Joost DeJongh1, Morris Muliaditan1, Esmée Vendel1, Stefan Zeiser1, Martijn Ruppert1, Martijn Van Noort1
1LAP&P Consultants bv
Introduction: Besides the classical FO and FOCE optimization methods in NONMEM, Expectation-Maximization (EM) methods have been available for over ten years. Potential benefits of these methods include reduced computing times and higher accuracy, but this depends on the problem. A limited number of papers reported on analysis of population PK or PD problems where the EM methods did offer added value compared to FOCE or performed a systematic comparison [1-5]. While the NONMEM user guide and some papers [6] provide general recommendations, it is difficult for a modeller to understand when and how to use the EM methods, how to choose their settings, especially to overcome specific convergence issues, and in particular how this should be matched to the quality of the data set. There is a clear need for practical insight and guidance into the usability of the EM methods. Objectives: •Investigate the effect of the sampling density of the data and the parameterization of the model on the convergence, stability, accuracy and efficiency of the EM methods ITS, IMP, IMPMAP and SAEM in NONMEM, in comparison with FOCE. •Provide practical guidance on the usability of the EM methods and the most obvious adjustments of their settings to overcome any issues in achieving successful convergence. Methods: The starting point for our evaluations was a literature TMDD model with a rich data set with 50 subjects [6]. Both FOCE and IMP were found to perform well on this dataset with IMP being more efficient [6]. We simulated a similar data set using the literature model, with similar parameter values but higher noise and a full random-effects matrix with small correlation, so that actual parameter and post-hoc values were available for analysis. This dataset contained 1569 observations of plasma PK and receptor levels, from 50 subjects. As this was a rich data set, all methods were expected to lead to accurate estimation. We investigated their performance in more taxing circumstances, by adapting the setup as follows: 1.Limit the dataset to 15 subjects and PK data only, so that inter-individual variability (IIV) becomes harder to identify, and the receptor-specific parameters can only indirectly be inferred, and 2.Compare a full IIV matrix with a diagonal one, and 3.Assess the influence of log-transformation on the structural parameters. Model fitting was performed with FOCE, ITS, IMP, IMPMAP and SAEM, with AUTO=1, or alternate settings where this did not suffice. All model runs were concluded with an IMP EONLY=1 step [2] and optionally preceded by an ITS step. For each case, 100 data sets of 15 subjects were sampled and fitted, so that statistics on the fit could be compiled. Results were assessed on successful convergence, numerical stability (condition number), accuracy (relative standard error and difference with actual parameter values and posthocs) and efficiency (i.e., computing time), using the full simulated data set with 50 subjects as benchmark. Results: On the full data set with all 50 subjects, the methods had good convergence and accuracy. IMP and IMPMAP were more efficient than FOCE, and for the new methods a full IIV matrix was more efficient than a diagonal one. With 15 subjects and a diagonal IIV matrix , SAEM and ITS had convergence issues, while the IMP and IMPMAP methods converged to a stable, accurate fit with less than ~20% difference between estimated and actual parameters. For FOCE, only 21% of the runs converged with these settings. This increased to 81% when IIV was limited to two PK parameters . For a full IIV matrix , SAEM did not converge, and the condition number suggested overparameterization for ITS, IMP and IMPMAP. SAEM minimization success benefited from a pre-run with ITS and/or log-transformation of the structural parameters . The other new methods did not benefit from either adjustment. IMP and IMPMAP proved to be the most robust methods in terms of successful minimization . For the runs that did converge, the estimates of the individual post-hocs were most accurate for SAEM (~10%). Conclusion: For a TMDD model with rich PK data in 15 subjects, IMP and IMPMAP outperformed FOCE on robustness and reached acceptable accuracy and efficiency. Whether covariance parameters can be included may depend on the specific problem, e.g., the amount of data, the population size and the degree of intra-subject variability. ITS and SAEM had convergence issues but were the most accurate methods when they did converge.
[1] Karlsson, Plan and Karlsson. Performance of Three Estimation Methods in Repeated Time-to-Event Modeling. AAPS 13(1), 2011. [2] Gibiansky, Gibiansky and Bauer. Comparison of Nonmem 7.2 estimation methods and parallel processing efficiency on a target-mediated drug disposition model. J Pharmacokinet Pharmacodyn 39(1), 2012. [4] Johansson et al. Evaluation of bias, precision, robustness and runtime for estimation methods in NONMEM 7. J Pharmacokinet Pharmacodyn 41, 2014. [5] Liu and Wang. Comparing the performance of FOCE and different expectation-maximization methods in handling complex population physiologically-based pharmacokinetic models. J Pharmacokinet Pharmacodyn 43(4), 2016. [6] Bauer. NONMEM Tutorial Part II: Estimation Methods and Advanced Examples. CPT: Pharmacometrics and Systems Pharmacology 8, 2019.
Reference: PAGE 33 (2025) Abstr 11725 [www.page-meeting.org/?abstract=11725]
Poster: Methodology - Estimation Methods