Ordinary differential equation PK/PD models using the SAS macro NLINMIX
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Updated: Aug 23, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Andrzej T Galecki1, Russell D Wolfinger, Oscar A Linares
1Institute of Gerontology, University of Michigan, Ann Arbor, Michigan 48109-2007, USA. agalecki@umich.edu
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.
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