Variance-Consistent Covariate Modeling from Posterior Summaries in Population Pharmacokinetics

Systematic covariate modeling in nonlinear mixed-effects (NLME) analysis is computationally intensive due to repeated refitting to concentration-time data. Although empirical Bayes estimates (EBEs) facilitate screening, η-shrinkage attenuates between-subject variability and distorts covariance structures, leading to shrinkage bias. We propose a variance-consistent framework enabling covariate modeling from a single base-model fit.

The proposed approach incorporates subject-specific posterior means and covariances from an NLME base model. A variance-matching penalty enforces consistency between the total between-subject covariance (model-explained and unexplained) and the base model estimates, preserving the covariance structure without refitting. Performance was compared with EBE regression, two-stage Bayesian estimation, and NLME covariate modeling. Stepwise covariate selection was evaluated using likelihood ratio tests, with the resulting structure compared against the NLME-identified structure as the gold-standard reference.

Under substantial η-shrinkage of approximately 30%, EBE regression and two-stage Bayesian estimation attenuated covariate-effect parameter estimates. The proposed method provided unbiased estimates, mitigating shrinkage bias and recovering covariate-effect parameter estimates obtained with NLME. It also reproduced NLME-based stepwise covariate selection with high computational scalability by avoiding repeated refitting to time-course data.

Variance-consistent posterior-based covariate modeling provides a statistically coherent and computationally scalable framework for systematic covariate identification in population PKPD analysis.