Diagnostics for nonlinear models with application to population pharmacokinetic modeling

Abstract

<p>Biological problems often involve fitting nonlinear models to data. In pharmacokinetics, analysts study a subject's response to drug doses, which will typically follow a quick increase in concentration as the drug circulates through the body, and a gradual nonlinear decrease as it is processed and eliminated. These models are diagnosed with the help of the experimental data.</p> <p>Specialist software exists for pharmacokinetic modeling: NONMEM, Monolix. General modeling software, such as PROC NLMIX in SAS and the package nlme in S/R, can also be used. A common problem is that these tools lack adequate diagnostic tools to assess the model fit. The Federal Drug Administration is encouraging the development of new approaches to model diagnosis.</p> <p>This thesis addresses this gap, with the following contributions: 1) Interactive graphics is applied to model building, including the exploratory data analysis, goodness of fit, model validation and model comparison. This is a new addition to the practice of population pharmacokinetic (PopPK) modeling. It provides a more systematic evaluation of these complicated models. 2) New visual methods have been developed to examine resampling statistics for PopPK modeling. Resampling statistics arise when multiple models are fit. The parameter estimates and fit diagnostics are extracted and results are visualized to diagnose PopPK models. Our new visual methods are developed from existing multivariate methods. 3) Preliminary work on exploring the effects of correlation between covariates on covariate selection in PopPK model building. Three algorithms for identifying the best covariates are compared. 4) To help users utilize the methods developed in this thesis for PopPK model diagnostics, I developed two R packages, PKgraph and PKreport. The PKgraph source code is distributed through http://cran.r-project.org/web/packages/PKgraph/index.html. PKreport is currently available at http://pkreport.sourceforge.net/.</p>