Shijun Wang, Gunnar Yngman, Andrew C. Hooker, Mats O. Karlsson
Dept. of Pharmaceutical Biosciences, Uppsala University
Objectives: The full random effects modeling (FREM) approach [1] has been developed for covariate model building in nonlinear mixed effects (NLME) models. In a FREM model, the covariates are assumed to have mean and between-subjects variability (BSV) and the covariate effect on a parameter is quantified based on the covariance between their BSV as covariate coefficients in the form of matrix. This study aims to compare alternative approaches to estimate the covariate coefficients and their uncertainty based on the BSV matrix.
Methods: With respect to estimate BSV matrix, the FREM approach was successfully implemented on 6 developed PKPD models based on real data. The models were estimated using FOCE and the uncertainty of estimates were obtained with both the sandwich matrix (COV) and through importance sampling estimation method (IMP) with only expectation step. Additionally, a nonparametric bootstrap (n=5000) was implemented to estimate the uncertainty as well as three methods for sampling-importance resampling (SIR) [2]: the SIR implemented in PsN (SIR_P); the built-in SIR method in NONMEM (SIR_T); and NONMEM built-in SIR with post-processing resampling without replacement according to the related importance (SIR_R). Two methods for estimation of the BSV matrix were based on multiple sampling (N=10) from the posterior distributions of individual parameters, using either the normality assumption (IPN) or direct sampling of the individual parameters (IPS). Given the simulated samples, a bootstrap was implemented with sample size being equal to the number of subjects and repeated 2000 times. For each of the bootstrap samples, a covariance matrix could be computed and the mean and variance of covariate coefficients were computed from these.
Results: With respect to the comparison in estimating the covariate coefficients in FREM model, the covariate coefficients matrices estimated by IPN and IPS were compared to the coefficients from FOCE as reference in terms of the Frobenius norm. The relative deviation of IPN and IPS were 0.5% (0.1% to 1%) and 0.5% (0.1% to 1%). In the comparison of uncertainty estimation, at least 2000 samples of BSV matrices were generated by either simulating with a multivariate normal distribution for COV and IMP method or by utilizing the existing samples for the remaining methods. Given the BSV matrices, the corresponding matrices of covariates coefficients could be computed and the variation of covariate coefficients matrix was quantified by the ratio of interquartile range (IQR) to the median of each entry in the matrix. In terms of the 50th percentile of the ratios across all the entries in the matrix, the order of the methods in the mean values of the ratios across all the 6 adopted models are: bootstrap (138%), IMP (133%), COV (124%), and SIR_P (105%); besides, IPN, IPS, SIR_T, and SIR_R obtained similar results from 82% to 87%; and similar order was observed in the 75th percentile of the ratios and the mean values are 441%, 249%, 249%, and 199% for bootstrap, IMP, COV, and SIR_P; 149% to 169% for the remaining method.
Conclusions: The IPN and IPS methods proposed in the project can estimate the BSV matrix in FREM model in a good precision; the order of the methods in estimating uncertainty of covariates coefficient from high to low is bootstrap, IMP, COV, SIR_P; and the estimations of IPN, IPS, SIR_T, and SIR_R are similar and lower than the other four methods.
References:
[1] Karlsson MO. A full model approach based on the covariance matrix of parameters and covariates. PAGE Abstr Annu Meet Popul Approach Gr Eur. 2012;21(6):Abstr 2455.
[2] Dosne AG, Bergstrand M, Harling K, Karlsson MO. Improving the estimation of parameter uncertainty distributions in nonlinear mixed effects models using sampling importance resampling. J Pharmacokinet Pharmacodyn. 2016.
Reference: PAGE 28 (2019) Abstr 9192 [www.page-meeting.org/?abstract=9192]
Poster: Methodology - Covariate/Variability Models