Wang derived the first-order (FO) method from an approximation of the Laplacian method, whereas we derived the FO method directly from the maximum likelihood estimation method. Wang systematically derived the objective functions for the major estimation methods used in NONMEM® and clearly demonstrated their relationships through the derivation. 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®. NONMEM® is regarded as the standard pharmacometrics tool. It is programmed in FORTRAN code and has evolved to its current version, 7.3. Beal of the University of California, San Francisco. NONMEM® is the most-widely used nonlinear mixed effects modelling tool introduced for population PK/PD analysis since its prototype was developed by Lewis B. The nonlinear mixed effects method that was introduced to the biomedical research field approximately 30 years ago is now an essential platform in population pharmacokinetic and pharmacodynamic (PK/PD) data analysis.
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