Improving the estimation of parameter uncertainty distributions in nonlinear mixed effects models using sampling importance resampling

Abstract

Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.Electronic supplementary materialThe online version of this article (doi:10.1007/s10928-016-9487-8) contains supplementary material, which is available to authorized users.

Population pharmacokinetics of vancomycin in obesity: Finding the optimal dose for (morbidly) obese individuals

“…The final model was internally validated by pcVPC based on 1000 simulations, split for obese and nonobese individuals. Parameter precision and robustness of the structural and final model were analysed by the sampling importance resampling procedure …”

Dose Selection Based on Modeling and Simulation for Rivipansel in Pediatric Patients Aged 6 to 11 Years With Sickle Cell Disease

“…More details about the structure and model building sequence of the integrated PK model are provided as part of Supplementary Figures S1–S11 and Tables S1 and S2 . The precision of parameter estimates was initially obtained from the covariance step in NONMEM, but for the final model, SEs and confidence intervals (CIs) were estimated using the sampling importance resampling (SIR) procedure …”

Population Pharmacokinetics of Total and Free Erdafitinib in Adult Healthy Volunteers and Cancer Patients: Analysis of Phase 1 and Phase 2 Studies

“…Prediction‐corrected visual predictive check was also used for model evaluation to provide a visual comparison between the distributions of simulated and observed erdafitinib C tot and C free using the final population PK model and the observed data. Sampling importance resampling was used in addition to the asymptotic variance‐covariance matrix to estimate parameter uncertainty and compute the 95%CI of model parameters …”