# Precision in the Specification of Ordinary Differential Equations and Parameter Estimation in Modeling Biological Processes

Sarah E. Holte

*Fred Hutchinson Cancer Research Center, Seattle, WA*

Yajun Mei

*Georgia Institute of Technology, Atlanta, GA*

CONTENTS

- 12.1 Introduction...............................................................................................257
- 12.2 Model Mis-Specification and Statistical Model Comparison.............259
- 12.3 Model Parameter Identifiability and Study Design............................266
- 12.3.1 The Sensitivity Matrix.................................................................267
- 12.3.2 TheFIM.........................................................................................269
- 12.3.3 Combining the Sensitivity Matrix and FIM............................270
- 12.3.4 Study Design: Impact of New Compartment or Time Points... 270
- 12.4 Examples....................................................................................................272
- 12.4.1 Model Parameter Identifiability: Lumped Parameters ..........272
- 12.4.2 Models for Viral Decay of HIV after Treatment ....................272
- 12.5 Discussion..................................................................................................278

References.............................................................................................................279