Model feature language (MFL)#

The MFL is a domain specific language designed to describe model features and sets of model features in a concise way. It can be used to describe model features for one single model or an entire space of model features, i.e. descriptions for multiple models. The basic building block of MFL is the feature description. A feature description consists of the name of a feature category followed by a comma separated list of arguments within parentheses. For example:

ABSORPTION(FO)

Each feature description describes one or multiple features of the same category, i.e. absorption, absorption delay, elimination, and distribution. Features of the same category are mutually exclusive and cannot be applied to the same model. Multiple model feature descriptions can be combined by separating them with either newline or a semi-colon.

The following two examples are equivalent:

ABSORPTION(FO);ELIMINATION(ZO)

ABSORPTION(FO)
ELIMINATION(ZO)

Option types#

MFL support the following types of options to feature descriptions:

Type	Example	Description
token or name	`FO`	The name of a feature within a category
number	`1`	A non-negative integer
range	`0..2`	A range of numbers (endpoints are included)
wildcard	`*`	All features of a category
array	`[FO, ZO]`	Multiple tokens or numbers
symbol	`@IIV`	A symbol with manual or automatic definition

Model features#

MFL support the following model features:

Category	Options	Description
ABSORPTION	`INST, FO, ZO, SEQ-ZO-FO, WEIBULL`	Absorption rate (instantaneous, first order, zero order, sequential zero order first order and Weibull)
ELIMINATION	`FO, ZO, MM, MIX-FO-MM`	Elimination rate (first order, zero order, Michaelis-Menten, mixed first order Michaelis-Menten)
PERIPHERALS	number, `DRUG/MET`	Number of peripheral compartments. If the peripheral compartment should be added to the drug compartment (default) and/or the metabolite compartment (if any). If `DRUG/MET` is omitted, it will be interpreted as `DRUG`. `MET` is only applicable to drug-metabolite models
TRANSITS	number, `DEPOT/ NODEPOT`	Number of absorption transit compartments and whether to keep the depot compartment
LAGTIME	`OFF/ON`	Absorption lagtime
COVARIATE	parameter, covariate, effect	Structural covariate effects (will always be added)
COVARIATE?	parameter, covariate, effect	Exploratory covariate effects (will be tested)
DIRECTEFFECT	`LINEAR, EMAX, SIGMOID, STEP, LOGLIN`	Direct effect PD models
EFFECTCOMP	`LINEAR, EMAX, SIGMOID, STEP, LOGLIN`	Effect compartment PD models
INDIRECTEFFECT	`LINEAR, EMAX, SIGMOID` , option	Indirect effect PD models. option can be either `PRODUCTION` or `DEGRADATION`
IIV	parameter, effect	(experimental) IIVs on parameters
IIV?	parameter, effect	(experimental) Exploratory IIVs on parameters
IOV	parameter, effect	(experimental) IOVs on parameters
IOV?	parameter, effect	(experimental) Exploratory IOVs on parameters
COVARIANCE	`IIV/IOV`, parameters	(experimental) Covariance between parameters
COVARIANCE?	`IIV/IOV`, parameters	(experimental) Exploratory covariances between parameters

Symbols#

The MFL supports certain automatically defined symbols that help with automating feature declaration. Currently, the only use of such symbols lies in declaring covariate effects via the syntax COVARIATE(@SYMBOL, …).

Symbol	Type	Description of automatic definition
@IIV	Parameter	All parameters with a corresponding IIV ETA
@PK	Parameter	All PK parameters
@PD	Parameter	All PD parameters
@PK_IIV	Parameter	All PK parameters with a corresponding IIV ETA
@PD_IIV	Parameter	All PD parameters with a corresponding IIV ETA
@ABSORPTION	Parameter	All PK absorption parameters
@ELIMINATION	Parameter	All PK elimination parameters
@DISTRIBUTION	Parameter	All PK distribution parameters
@BIOAVAIL	Parameter	All bioavailability parameters
@CONTINUOUS	Covariate	All continuous covariates
@CATEGORICAL	Covariate	All categorical covariates

New symbols can be manually defined via the syntax LET(SYMBOL, […]). The same syntax can be used to override the automatic definition of a symbol. For instance, to declare an explicit list of distribution parameters use LET(DISTRIBUTION, [V, K12, K21]).

Describe intervals#

It is possible to use ranges and arrays to describe the search space for e.g. transit and peripheral compartments.

To test 0, 1, 2 and 3 peripheral compartments:

TRANSITS(0)
TRANSITS(1)
TRANSITS(2)
TRANSITS(3)

This is equivalent to:

TRANSITS(0..3)

As well as:

TRANSITS([0, 1, 2, 3])

Redundant descriptions#

It is allowed to describe the same feature multiple times, however, this will not make any difference for which features are described.

ABSORPTION(FO)
ABSORPTION([FO, ZO])

This is equivalent to:

ABSORPTION([FO, ZO])

And:

PERIPHERALS(0..2)
PERIPHERALS(1)

Is equivalent to:

PERIPHERALS(0..2)

Examples#

Structural PK model#

An example of a search space for PK models with oral data:

ABSORPTION([ZO,SEQ-ZO-FO])
ELIMINATION([MM,MIX-FO-MM])
LAGTIME(ON)
TRANSITS([0, 1, 3, 10],*)
PERIPHERALS(0..1)

An example of a search space for PK models with IV data:

ELIMINATION([FO,MM,MIX-FO-MM])
PERIPHERALS([0..2])

Search through all available absorption rates:

ABSORPTION(*)

Allow all combinations of absorption and elimination rates:

ABSORPTION(*)
ELIMINATION(*)

Structural PD model#

Example for a PD model search space:

DIRECTEFFECT([linear, emax])
EFFECTCOMP(*)

Drug-metabolite#

Trying multiple drug-metabolite models with a peripheral compartment on the metabolite:

METABOLITE([PSC,BASIC]);PERIPHERALS([0,1],MET)

Covariates#

All covariate effects on parameters with IIV (exponential effects on continuous covariates and categorical effects on categorical covariates):

COVARIATE(@IIV, @CONTINUOUS, EXP)
COVARIATE(@IIV, @CATEGORICAL, CAT)

With fixed lists of covariates for which to add effects:

LET(CONTINUOUS, [AGE, WGT])
LET(CATEGORICAL, SEX)
COVARIATE(@IIV, @CONTINUOUS, *)
COVARIATE(@IIV, @CATEGORICAL, CAT)

All continuous covariate effects of WGT on distribution parameters:

COVARIATE(@DISTRIBUTION, WGT, *)

Variability#

Note

Currently under development and can be used experimentally in IIVSearch.

Specifying IIV on all PK parameters and covariances between them:

IIV(@PK,EXP);COVARIANCE(IIV,@IIV)

To specify which parameters explicitly and covariance between CL and VC:

IIV([CL,VC,MAT],EXP);COVARIANCE(IIV,[CL,VC])

Different types of effects can be specified for different parameters in a PKPD model:

IIV(@PK,EXP);IIV(@PD,ADD));COVARIANCE(IIV,@PK_IIV);COVARIANCE(IIV,@PD_IIV)