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Improved numerical stability for the bounded integer model.

Sebastian Ueckert1, Mats O Karlsson2

  • 1Department of Pharmacy, Uppsala University, Uppsala, Sweden. sebastian.ueckert@farmaci.uu.se.

Journal of Pharmacokinetics and Pharmacodynamics
|November 26, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces an improved numerical method for the bounded integer model, enhancing composite score modeling. The new approach offers more precise and less biased parameter estimates, particularly with the Laplace algorithm.

Keywords:
Composite scoreNONMEMNumeric stability

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Area of Science:

  • Statistics
  • Computational Statistics
  • Psychometrics

Background:

  • Implementing the bounded integer model for composite score modeling presents numerical challenges.
  • Existing log-likelihood implementations may suffer from precision and bias issues.

Purpose of the Study:

  • To propose and validate an improved numerical implementation for the bounded integer model.
  • To address the limitations of naive log-likelihood calculations in composite score modeling.

Main Methods:

  • Developed an improved log-likelihood implementation using an approximation of the logarithm of the error function.
  • Compared the performance against a naive implementation via simulations and a real data example.
  • Utilized both Laplace and Stochastic Approximation Expectation-Maximization (SAEM) algorithms for estimation.

Main Results:

  • The improved algorithm provided more precise and less biased parameter estimates in simulations, especially with small within-subject variability using the Laplace algorithm.
  • No significant differences were observed between implementations when using the SAEM algorithm.
  • Bootstrap results for the real data example favored the improved implementation, yielding identical or superior objective function values.

Conclusions:

  • The improved log-likelihood implementation demonstrates superior performance for the bounded integer model under specific conditions.
  • The enhanced method is recommended as the new default for log-likelihood calculations in bounded integer models.
  • Numerical accuracy and efficiency in composite score modeling are significantly improved.