE TIME CMT FILE=tab3.txt # ID TIME AMT RATE CMT DV 1 0 1000 -2 1 . 1 1 0 0 0 10 1 2 0 0 0 10 1 3 0 0 0 10 1 10 0 0 0 10 # ID TIME AMT RATE BAT CMT DV 1 0 1000 -2 1 1 . 1 0 1000 -2 2 1 . 1 1 0 0 0 0 10 1 2 0 0 0 0 10 1 3 0 0 0 0 10 1 10 0 0 0 0 10 $PROB batch1 $DATA datp.txt IGNORE=# $INPUT ID TIME AMT RATE CMT DV $SUBR ADVAN6 TOL=6 $MODEL COMP=(B1) COMP=(B2) $PK F1=1 D1=1 ALAG1=1 F2=.5 D2=.5 ALAG2=.5 K10=1 K20=1 S1=1+ETA(1) S2=1+ETA(1) $ERROR Y=A(1)/S1+A(2)/S2+ERR(1) $DES DADT(1)=-K10*A(1) DADT(2)=-K20*A(2) $OMEGA 1 $SIGMA 1 $TABLE TIME CMT FILE=tabd.txt $PROB batch1 $DATA datp.txt IGNORE=# $INPUT ID TIME AMT RATE CMT DV $SUBR ADVAN7 $MODEL COMP=(B1) COMP=(B2) $PK F1=1 D1=1 ALAG1=1 F2=.5 D2=.5 ALAG2=.5 K10=1 K20=1 S1=1+ETA(1) S2=1+ETA(1) $ERROR Y=A(1)/S1+A(2)/S2+ERR(1) $OMEGA 1 $SIGMA 1 $TABLE TIME CMT FILE=tabp.txt # ID TIME AMT RATE CMT DV 1 0 1000 -2 1 . 1 0 1000 -2 2 . 1 1 0 0 0 10 1 2 0 0 0 10 1 3 0 0 0 10 1 10 0 0 0 10 I am resending this email. The original version was too complicated. The control streams cs1.txt and cs2.txt are simpler, which should make the issue a little more clear. ------------------------- Original question: Sometimes the same subjects receive the same drug from different batches. Potentially, half-life can be different accross batches. Theoretically, it is easy to model if PKis linear because NONMEM superimposes single-dose processes to obtain predicted concentrations for multiple doses. Does enyone know how to implement it in NONMEM? ------------ To me, this is a very interesting question. No one has posted a response that addresses the modeling issue. I will make an attempt, although (as I do not read the literature or attend conferences) it may well be that this has already been worked on and is well understood, and this email is uneeded. Also, my understand of the manufacturing issues may be naive. With any ADVAN, there are three additional PK parameters that might differ from batch to batch: bioavailability (difference in amount of active ingredient vs. filler). absorption lag (difference in thickness of coating) duration of zero-order entry into compartment (difference in how fast tablet dissolves, once the coating is gone.) These will make a difference in the cp vs.time profile, even when the kinetics of the two drugs are identical. (Remember that, although you can parameterize in terms of halflife or anything you choose, ultimately PREDPP uses rate constants.) With the superimposition principle, doses from different batches move thru the system without affecting each other. I did some little runs with ADVAN1. I created only one subject's data The dose enters directly into compartment 1, but with lag time and modelled duration (which gives somewhat the flavor of drug entering from a depot compartment.) I attach control streams and data files for 3 runs: cs1.txt, cs2.txt, cs3.txt data files dat1.txt and dat3.txt Both cs1 and cs2 use the same data file, dat1.txt. There is a single dose into the central compartment. The values of F1, D1 and ALAG1 differ between cs1 and cs2. The values of PRED in the resulting tables (tab1.txt and tab2.txt) are different. cs3 uses dat3.txt, which puts two doses into the same compartment. One dose has BAT=1 and the other has BAT=2. In $PK, the value of BAT is tested and values are assigned to F1, D1 and ALAG1 equal to those of cs1 (for BAT=1) and cs2 (for BAT=2). If you do the three runs, you will see that the PRED values in the table (tab3.txt) add up to those from tab1.txt and tab2.txt at every time point. This is indeed superimposition. (Note that the $BIND record is needed. BAT would, by default, be the value for the next event record when lag time is completed. $BIND tells PREDPP to use the value of BAT from the originating dose event record, enabling $PK to compute the values of F1 and D1 appropriate to the value of BAT.) Pavel asks about different half-lifes, as if the kinetics (rate constants) could differ. Perhaps this might be due to a diffence in the molecular structure. For this, I suggest a set of parallel compartments. One set of compartments is for batch 1, another is for batch 2. In the $ERROR block, the prediction Y is obtained by adding the concentrations from the two "central" compartments. I attach the following control and data files: csp.txt, datp.txt ADVAN7 is used. Again, there is only a single compartment for each batch. Notice that there is no need for $BIND, or indeed for the BAT data item, as the doses enter different compartments. The PRED values are the same with cs3.txt and csp.txt, again demonstrating superimposition. Finally, the same model is implemented with differential equations ADVAN6: csd.txt (uses datp.txt) Results are identical to those with ADVAN7. Now you can get fancy with the modelling. E.g., include an absorption compartment, use different models for the rate constants K13 and K23, or different models for S1 and S2. With ADVAN6, even the differential equations could differ. The idea is the same: define parallel (sets of) compartments for the two batches. In $ERROR, add together the concentrations. This should work for any system having linear kinetics for which doses can be superimposed.