caa a22 4500 605533938 CHVBK 20210128100840.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10928-015-9409-1 doi (NATIONALLICENCE)springer-10.1007/s10928-015-9409-1 Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood [Elektronische Daten] [Joachim Almquist, Jacob Leander, Mats Jirstrand] The first order conditional estimation (FOCE) method is still one of the parameter estimation workhorses for nonlinear mixed effects (NLME) modeling used in population pharmacokinetics and pharmacodynamics. However, because this method involves two nested levels of optimizations, with respect to the empirical Bayes estimates and the population parameters, FOCE may be numerically unstable and have long run times, issues which are most apparent for models requiring numerical integration of differential equations. We propose an alternative implementation of the FOCE method, and the related FOCEI, for parameter estimation in NLME models. Instead of obtaining the gradients needed for the two levels of quasi-Newton optimizations from the standard finite difference approximation, gradients are computed using so called sensitivity equations. The advantages of this approach were demonstrated using different versions of a pharmacokinetic model defined by nonlinear differential equations. We show that both the accuracy and precision of gradients can be improved extensively, which will increase the chances of a successfully converging parameter estimation. We also show that the proposed approach can lead to markedly reduced computational times. The accumulated effect of the novel gradient computations ranged from a 10-fold decrease in run times for the least complex model when comparing to forward finite differences, to a substantial 100-fold decrease for the most complex model when comparing to central finite differences. Considering the use of finite differences in for instance NONMEM and Phoenix NLME, our results suggests that significant improvements in the execution of FOCE are possible and that the approach of sensitivity equations should be carefully considered for both levels of optimization. The Author(s), 2015 Nonlinear mixed effects modeling nationallicence First order conditional estimation (FOCE) nationallicence Sensitivity equations nationallicence Almquist Joachim Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut Leander Jacob Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut Jirstrand Mats Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut Journal of Pharmacokinetics and Pharmacodynamics Springer US; http://www.springer-ny.com 42/3(2015-06-01), 191-209 1567-567X 42:3<191 2015 42 10928 https://doi.org/10.1007/s10928-015-9409-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10928-015-9409-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Almquist Joachim Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut NATIONALLICENCE 700 1- Leander Jacob Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut NATIONALLICENCE 700 1- Jirstrand Mats Fraunhofer-Chalmers Centre, Chalmers Science Park, 41288, Gothenburg, Sweden aut NATIONALLICENCE 773 0- Journal of Pharmacokinetics and Pharmacodynamics Springer US; http://www.springer-ny.com 42/3(2015-06-01), 191-209 1567-567X 42:3<191 2015 42 10928