Prediction of Shrinkage of Individual Parameters Using the Bayesian Information Matrix in Non-Linear Mixed Effect Models with Evaluation in Pharmacokinetics

Purpose

When information is sparse, individual parameters derived from a non-linear mixed effects model analysis can shrink to the mean. The objective of this work was to predict individual parameter shrinkage from the Bayesian information matrix (M _BF ). We 1) Propose and evaluate an approximation of M _BF by First-Order linearization (FO), 2) Explore by simulations the relationship between shrinkage and precision of estimates and 3) Evaluate prediction of shrinkage and individual parameter precision.

Methods

We approximated M _BF using FO. From the shrinkage formula in linear mixed effects models, we derived the predicted shrinkage from M _BF . Shrinkage values were generated for parameters of two pharmacokinetic models by varying the structure and the magnitude of the random effect and residual error models as well as the design. We then evaluated the approximation of M _BF FO and compared it to Monte-Carlo (MC) simulations. We finally compared expected and observed shrinkage as well as the predicted and estimated Standard Errors (SE) of individual parameters.

Results

M _BF FO was similar to M _BF MC. Predicted and observed shrinkages were close . Predicted and estimated SE were similar.

Conclusions

M _BF FO enables prediction of shrinkage and SE of individual parameters. It can be used for design optimization.