Assessing robustness of designs for random effects parameters for nonlinear mixed-effects models

Area of Science:

• Statistics
• Biostatistics
• Pharmacometrics

Background:

• Optimal designs for nonlinear models depend on parameter values.
• Robust designs address uncertainty in prior parameter estimates.
• Computational challenges exist for high-dimensional models.

Purpose of the Study:

• To explore the influence of random effects variance on optimal designs in nonlinear mixed-effects models.
• To evaluate the impact of different likelihood approximation methods on design robustness.

Main Methods:

• Estimation of the determinant of the information matrix over prior parameter distributions.
• Approximation of expectation and variance of the likelihood.
• Analysis of designs under a first-order Taylor series approximation.

Main Results:

• The method for approximating likelihood expectation and variance is crucial for random effects.
• First-order Taylor approximations yield designs insensitive to random effects variance.
• Uncertainty in fixed-effects parameters is sufficient under common approximations.

Conclusions:

• First-order approximations simplify optimal design by reducing the need to account for random effects variance.
• The choice of likelihood approximation method significantly impacts design robustness to random effects.
• For practical applications using common approximations, focusing on fixed-effects uncertainty may suffice.