Dataset Information

Shrinkage in nonlinear mixed-effects population models: quantification, influencing factors, and impact.

ABSTRACT: Shrinkage of empirical Bayes estimates (EBEs) of posterior individual parameters in mixed-effects models has been shown to obscure the apparent correlations among random effects and relationships between random effects and covariates. Empirical quantification equations have been widely used for population pharmacokinetic/pharmacodynamic models. The objectives of this manuscript were (1) to compare the empirical equations with theoretically derived equations, (2) to investigate and confirm the influencing factor on shrinkage, and (3) to evaluate the impact of shrinkage on estimation errors of EBEs using Monte Carlo simulations. A mathematical derivation was first provided for the shrinkage in nonlinear mixed effects model. Using a linear mixed model, the simulation results demonstrated that the shrinkage estimated from the empirical equations matched those based on the theoretically derived equations. Simulations with a two-compartment pharmacokinetic model verified that shrinkage has a reversed relationship with the relative ratio of interindividual variability to residual variability. Fewer numbers of observations per subject were associated with higher amount of shrinkage, consistent with findings from previous research. The influence of sampling times appeared to be larger when fewer PK samples were collected for each individual. As expected, sample size has very limited impact on shrinkage of the PK parameters of the two-compartment model. Assessment of estimation error suggested an average 1:1 relationship between shrinkage and median estimation error of EBEs.

SUBMITTER: Xu XS

PROVIDER: S-EPMC3475840 | biostudies-other | 2012 Dec

REPOSITORIES: biostudies-other

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Shrinkage in nonlinear mixed-effects population models: quantification, influencing factors, and impact.

Xu Xu Steven XS Yuan Min M Karlsson Mats O MO Dunne Adrian A Nandy Partha P Vermeulen An A

The AAPS journal 20120920 4

Shrinkage of empirical Bayes estimates (EBEs) of posterior individual parameters in mixed-effects models has been shown to obscure the apparent correlations among random effects and relationships between random effects and covariates. Empirical quantification equations have been widely used for population pharmacokinetic/pharmacodynamic models. The objectives of this manuscript were (1) to compare the empirical equations with theoretically derived equations, (2) to investigate and confirm the in ...[more]

PMID: 22993107

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Project description: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.

Dataset Information

Shrinkage in nonlinear mixed-effects population models: quantification, influencing factors, and impact.

Publications

Shrinkage in nonlinear mixed-effects population models: quantification, influencing factors, and impact.

Similar Datasets

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