132  General Concepts

Generated from nmhelp plain-text source files (*.gen) of the NONMEM 7.6.0 distribution. These mirror the content presented by nmhelp and complement the formatted Part VIII Help Guide.

1 INDIVIDUALS

MEANING: A data analysis unit

CONTEXT: NONMEM input/output

DISCUSSION:

Data to be analyzed with NONMEM are often population data, by which is meant multiple data arising from each of a number of individual units. Individuals are typically persons, but they may be any other appropriate units, such as families, geographic localities, etc. Data are regarded as being statistically independent from unit to unit.

With NONMEM, there are two nested levels of random effects, The first level applies to individuals; different individuals are regarded as having different realizations of level-one random effects. A second level of random effects applies to the observations from each individual; different (univariate) observations are regarded as having different realizations of level-two randoms effects, but the same realization of level-one random effects.

The data from an individual is given in the data set by a contiguous group of data records, with one observation on each data record, and all data records having the same identification (ID) data item. This group of data records is called the individual record, or level-one (L1) record. (Do not confuse a data record, which is one record in a data file, with an individual record, which is a group of data records.)

Data to be analyzed may be single-subject data. These are data that appear to require at most one level of random effects. (In fact, there are population data which require only one level of the two NONMEM levels of random effects, along with a second level of random effects which may be expressed in a way that is transparent to NONMEM. This type of situation is communicated in such a way that NONMEM does not mistake these data for single-subject data.) Such data may actually arise physically from different individual units, or individuals. Indeed, when they do, they may even be comprised of multiple data from different units, e.g. pairs of plasma and saliva concentrations obtained at the same time point, each from a number of different subjects. However, if as with this example, only one level of random effects is needed, these data are nonetheless considered to be single-subject data. The data are regarded as being statistically independent from unit to unit. When single-subject data indeed arise physically from the same subject, the data can also be grouped into individual units such that the data are regarded as being statistically independent from unit to unit. These units are also called “individuals”. As an example, there may be pairs of plasma and saliva concentrations from the same subject. More precisely, NM-TRAN recognizes population data to be data that do not qualify as single-subject data.

NONMEM counts the number of distinct individuals in the data set, and reports this count as a check.

E.g., TOT. NO. OF INDIVIDUALS: 166

NONMEM 7 also reports how the data is to be analyzed:

ANALYSIS TYPE: SINGLE-SUBJECT
ANALYSIS TYPE: POPULATION
ANALYSIS TYPE: POPULATION WITH UNCONSTRAINTED ETAS

Population analysis with unconstrained etas is new with NONMEM 7, and can be used to analyze a population data set as separate individuals. OMEGA diagonal values are fixed to a special value 1.0E+06.

See Guide Introduction_7 “Analyzing Single-subject data as Population with Unconstrained etas”. (See recid2.exa).

REFERENCES: Guide I, section E; Guide Introduction_7

2 INTRA AND INTER-INDIVIDUAL

MEANING: Types of random errors

CONTEXT: NONMEM terminology

DISCUSSION:

Random intra-individual (“within an individual”) and inter-individual (“between individuals”) variability are terms that are used in discussing NONMEM output.

Case 1. When the data are population

Random inter-individual variability refers to the unexplained difference between individuals’ parameter values and the typical values in the population. It is described in NM-TRAN using ETA(n) variables. PRED describes the effect of these variables to NONMEM via the partial derivatives in the G array. The variance of these variables is given in the OMEGA matrix. Random intra-individual variability refers to unexplained (residual) error in a model (the difference between observed and predicted values). It is described in NM-TRAN using EPS(n) or ERR(n) variables. PRED describes the effect of these variables to NONMEM via the partial derivatives in the H array. The variance of these variables is given in the SIGMA matrix.

Case 2. When the data are single-subject

Random inter-individual variability refers unexplained (residual) error in a model (the difference between observed and predicted values). This, despite the fact that data may come from a single subject, is because each observation is placed into a separate individual record, and because only level-one random effects are needed to describe it. It is described in NM-TRAN using ERR(n) or ETA(n) variables. PRED describes the effect of these variables to NONMEM via the partial derivatives in the G array. The variance of these variables is given in the OMEGA matrix. However, when the data are in fact from a single subject, and when there is no need to use NONMEM terminology, then users often associate the ETA(n) and OMEGA with intra-individual variability, which corresponds to their experimental point of view.

REFERENCES: Guide I, section A.5 , E

3 NONMEM MODEL

MEANING: The name of a type of statistical model.

CONTEXT: NONMEM input/output

DISCUSSION:

The acronym NONMEM denotes both the model and the program used to analyze data according to such a model. (See nonmem_program) This entry discusses the NONLINEAR MIXED EFFECTS MODEL (NONMEM).

Regression models structurally link (possibly multivariate) observations (Dependent variables, DV) to independent variables (fixed effects, represented by other data items) through a functional form (model) quantified by (fixed effect) parameters. These model forms may be nonlinear in the parameters.

Random effects may also enter the model. In NONMEM they are of two types which usually enter the model at two different levels. The first type, ETA, describes differences between individuals; the second type, EPSILON, describes errors between model predictions and observations. (When all data come from the same individual, or when each observation is to be treated as statistically independent from all others, then ETA-type random effects describe all errors, and EPSILON-type random effects do not appear).

Within an individual, ETA may be a vector. Likewise, within one observation, EPSILON may be a vector, especially if the observations are multivariate, as several random effects of each type may be needed to characterize the data adequately.

The parameter vector THETA contains all fixed effect population parameters.

The OMEGA matrix, a random effects parameter, is the variance-covariance matrix of ETA (across individuals); the SIGMA matrix serves the same function for EPSILON (its variance covariance is assumed identical across all observations).

(See eta, eps, theta, effect). (See parameter, model, omega, sigma).

REFERENCES: Guide I, section C , D , E; Guide V, section 3 , 4

4 NONMEM PROGRAM

MEANING: The name of a computer program.

CONTEXT: NONMEM input/output

DISCUSSION:

The acronym NONMEM denotes both a type of statistical model and the program used to analyze data according to such a model. (See non-mem_model). This entry briefly describes the NONLINEAR MIXED EFFECTS MODEL (NONMEM) program.

NONMEM is a computer program written in FORTRAN 90 used to analyze data according to a Non-linear Mixed Effects Model. NONMEM is batchoriented. It is accompanied by an input preprocessor (NM-TRAN) that provides a SAS-like user communication interface, and by a suite of subprograms (PREDPP) that, within the context of the NONMEM program, implements most of the common simple pharmacokinetic models used by pharmacokineticists. PREDPP also has code for solving general linear and non-linear differential equations describing more complicated pharmacokinetic models.

The user generally will have to supply data and a code (either in an abbreviated form understood by NM-TRAN, or in a FORTRAN subroutine) specifying the dependence on the mixed effects. He will also have to make choices regarding the NONMEM process: e.g., whether to estimate parameters, and if so, which of several estimation methods to use (each method minimizes a different objective function).

NONMEM output reports the minimum value of the objective function, parameter estimates, standard errors, tables, and line-printer scatterplots, etc., as requested. NONMEM computes model predictions using the parameter estimates, and similarly, residuals and weighted residuals, and makes these available for tables and scatterplots.

NONMEM can also easily be used to simulate data under a NONMEM model.

With NONMEM 7, there are additional output files, called the “raw” and “additional” output files. Here, “root” is the name of the NM-TRAN input file specified on the nmfe7 command (not including extension). These provide an efficient way of way of extracting numerical results from the analysis. By default, the raw output file is root.ext. The additional output files include root.ext root.cov root.coi root.cor root.phi, etc., where root is the name of the control file (not including extensions).

(See raw_output_files). (See additional_output_files). (See estimate, method, parameter, parameter_estimate). (See objective_function, table, scatterplot). (See residual, weighted-residual, predpp).

REFERENCES: Guide I, section A; Guide V, section 1 , 2