ENCODING NON LINEAR MIXED

EFFECTS MODEL

EBI, June 20th, 2011

Marc LavielleINRIA Saclay

Population approach & mixed effects model

Daily seizure counts (epilepsy)

Some examples of PK/PD data

Viral load CD4 count

Daily seizure counts (epilepsy)

Some examples of PK/PD data

Viral load CD4 count

The statistical model of the observations

Statistical model for continuous data

The model of the observations y is completely defined by :

- The prediction f

-The standard deviation g

- The distribution of the residual errors

The statistical model

prediction = fstandard deviation = gdistribution = normal

Statistical model for continuous data

The statistical model

prediction = fstandard deviation = gdistribution = normal

Any application dedicated to a given task should be able to understand/interpret this description of the

model

Statistical model for continuous data

The statistical model

prediction = fstandard deviation = gdistribution = normal

222

1

Estimation

2

1)(

fyge

gyp

Any application dedicated to a given task should be able to understand/interpret this description of the

model

Statistical model for continuous data

The statistical model

prediction = fstandard deviation = gdistribution = normal

),(~ 2

Simulation

gfNy

222

1

Estimation

2

1)(

fyge

gyp

Any application dedicated to a given task should be able to understand/interpret this description of the

model

Statistical model for continuous data

The statistical model

prediction = fstandard deviation = gdistribution = normal

),(~ 2

Simulation

gfNy

222

1

Estimation

2

1)(

fyge

gyp

gfy edition

Any application dedicated to a given task should be able to understand/interpret this description of the

model

Statistical model for continuous data

The statistical model

hazard =

Statistical model for time-to-event data

The statistical model

hazard =

t

duu

etTP 0

)(

Simulation

)(

t

t

duu

duu

etTP

ettp

0

0

)(

)(

Estimation

)(

)()(

Statistical model for time-to-event data

P(Y=k) , k=1,2,..K

Statistical model for discrete data

Categorical data: KY ,...,2,1

Count data: ,...,2,1,0Ydistribution = poisson

parameter = lambda

Y ~ parametric distribution

example: Y ~Poisson

The statistical model of the individual parameters

General model:

Statistical model of the individual parameters

General model:

Linear model:

Statistical model of the individual parameters

The statistical model

distribution = log-normalstandard deviation = omegacovariate = c

Statistical model of the individual parameters - Example

The statistical model

distribution = log-normalstandard deviation = omegacovariate = c

),)(log(~ 2

Simulation

cNLog pop

22

)log()log(2

1

Estimation

2

1)(

cpop

ep

cpop )log()log(

edition

Statistical model of the individual parameters - Example

Coding non linear mixed effects models with MONOLIX

The main Graphical User Interface of MONOLIX

All the information related to the statistical model is stored:

- in a Matlab structure

- in a XML file

- in a « human-readable » script file

Defining the statistical model with the MONOLIX GUI

<project name="theophylline_project.xml"><covariateDefinitionList>

<covariateDefinition columnName="WEIGHT" name="t_WEIGHT" transformation="log(cov/70)" type="continuous"/><covariateDefinition columnName="SEX" type="categorical">

<groupList><group name="F" reference="true"/><group name="M"/>

</groupList></covariateDefinition>

</covariateDefinitionList><data columnDelimiter="\t" headers="ID,DOSE,TIME,Y,COV,CAT" uri="%MLXPROJECT%/theophylline_data.txt"/><models>

<statisticalModels><parameterList>

<parameter name="ka" transformation="L"><intercept initialization="1.000000"/>

</parameter><parameter name="V" transformation="L">

<intercept initialization="1.000000"/> <betaList><beta covariate="t_WEIGHT" initialization="0"/></betaList>

<variability initialization="1.000000" level="1.000000" levelName="IIV"/></parameter><parameter name="Cl" transformation="L">

<intercept initialization="1.000000"/><variability initialization="1.000000" level="1.000000" levelName="IIV"/>

</parameter></parameterList><residualErrorModelList>

<residualErrorModel alias="const" output="1.000000" outputName="concentration"><parameterList>

<parameter initialization="1.000000" name="a"/></parameterList>

</residualErrorModel></residualErrorModelList>

</statisticalModels>

$DESCRIPTION PK of theophylline  $FILE D:/Myproject/theophylline_data.txt $VARIABLES ID, TIME, AMT, OBS use=DV,WT, SEX use=cov type=cat,LW70 = log(WT/70) use=cov  $INDIVIDUAL default distribution=log-normal,ka iiv=no, V cov=LW70, Cl, $EQUATION Cc=PKMODEL(ka,V,Cl)

$OBSERVATIONConcentration type=continuous pred=Cc err=constant

Coding the (statistical) model with MLXTRAN