Individual Bayesian Information Matrix for Predicting Estimation Error and Shrinkage of Individual Parameters...

In mixed models, the relative standard errors (RSE) and shrinkage of individual parameters can be predicted from the individual Bayesian information matrix (M_BF). We proposed an approach accounting for data below the limit of quantification (LOQ) in M_BF.

M_BF is the sum of the expectation of the individual Fisher information (M_IF) which can be evaluated by First-Order linearization and the inverse of random effect variance. We expressed the individual information as a weighted sum of predicted M_IF for every possible design composing of measurements above and/or below LOQ. When evaluating M_IF, we derived the likelihood expressed as the product of the likelihood of observed data and the probability for data to be below LOQ. The relevance of RSE and shrinkage predicted by M_BF in absence or presence of data below LOQ were evaluated by simulations, using a pharmacokinetic/viral kinetic model defined by differential equations.

Simulations showed good agreement between predicted and observed RSE and shrinkage in absence or presence of data below LOQ. We found that RSE and shrinkage increased with sparser designs and with data below LOQ.

The proposed method based on M_BF adequately predicted individual RSE and shrinkage, allowing for evaluation of a large number of scenarios without extensive simulations.