Purpose <p>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.</p> Methods <p>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&#xa0;the resulting structure compared against&#xa0;the NLME-identified structure as the gold-standard reference.</p> Results <p>Under substantial η-shrinkage of&#xa0;approximately&#xa0;30%, EBE regression and two-stage Bayesian estimation attenuated covariate-effect parameter&#xa0;estimates. The proposed method provided unbiased estimates, mitigating shrinkage bias and recovering covariate-effect parameter&#xa0;estimates obtained with NLME. It also reproduced NLME-based stepwise covariate selection with high computational scalability by avoiding repeated refitting to time-course data.</p> Conclusions <p>Variance-consistent posterior-based covariate modeling provides a statistically coherent and computationally scalable framework for systematic covariate identification in population PKPD analysis.</p>

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Variance-Consistent Covariate Modeling from Posterior Summaries in Population Pharmacokinetics

  • Junya Ooka,
  • Mizuki Uno,
  • Yuta Nakamaru,
  • Yiran Song,
  • Mengqi Fang,
  • Kanako So,
  • Tomoko Kita,
  • Fumiyoshi Yamashita

摘要

Purpose

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.

Methods

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.

Results

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.

Conclusions

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