R-based reproduction of the estimation process hidden behind NONMEM® Part 1: First-order approximation method

NONMEM® is the most-widely used nonlinear mixed effects modelling tool introduced into population PK/PD analysis. Even though thousands of pharmaceutical scientists utilize NONMEM® routinely for their data analysis, the various estimation methods implemented in NONMEM® remain a mystery for most users due to the complex statistical and mathematical derivations underlying the algorithm used in NONMEM®. In this tutorial, we demonstrated how to directly obtain the objective function value and post hoc η for the first order approximation method by the use of R. We hope that this tutorial helps pharmacometricians understand the underlying estimation process of nonlinear mixed effects modelling.