Robust designs in longitudinal studies accounting for parameter and model uncertainties - application to count data.

Area of Science:

• Statistics
• Pharmacometrics
• Biostatistics

Background:

• Nonlinear mixed-effects models (NLMEMs) are crucial for longitudinal data analysis.
• Optimal study design often relies on the Fisher Information Matrix (FIM).
• Existing FIM evaluation methods using Monte-Carlo Hamiltonian Monte-Carlo (MC-HMC) yield locally optimal designs due to reliance on prior parameter knowledge.

Purpose of the Study:

• To extend MC-HMC methods for FIM evaluation in NLMEMs.
• To incorporate uncertainty in population parameters and candidate models.
• To develop robust optimal designs that account for both parameter and model uncertainties.

Main Methods:

• Evaluated a robust FIM by averaging MC-HMC computed FIMs over parameter distributions.
• Employed compound D-optimality (CD optimality) for designs balancing multiple candidate models.
• Introduced compound DE-optimality (CDE optimality) for designs robust to parameter and model uncertainty.

Main Results:

• Accounting for parameter uncertainty can alter optimal study designs.
• Model misspecification can significantly reduce design efficiency.
• CD- and CDE-optimal designs offer a robust compromise across various candidate models.
• The approach was successfully applied to a longitudinal Poisson count model.

Conclusions:

• The developed methods enable robust optimal design for NLMEMs.
• This work provides the first approach for optimizing designs of repeated discrete data with parameter and model uncertainties.
• Robust designs are essential to mitigate risks associated with parameter and model uncertainty in NLMEM studies.