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A non-parametric optimal design algorithm for population pharmacokinetics

Markus Hovd, Alona Kryshchenko, Michael N. Neely, Julian Otalvaro, Alan Schumitzky, Walter M. Yamada

TL;DR

The paper proposes the Non-parametric Optimal Design (NPOD) algorithm for population pharmacokinetics, aiming to retain NPAG-level accuracy while dramatically reducing convergence time. NPOD replaces ad-hoc support-point generation with a gradient-based, directional-derivative approach to add informative support points, coupled with primal-dual interior-point optimization for weights and rank-revealing pruning to control complexity. Across two datasets (synthetic and real), NPOD achieves comparable likelihoods and joint parameter distributions to NPAG but with substantially fewer cycles, yielding meaningful runtime improvements especially as model size grows. The method leverages D-optimal design theory and Lindsay’s results to guide point selection, and is implemented in Rust within the Pmetrics framework for scalability and robustness.

Abstract

This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.

A non-parametric optimal design algorithm for population pharmacokinetics

TL;DR

The paper proposes the Non-parametric Optimal Design (NPOD) algorithm for population pharmacokinetics, aiming to retain NPAG-level accuracy while dramatically reducing convergence time. NPOD replaces ad-hoc support-point generation with a gradient-based, directional-derivative approach to add informative support points, coupled with primal-dual interior-point optimization for weights and rank-revealing pruning to control complexity. Across two datasets (synthetic and real), NPOD achieves comparable likelihoods and joint parameter distributions to NPAG but with substantially fewer cycles, yielding meaningful runtime improvements especially as model size grows. The method leverages D-optimal design theory and Lindsay’s results to guide point selection, and is implemented in Rust within the Pmetrics framework for scalability and robustness.

Abstract

This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.

Paper Structure

This paper contains 22 sections, 13 equations, 3 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. Design of the Non-parametric Optimal Design Estimation Algorithm
  4. Design principles and theoretical foundation
  5. Algorithm Implementation
  6. Initialization:
  7. Likelihood Calculation:
  8. Optimization:
  9. Rank revealing function:
  10. Support Point Adjustment:
  11. Convergence:
  12. Computational considerations and optimizations
  13. Initial search space:
  14. Hyperparameters:
  15. Software implementation
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Comparison of objective function between NPAG and NPOD for different number of initial grid points in the parameter search space. Gridsizes are chosen as multiples of the number of subjects (n = 51).
  • Figure 2: Kernel density estimate for the joint parameter distribution. The support points estimated by NPAG are shown as blue circles, and those by NPOD is shown as red crosses. The bimodal distribution of $K_e$ is readily apparent, with the univariate distribution of $V_d$, and the inclusion of an extreme outlier.
  • Figure 3: For dataset B, the comparison of objective function between NPAG and NPOD for different number of initial grid points in the parameter search space. For simplicity, the same grid sizes in the first example was used.