Ordinary Differential Equation PK/PD Models Using the SAS Macro NLINMIX

Abstract

We describe some theory and recent enhancements for the SAS macro NLINMIX (Wolfinger, R. D. (1993). Laplace's approximation for nonlinear mixed effects models. Biometrika 80:791–795) that enable model calculation to take place within the interaction matrix language SAS/IML (SAS Institute Inc. (1999a). SAS/IML User's Guide Version 7. Cary, NC: SAS Institute Inc.). They provide greater flexibility and scope for the specification and analysis of complex nonlinear mixed models. For example, using data from a frequently sampled intravenous glucose test, we fit a two-compartment kinetics model that has no closed-form representation. It is derived as the solution of a system of ordinary differential equations and specified as such in SAS/IML. Additional details and example NLINMIX code are available in Appendix A.

Key Words:

• Nonlinear mixed effects model
• Longitudinal data analysis
• Population pharmacokinetics and pharmacodynamics models
• Linearization method
• SAS/IML macro
• Glucose disappearance model

Mathematics Subject Classification:

• 62-07
• 62H12
• 62P10
• 65Y15
• 65L99

Acknowledgments

The authors thank José Pinheiro and Richard Watanabe for their helpful comments and suggestions and Shu Chen for technical assistance. Support for this research was provided in part by NIA grant No. P30 AG08808.