Continuous observation model

Syntax compatible with Monolix

The DEFINITION: block in the [LONGITUDINAL] section is used to define the observational model:

CODE

DEFINITION: 
observationName = {distribution = distributionType, prediction = predictionName, errorModel = errorModel(param)}

with:

observationName: to be replaced by the name of the observation, e.g y1
distributionType: to be replaced by logNormal, normal or logitNormal
predictionName: to be replaced by a variable defined in the structural model, e.g Cc
errorModel(param): to be replaced by combined1(a, b), combined2(a, b), proportional(b) or constant(a). The error model parameters a and b must also be listed as input of the [LONGITUDINAL] section. a and b are commonly used as variable names, but any variable name is accepted (e.g a1, aEffect, etc)

For example, if the observation is a concentration with a combined error model (DV = Cc + (a+b*Cc)*e), the observational error model is written as

CODE

DEFINITION: 
DV = {distribution = normal, prediction = Cc, errorModel=combined1(a, b)}

When the observational error is defined in the Mlxtran model file, the user must declare the observational model parameters (a and b in the presented example) as inputs of the [LONGITUDINAL] section.

CODE

[LONGITUDINAL] 
input = {ka, V, Cl, a, b}

When a logitNormal distribution is selected, the boundaries (min and max) must also be defined:

CODE

DEFINITION: 
yE = {distribution = logitNormal, min=0, max=100, prediction = E, errorModel=constant(a)}

Syntax specific to Simulx (incuding time-varying error models)

The following is accepted in Simulx. However Simulx projects using this syntax cannot be exported to Monolix.

The DEFINITION: block in the [LONGITUDINAL] section is used to define the observational model:

CODE

DEFINITION: 
observationName = {distribution = distributionType, prediction = predictionName, sd = sdErr}

with:

observationName: to be replaced by the name of the observation, e.g y1
distributionType: to be replaced by logNormal, normal or logitNormal
predictionName: to be replaced by a variable defined in the structural model, e.g Cc
sdErr: to be replaced by a variable defined in the structural model representing the standard deviation of the random observation, e.g sd = sdErr with sdErr = b*Cc defined in the EQUATION: block. Note that the variable representing the sd can vary over time and be defined using if/else statements.

Below we show an example of an error model that varies over time: before time 0.1, the residual error is zero, afterwards a proportional error model is used.

CODE

[LONGITUDINAL]
input = {Cc, IC50, E0, kout, b}
Cc = {use = regressor}

EQUATION:
kin = E0*kout

E_0 = E0
ddt_E = kin*(1 - Cc/(Cc + IC50)) - kout*E

if t<0.1
sdErr = 0
else
sdErr = b*E
end

DEFINITION:
yE = {distribution = normal, prediction = E, sd=sdErr}

OUTPUT:
output = {E, yE}

Rules and best practices

The arguments of the errorModel can not be calculations (e.g errorModel=constant(a) with a = 10*Cc is not accepted), only parameters listed in the input list.
A parameter can not be shared by two different errorModel arguments for two different observations.
The argument sd cannot be directly a formula (e.g sd = b*Cc), an intermediate variable name must be used (e.g sd = sdErr with sdErr=b*Cc)