How does NONMEM $DES work?

From: "Wang, Yaning" WangYA@cder.fda.gov Subject: [NMusers] How does NONMEM $DES work? Date: Tue, December 21, 2004 Nick: I just want to make sure I correctly understand your response. By default, NONMEM uses the value of C2(=1 in your example) at TIME2 as the value for C throughout the interval from TIME1 (=1) to TIME2 (=2) in order to solve the DE system for DV at TIME2 (=2). Is this right? By following this, I derived the interpolated value for C between TIME1 and TIME2. Suppose at TIME=1.3, we assume C should be 0.3 based on a linear interpolation. In eqation CNOW=C-SLOPE*T, I think C=1 and SLOPE=1 at TIME=1.3(C2 and SLOPE2 in data set are used throughout the interval by default). In order to get CNOW=0.3, T has to be 0.7 at TIME=1.3. How is T in $DES related to the TIME variable in the data set? Again, thanks a lot for the help. Yaning

From: "Wang, Yaning" WangYA@cder.fda.gov Subject: [NMusers] How does NONMEM $DES work? Date: Tue, December 21, 2004 7:46 pm Dear all: I am using an indirect model to describe the profile of an endogenous compound (A). And the elimination of this compound is affected by the exposure of a drug (B). Since it is almost impossilbe to find a model to describe the time course of drug B and there are enough pairs of drug B concentration and compound A level, I want to use the observed drug B concentration in the indirect model as follows: $DES DADT(1)=K0-KE{1+EMAX*C/(EC50+C)}*A(1) where C is the observed drug B concentration and A(1) is the endogenous compound level. I am concerned about how NONMEM handles this differential equations during the time interval where there are no inputs for C. For example, if we have data rows at day 1 and day 2 (for both A and B), how can NONMEM fit compound A level at day 2 without the drug B level information (C) during the interval between day 1 and day2? Is NONMEM assuming some interpolated values for C based on C1 and C2? If this approach is wrong, then consider another case. Suppose clearance (CL) follows a covariate model, e.g. CL=THETA(1)*(WT/70)**THETA(2). CL=THETA(1)*(WT/70)**THETA(2)*EXP(ETA()) $DES DADT(1)=-KA*A(1) DADT(2)=KA*A(1)-CL*A(2) Even though we have the same body weight at each row for one subject, how can NONMEM know WT is not a time dependent covariate? What if WT IS a time dependent covariate? Has anyone used the covariate model this way(or in a closed-form equation pattern)? Thanks a lot for any comment. Yaning Wang, PhD Pharmacometrician OCPB, FDA

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] How does NONMEM $DES work? Date: Tue, December 21, 2004 8:58 pm Yaning, NONMEM uses the value of the data item, e.g. C, specified in the record for which a solution is sought e.g. ID TIME C DV 1 1 0 10 1 2 1 8 When NONMEM solves the DE system for the second record (TIME=2) it will assume that C is 1 throughout the interval from TIME=1 to TIME=2. If you are unable to find a model for C then you can interpolate a value using the T variable in $DES. There are several ways to do this but the most efficient might be to pre-compute the slope connecting each two values of C and use this to predict C at T. Add this slope to the data set and use it in $DES. e.g. ID TIME C DV SLOP 1 1 0 10 0 1 2 1 8 1 $DES CNOW=C-SLOP*T Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] How does NONMEM $DES work? Date: Wed, December 22, 2004 2:37 pm Yaning, Sorry for the confusion. I wrote the reply in some haste because of pre-Christmas pressures and got the predictive formula for C(T) wrong. One solution is to add C from the previous record as a data item (CPRE) and TIME as TPRE: ID TIME TPRE C CPRE SLOP DV 1 1 1 0 0 0 10 ; first record for this subject 1 2 1 1 0 1 8 1 3 2 3 1 2 4 then compute C(T) in $DES: $DES CNOW=CPRE+SLOP*(T-TPRE) Nick -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ _______________________________________________________