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ENCODING NON LINEAR MIXED EFFECTS MODEL

ENCODING NON LINEAR MIXED EFFECTS MODEL. M arc Lavielle INRIA Saclay. EBI, June 20th, 2011. Population approach & mixed effects model. Some examples of PK/PD data. Daily seizure counts (epilepsy). Viral load CD4 count.

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ENCODING NON LINEAR MIXED EFFECTS MODEL

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  1. ENCODING NON LINEAR MIXED EFFECTS MODEL Marc Lavielle INRIA Saclay EBI, June 20th, 2011

  2. Population approach & mixed effects model

  3. Some examples of PK/PD data Daily seizure counts (epilepsy) Viral load CD4 count

  4. Some examples of PK/PD data Daily seizure counts (epilepsy) Viral load CD4 count

  5. The statistical model of the observations

  6. 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 e

  7. Statistical model for continuous data The statistical model prediction = f standard deviation = g distribution = normal

  8. Statistical model for continuous data Any application dedicated to a giventaskshouldbe able to understand/interpretthis description of the model The statistical model prediction = f standard deviation = g distribution = normal

  9. Statistical model for continuous data Any application dedicated to a giventaskshouldbe able to understand/interpretthis description of the model The statistical model prediction = f standard deviation = g distribution = normal

  10. Statistical model for continuous data Any application dedicated to a giventaskshouldbe able to understand/interpretthis description of the model The statistical model prediction = f standard deviation = g distribution = normal

  11. Statistical model for continuous data Any application dedicated to a giventaskshouldbe able to understand/interpretthis description of the model The statistical model prediction = f standard deviation = g distribution = normal

  12. Statistical model for time-to-event data The statistical model hazard = l

  13. Statistical model for time-to-event data The statistical model hazard = l

  14. Statistical model for discrete data P(Y=k) , k=1,2,..K Categorical data: Count data: distribution = poisson parameter = lambda Y ~ parametric distribution example: Y ~Poisson(l)

  15. The statistical model of the individual parameters

  16. Statistical model of the individual parameters General model:

  17. Statistical model of the individual parameters General model: Linear model:

  18. Statistical model of the individual parameters - Example The statistical model distribution = log-normal standard deviation = omega covariate= c

  19. Statistical model of the individual parameters - Example The statistical model distribution = log-normal standard deviation = omega covariate= c

  20. Coding non linear mixed effects models with MONOLIX

  21. The main Graphical User Interface of MONOLIX

  22. Defining the statistical model with the MONOLIX GUI • All the information related to the statistical model is stored: • in a Matlab structure • in a XML file • in a « human-readable » script file

  23. <projectname="theophylline_project.xml"> <covariateDefinitionList> <covariateDefinitioncolumnName="WEIGHT" name="t_WEIGHT" transformation="log(cov/70)" type="continuous"/> <covariateDefinitioncolumnName="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> <parametername="ka" transformation="L"> <interceptinitialization="1.000000"/> </parameter> <parametername="V" transformation="L"> <interceptinitialization="1.000000"/> <betaList> <beta covariate="t_WEIGHT" initialization="0"/> </betaList> <variability initialization="1.000000" level="1.000000" levelName="IIV"/> </parameter> <parametername="Cl" transformation="L"> <interceptinitialization="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>

  24. Coding the (statistical) model with MLXTRAN $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) $OBSERVATION Concentration type=continuous pred=Cc err=constant

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