Optimal design for linear interpolation of curves.

Area of Science:

• Pharmacokinetics
• Statistical Modeling
• Experimental Design

Background:

• Non-parametric methods are crucial for pharmacokinetic trial analysis, but design procedures are limited.
• Linear interpolation is common for curve estimation with sparse sampling in pharmacokinetics.
• Existing smoothing and local fit designs are inadequate due to ignored bias and reliance on asymptotic properties.

Purpose of the Study:

• To propose optimal designs for non-parametric estimation in pharmacokinetic trials.
• To minimize the mean squared error of linear interpolation for improved pharmacokinetic curve estimation.
• To address design challenges in single curve, mixed-effects, and destructive sampling scenarios.

Main Methods:

• Development of optimal designs minimizing mean squared error for linear interpolation.
• Consideration of three scenarios: single non-linear model, non-linear mixed model with average MSE, and destructive sampling.
• Proposal of an approximate algorithm for destructive sampling designs, implementable in statistical packages.

Main Results:

• The proposed designs optimize linear interpolation for pharmacokinetic data, especially with sparse sampling.
• The first scenario yields the best linear interpolation under constant variance.
• An effective algorithm is presented for destructive sampling, enhancing average curve estimation.

Conclusions:

• Optimal designs significantly improve non-parametric estimation accuracy in pharmacokinetic studies.
• The developed methods provide practical solutions for curve estimation with sparse and destructive sampling.
• The proposed algorithm facilitates the implementation of optimal designs in standard statistical software.