Re: Question regarding Calculation Process in $DES BLOCK

On Wed, 01 Jun 2011 17:57 -0400, "Luann Phillips" <[email protected]> wrote: > Alison, > > Thank you for the additional information. Especially the part about $DES > computing at the event time in a data record for output to the $TABLE. I > would like to make sure that I understand a specific point correctly. > > During a step from t=T1 to t=T2, NONMEM may still take on a value of > t=T2+i (i=a tiny number) and compute the equations at this time point. > When it is done, it goes back and computes the values at t=T2 for output > to the table file. > > So if you have an expression like the following in your $DES block, > would you still need to set flags to 'help' processing along at t=T2. > (context of example from a previous note from Li Li) > > Example: > integrating from TIME=T1 to TIME=T2 (which = a multiple of 24) > > RM=THETA(1) > > $DES > > TS=T-24*INT(T/24) > KIN=TS*RM > DADT(1) = -KIN*A(1) > > This function for Kin creates a cusp at every multiple of 24. So the > limit of Kin as you approach a multiple of 24 from the left is a maximum > and as you approach from the right the limit of Kin=0 (similar if not > same situation that occurs for an absorption alag). So if an integral > step of size h (within the advance from T1 to T2) encompasses a multiple > of 24 should flags be set to allow the integration routine to use > TS=T- 24*INT(time at beginning of interval h/24) for the full step? > > Or in terms of the an ALAG situation: > > What happens if NONMEM is taking a step (size h within an advance from > T1 to T2) that encompasses the value of ALAG? > > Does it use DADT(1) = 0*A(1) until t=ALAG and then switch to > DADT(1)=-Ka*A(1) at t >= ALAG (creating a cusp within the interval h)? > > or > > Does it use DAD(1) = 0 until t=end of the h interval (even though it's a > small bit past ALAG) and then switch to DADT(1)=-Ka*A(1) at the end of > the h interval? > > I really appreciate that you take the time to continue expanding our > knowledge about NONMEM. > > Best Regards, > > Luann Phillips > Director PK/PD > Cognigen Corporation > (716) 633-3463 ext. 236 > > > > > > > Alison Boeckmann wrote: > > Here is a little background on how it works. > > > > ADVAN routines such as ADVAN6 use a subroutine from third party sources > > to do the integration. For example, ADVAN6 calls DVERK from IMSL, > > ADVAN13 calls LSODA, etc. These subroutines are the ones that call DES. > > They call DES with various values of T during the integration > > ("advance") from T1 to T2. (T1 and T2 are beginning and ending event > > time. Typically, these are the times on a pair of event records.) The > > integrating subroutine may decide it has enough information after a call > > with a value of T that is not exactly T2 (might be a little less or a > > little more.) > > > > A change was made with NONMEM V so that, after an advance, DES is called > > by the ADVAN routine itself (i.e., $DES statements are evaluated) at the > > exact value of the event time. > > > > From the NONMEM V Supplemental Guide of March 1998 (guides/supp.pdf): > > 39. Displayed DES-defined Items > > DES-defined items may be displayed in tables or scatterplots and are > > computed at the event time in the data record. With previous versions > > of PREDPP, the displayed items might have been computed at a slightly > > different time and might have had slightly different values. > > > > This fixes the difficulty that Luann mentioned. > > > > Paul says: > > A related caveat is that during integration between two time points, > > the value of data items (in the $DES block) are set to the values > > defined at the end time, not the start time. I'm afraid that I can't > > give you a good explanation for this design decision. > > > > Every variable displayed via $TABLE has the value that was calculated by > > the last call to DES with the current event record. This is not a design > > decision; it is inevitable. Values created by PREDPP for display by > > NONMEM are stored in a common area (formerly COMMON NMPRD4; now MODULE > > NMPRD4). To display values at the start time would require PREDPP to > > save the values and to restore that part of NMPRD4. This could be rather > > difficult. Also, Stuart Beal preferred to see DES-computed values at > > the end time and that is why the change for a final call to DES at the > > event time was made. > > > > This also explains why the values for the first event record of the > > individual are those from the last event record of the previous > > individual. If there is no advance in time, then there is no call to > > the integrating subroutine, and no call to DES, so the values in NMPRD4 > > are unchanged. Warning 48 was new with NONMEM V in 1998. Why did we not > > at that time add a call to DES from the ADVAN routine with the first > > event record? I can't remember. Stuart Beal may have been afraid that > > some of the computations in a complicated DES might fail with values > > from the first event record, whereas they were ok with values from the > > second and subsequent event records. > > > > > > > > On Thu, 26 May 2011 16:28 -0400, "Luann Phillips" > > <[email protected]> wrote: > >> Hi Lili, > >> > >> In addition to the information Paul provided. DDTI for a specific row > >> should be the last value of T (continuous time) that the integration > >> step took. This may not match the event time identically. As NONMEM is > >> performing numerical integration between two event times T is taking > >> on many values between the two event times (TIME, discrete). During > >> this process, it may actually require taking a step that goes a small > >> amount past the 2nd event time. > >> > >> Best regards, > >> > >> Luann Phillips Director, PK/PD Cognigen Corporation > >> (716) 633-3463 ext. 236 > >> > >> Paul Matthias Diderichsen wrote: > >>> Hi Lili, > >>> > >>> On 5/26/2011 1:52 AM, Li Li wrote: > >>> > When I output DDT1, the table will be: Subject Time (hr) DDT1 > >>> > 1 0 4??? > >>> [...] > >>> > 2 0 5??? > >>> [...] > >>> > Why the DDT1 for subject 1 at first time point is 4 and subject 2 > >>> > at first time point is 5? Why it holds the last time point value > >>> > of each subject? > >>> > >>> In the output, nonmem tells you that this is going to happen: > >>> > >>> " (WARNING 48) DES-DEFINED ITEMS ARE COMPUTED ONLY WHEN EVENT TIME > >>> INCREASES. E.G., DISPLAYED VALUES ASSOCIATED WITH THE FIRST EVENT > >>> RECORD OF AN INDIVIDUAL RECORD ARE COMPUTED WITH (THE LAST ADVANCE > >>> TO) AN EVENT TIME OF THE PRIOR INDIVIDUAL RECORD. " > >>> > >>> A related caveat is that during integration between two time points, > >>> the value of data items (in the $DES block) are set to the values > >>> defined at the end time, not the start time. > >>> > >>> I'm afraid that I can't give you a good explanation for this design > >>> decision. > >>> > >>> Kind regards, > >>> > > > -- Alison Boeckmann [email protected] Luann, For ALAG parameters, PREDPP creates an event time. It advances the system (integrates the differential eqns) to the event time. Even if the model describes an abrupt change at the event time, the same values of DADT should be used across the change point. The integrating subroutine may go a little past the end time to refine its value at the end point. It should not be getting a sudden change from DES. That will confuse it, and is inappropriate. The derivatives at the event time are left hand deriviatives, as if the DADT stayed the same. You ask: -------- What happens if NONMEM is taking a step (size h within an advance from T1 to T2) that encompasses the value of ALAG? Does it use DADT(1) = 0*A(1) until t=ALAG and then switch to DADT(1)=-Ka*A(1) at t >= ALAG (creating a cusp within the interval h)? or Does it use DAD(1) = 0 until t=end of the h interval (even though it's a small bit past ALAG) and then switch to DADT(1)=-Ka*A(1) at the end of the h interval? ------- Basically the latter. However, I can't understand what model you are describing. At ALAG, KA changes from 0 to a non-zero value. Is this a case where there is no absorption till ALAG, and then the absorption process starts? Or, iF you are thinking of a bolus dose at time ALAG, then the equations are DADT(1)=-KA*0 till t=ALAG (because A1 is 0) DADT(2)=-KA*A(1) when t>=ALAG PREDPP does not add the dose into the compartment while the first advance (to ALAG1) is in process. It waits till the advance is finished, applies the dose, and then starts a new advance to the next event time. That is why I can use t=ALAG in both equations; the end point of the first advance is the starting point of the next advance, though PREDPP has changed A(1). (With $DES, read "integration interval" for "advance") Now about Li Li's original model with INT function. In general, I don't comment on complicated PK/PD models; there are many people on the nmusers list who are far more experienced than I am at modelling and I am unfamiliar with the physiology of the models. However, abrupt changes in DADT values at time points that depend on thetas and etas reminds me of models for EHC (Entero Hepatic Clearance). As I recall, the best way to handle abrupt changes was to model the change times as event times. Originally ALAG times were used for this; as I recall the MTIME (model event time) feature was provided to do the same thing, but avoid the need for artificial compartments and doses. I think LiLi's model should be using MTIMEs for TMIN and TGAP. There should be no IF/THEN statements in $DES. Instead, use the MPAST and MNEXT indicator variables in DADTs to select different terms (i.e., compute different values of DADT depending on values of T) . During the integration to an event time, values of MPAST and MNEXT will not change, even if the integrating subroutine goes a little past the end time. Maybe some one among the users can supply an example of EHC or a model that uses MTIME for a similar purpose, or can give suggestions tailored to Li Li's model.