NONMEM Users Guide Part VI - PREDPP - Chapter I

I. Overview of PREDPP

PRED is a NONMEM subroutine that needs to be supplied by the user. Its basic function is to compute model-based predictions for observations. A PRED for population pharmacokinetic data analysis can be very complicated and difficult to write, and the NONMEM Project Group has tried to help by writing PREDPP, a general version of this subroutine that is particularly suited for the analysis of population pharmacokinetic data. This version of PRED is informally called PREDPP -- for PRED Population Pharmacokinetics, but the formal name of the subroutine is simply PRED, since this is the entry name used by the calling programs in NONMEM. PREDPP can also be used with NONMEM to analyze pharmacokinetic data from a single subject, because the required predictions are of a similar nature, and it can be used with NONMEM to simulate either population or single-subject pharmacokinetic data. As the reader shall see, PREDPP is a very powerful tool for computing pharmacokinetics.

There are a number of different basic kinetic models that can be invoked by PREDPP. The user selects the basic model by selecting one or more subroutines from a library of subroutines of PREDPP and linking the selected subroutines with the NONMEM and PREDPP subroutines that must always be present in a load module.†
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† The NONMEM load module is also referred to as the NONMEM executable.
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This process is described in detail in chapter VII. The library is called the PREDPP Library

For example: If the user is interested in a one compartment linear model, he chooses subroutine ADVAN1 from a list of PREDPP Library subroutines: ADVAN1, ADVAN2, ADVAN3, etc., which, though distinguishable by the different models they compute and by their informal names as just stated, actually have the same formal name, ADVAN, since this is the entry name used by the calling program in PREDPP. ADVAN stands for ADVANCE because it is the task of each ADVAN routine to advance the state vector of compartment amounts (and partial derivatives of the compartment amounts with respect to random variables, when appropriate) from each point in time to the next. For all the ADVAN subroutines, PREDPP does the housekeeping for the state vector. For example PREDPP initializes compartments to zero at the start of an individual record, resets compartments to zero when requested, applies bolus doses, turns compartments on and off, keeps track of event and non-event times such as infusion start and stop times, additional dose times, and model event times, and computes amounts in the the output compartment if it is on. Another possible name for ADVAN would have been SOLVER, because most ADVAN routines solve a set of differential equations, either analytically (ADVAN1-5, ADVAN7, ADVAN10, ADVAN11, ADVAN12) or by integration (ADVAN6, ADVAN8, ADVAN13, ADVAN14, ADVAN16, ADVAN18). ADVAN9, ADVAN15, ADVAN17 solve a set of simultaneous differential and algebraic equations.
ADVAN16 and ADVAN18 (or ADVAN17 if there are equilibrium compartments) may be used to solve a set of differential equations with delay differential equations.

The kinetic models that may be selected are:

As will be discussed momentarily, this list covers a good deal more than appears to be covered at first glance. First, though, the distinction between a general linear and a general nonlinear compartmental model is clarified. A general linear compartmental model describes linear kinetics with up to 999 compartments, and the computational algorithm employed is based on use of the matrix exponential. Linear systems with only real eigenvalues, or with possibly complex eigenvalues, are reliably handled. A general nonlinear model describes either linear or nonlinear kinetics with up to 999 compartments, and the computational algorithm employed is based on a differential equation solver.

Most often with population pharmacokinetic data analysis, a one or two compartment model suffices. Although these models can also be implemented with a general linear or nonlinear model, the specific implementations that have been written for PREDPP are based on the traditional sums of exponential forms, and are therefore computationally very much faster than are implementations with the general models.

With any of the models, a peripheral output compartment is always present. Associated with this compartment is a dimensionless pharmacokinetic parameter, . Of the entire amount, , of drug introduced into the system and eliminated from it, a fraction of this amount goes into this output compartment. The output compartment may be turned on and off; while on, drug accumulates therein, and when turned off, the amount therein is reset to zero. So, for example, if the output compartment is regarded as a urine compartment (so might be the ratio of renal to total clearance), the initiation and termination of a urine collection can be simulated. Alternatively, using general linear or nonlinear models, compartments from which no distribution can occur into any other compartments can be defined within the system itself. Such compartments may also be turned on and off. If a user-defined comparment is initally off, may be turned on and off, and may not receive a dose, it is called an output-type compartment.†
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† Output-type compartments have been part of PREDPP since the first version, but were not discussed in detail. See Chapter V Section H and VI Section B.
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The kinetics, i.e. drug amounts, described by any of these models can be parameterized by either microconstants, i.e. rate constants, or certain reparameterizations of the microconstants, possibly involving other parameters such as volume of distribution. The value of a kinetic parameter can depend in turn on the values of physiological and other concomitant variables. For any individual, the values of these concomitant variables can change at discrete times, and so, therefore, can the value of the PK parameter.

Drug can be input into any of the compartments (except the output compartment) at any time. Bolus doses can be given. In the case of the one compartment model with first order absorption, for example, an IV bolus dose can be input into the central compartment, and another oral bolus dose can be input into the drug depot compartment at the same or different time as the first dose is input. Also, infusions of known amount and duration can be given. Also, a bolus dose of a known amount can be given whose appearance into a specified dose compartment, rather than being instantaneous, is actually governed by a zero-order process, the rate or time-duration of which may be regarded as a kinetic parameter whose value may be specified or estimated. So for example, a bolus dose in the form of a tablet may be placed in a compartment, but due to the dissolution process, its appearance in the compartment may be better described by a zero-order process.

If many doses are given over time, as may happen in a clinical setting, the specification of this in the data record structure can be tedious, and the computation time is affected since a state vector is updated at each time point that a dose is given. If, however, these doses are given in a regular cyclic fashion (e.g. 5 mg at 8 AM, 1 mg at 8 PM; daily) and over such a sufficiently long time that the system can be regarded as being at steady-state at the times the doses of some particular cycle, i.e. the "steady-state cycle", are given, then steady-state kinetics can be used to greatly mitigate the dose specification and computation time problems. Only the steady-state cycle of doses need be specified, and the state vector will only need to be updated at the times these doses are given. Steady-state kinetics may be invoked for this purpose with any of the PREDPP models (except with a general nonlinear compartmental model when the nonlinear kinetics imply that steady-state cannot be achieved).

Note that steady-state kinetics cannot be used with some systems of differential equations. This includes delay differential equations and also other systems, for example, those in which there is a change in kinetics outside the dosing interval. With NONMEM 7.5, an Empirical method of Achieving Steady State may be used.
See INTRODUCTION TO NONMEM 7, section "An Empirical Method of Achieving Steady State"

If several doses are given over time, but they do not lead to a steady-state, the specification of this in the data record structure might still be tedious. However, if these doses are the same type of dose, given with a constant interdose interval, then in this case there is still a convenient way to mitgate the specification problem.

All the kinetic models are augmented by the ability to allow any dose to appear in the system at some lag time (called an absorption lag time) after the time the dose is nominally given. All kinetic models are augmented by the ability to allow a fraction (called a bioavailability fraction) of any dose to appear in the system, rather than the nominal dose. Absorption lag times and bioavailability fractions may be specified or estimated.

All the kinetic models allow model event time parameters, which allow the modelling of discrete times at which some aspect of the system can be changed. Model event times may be specified or estimated.

All the kinetic models allow the use to supply initial values for the compartments, using the compartment initialization feature (See A_0, Chapter III, Section I.B).

As of NONMEM 7.5, all the kinetic models allow the user to update compartment amounts at any time, using the A_UFLG Flag feature (See A_U, Chapter III, Section I.B)

With general non-linear models (ADVAN6, ADVAN8, ADVAN9, ADVAN13, ADVAN14, ADVAN15, ADVAN16, ADVAN17, ADVAN18) the differential equations may include terms for endogenous drug production. The Initial Steady State feature of PREDPP may be used to compute steady state compartment amounts without using dose event records. (See I_SS, Chapter III, Section I.B and Chapter V, Section F.3). This feature may be used with the compartment initialization feature.

Not only must PRED compute model based predictions, it must also compute partial derivatives of the statistical model for the observations with respect to all random variables occurring in the model (see Guide I. See also the Introduction to NONMEM 7. Classical NONMEM methods require the partial derivatives, but new methods may not). This computation has proved to be a particularly difficult one for many users to program. Just as PREDPP serves the important purpose of greatly simplifying the programming the user must undertake to compute complicated population-type pharmacokinetic predictions, it also serves the important purpose of greatly simplifying the user-required programming of the derivative computation for population pharmacokinetic models.

The user must still be concerned with generating a small amount of code in the form of two user-supplied subroutines of PREDPP. The first routine, PK, functions essentially to compute the values of pharmacokinetic parameters, e.g. clearance, in terms of the values of covariables, e.g. age and weight, and the values of random interindividual effects accounting for random interindividual variability. The second routine, ERROR, functions essentially to specify the residual error structure, e.g. to specify that residual error is additive, or that it is multiplicative. However, PREDPP allows pharmacodynamics along with pharmacokinetics to be modeled, and it does so by allowing pharmacodynamic models to be specified in the ERROR routine. This may strike the user as a strange design, which it is. The design for PREDPP allows pharmacokinetic models to be specified conveniently, and only as an "afterthought" does it allow the specification of pharmacodynamic models. Detailed discussion of PK and ERROR is to be found in chapters III and IV. A few other user-supplied subroutines are at times required. Detailed discussion of these is to be found in chapter VI. In particular, use of a general nonlinear compartmental model requires the user to supply code for the involved differential equations, but as seen in section VI.C, this need not be a hard task. With NM-TRAN, which is a pre-processor to NONMEM and PREDPP, the task of creating PK and ERROR routines is simplified, and the user need not write the code to compute partial derivatives of the statistical model for the observations with respect to the random variables. $PK and $ERROR blocks describe the statistical model. NM-TRAN supplies the code to compute the partial derivatives.

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