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Introduction

NONMEM (NONlinear Mixed Effects Model) is a software for fitting nonlinear regression models using the mixed-effects framework. Designed for pharmacokinetic and pharmacodynamic applications, NONMEM takes account of the variability between subjects (random effects) and within the subjects, as well as the influence of measured covariates (fixed effects), while incorporating the nonlinear nature of the biochemical and physiological processes. It can handle situations such as each subject has only a few measurements, and when sampling times differ between subjects. The underlying method of NONMEM is general and can be applied to many problems beyond pharmacometrics.

Data records

NONMEM mainly uses longitudinal tabular data for analysis: each row of the data set identifies an event. There are two types of events: observation and nonobservation. Observation records identifiy events when dependent values are observed and stored in the reserved DV (dependent variable) field; Nonobservation records can represent a variety of events, such as dosing and change of covariates. NONMEM data set can also incorporate missing data, identified by MDV (Missing Dependent Variable) field: the record is not an observation if MDV = 1. NONMEM expects that different data records, ordered in time, are associated with different events.

Population data are organized into individual records, a group of contiguous data records having the same identification (ID) data item, associated with the same individual. In this case the time ordering refers to data records within an individual record.

A typical NONMEM analysis data set looks like this:

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 ID      TIME    C1      C2  ...  CN      DV     MDV
  1       1.     .5      10        5              1
  1       3.              9       10              1
  1       6.              6              4.1      0
  1       7.              7       10              1
  1      10.              7              5.3      0
  2       2.     .9       8        8              1
  2       2.5             6                       1
  2       6.              7                       1
  2       7.              8              6.4      0

It contains two individuals' records, with the following data items.

  • ID: subject identification;
  • TIME: time data;
  • C1, C2, …, CN: concomitant variable data items such as covariates.
  • DV: dependent value;
  • MDV: missing dependent value;

Note that blank data items are treated as nulls in NONMEM. They are read as zeros and appear as zeros in tables and scatterplots.

We discuss event record in detail in Chapter 5.

Example

Below is a simple NONMEM model's control stream.

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  $PROBLEM PHENOBARB ;# simple example
  $INPUT   ID TIME AMT DV
  $DATA    PHENO
  $SUBROUTINE ADVAN1
  $PK
     TVCL=THETA(1)
     CL=TVCL+ETA(1)
     TVVD=THETA(2)
     V=TVVD+ETA(2)
     K=CL/V
     S1=V
  $ERROR
     Y=F+ERR(1)
  $THETA  (0,.0047) (0,.99)
  $OMEGA  .0000055, .04
  $SIGMA  25
  $ESTIMATION  PRINT=5
  $TABLE     ID TIME AMT
  $COVARIANCE
  • NONMEM models consist of control records. Each control record starts with a "$" symbol followed by a reserved name. Control record $PROB on line 1 specifies string "PHENOBARB" as problem's name. The rest of the line is ignored as ";" indicates comments.
  • Line 2 says that the data file column 1-4 contain subject ID, observation time (TIME), dosing amount (AMT), and dependent value (DV), respectively.
  • Line 3 says the data is contained in file "PHENO".
  • Line 4 says we use a built-in one-compartment model called ADVAN1. Later in this document you will see that this specifies the one-compartment model without first-order absorption.
  • Line 5-11: the $PK record specifies the parameters of the ADVAN1 model. In this case, there is only one parameter: the elimination rate constatnt K. It is shown that K is calulated from Clearance CL and Volume of Distribution V. Some reserved NONMEM parameters (THETA and ETA) are used to obtain CL and V. There is also a scale parameter S1 based on V.
  • Line 12-13 says that we model observation Y as the sum of the prediction F (from the one-compartment model) and an error term ERR(1).
  • Line 14-16 give initial estimate of the parameters THETA, OMEGA, and SIGMA.
  • Line 17-19 request NONMEM to fit the model (ESTIMATE the model parameters), print some variables in a TABLE, and calculate the COVARANCE of the estimation.

As we go through this guide we will provide details of each record and symbol in the above model.

Notations

In this document we use the following notations to describe functions, arguments, and options.

  • Any or all arguments in [ ] are optional, e.g. [foo bar], and equivalently [foo] [bar], means foo and bar are both optional.
  • Options delimited by | cannot be used together, e.g. option=a|b means one must choose to specify option=a or option=b.
  • ... indicates reaptable arguments, e.g. filename ... means one can supply multiple files, and [label|value]... means label1 value2 value3 label4 is allowed.
  • A keyword with "(NONMEM version)" appended indicates the record/option as introduced in that version. For example "$DEFAULT (NM74)" means the record was introduced in NONMEM v7.4.
  • Starting in v7.2 NONMEM is no longer case-sensitive to reserved keywords, reserved variables, or user-defined variables.