Efficient algorithms for optimal designs with correlated observations in pharmacokinetics and dose-finding studies

Area of Science:

• Pharmacometrics and Biostatistics
• Experimental Design and Optimization

Background:

• Random effects models are standard in population pharmacokinetics and dose-finding.
• Correlated observations from multiple patient measurements complicate optimal experimental design.
• Existing methods struggle with shared random effects and serial correlation.

Purpose of the Study:

• Introduce novel multiplicative algorithms for handling correlated data in experimental design.
• Enable numerical calculation of optimal designs in complex pharmacokinetic and dose-finding scenarios.
• Develop a method to assess design efficiency without prior knowledge of the optimal design.

Main Methods:

• Developed a class of multiplicative algorithms to manage correlated observations.
• Applied algorithms to crossover dose-finding trials and population pharmacokinetics examples.
• Derived a lower bound for design efficiency to monitor algorithm progress and evaluate designs.

Main Results:

• Successfully demonstrated the application of new algorithms in concrete pharmacokinetic and dose-finding examples.
• The derived lower bound effectively monitors algorithm convergence and assesses design efficiency.
• Extended methodology to incorporate requirements for minimal treatment numbers under various conditions.

Conclusions:

• The proposed multiplicative algorithms effectively address correlated data challenges in experimental design.
• This approach facilitates the numerical calculation of optimal designs in pharmacokinetics and dose-finding.
• The efficiency bound provides a valuable tool for algorithm monitoring and design evaluation.