Finding D-Optimal Design for Multi-Toxicant Poisson Model via Ultra-Dimensional Particle Swarm Optimization

• Activity Number: 133
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Jiaheng Qiu*+ and Weng Kee Wong
• Companies: UCLA and Department of Biostatistics, UCLA
• Keywords: Poisson regression model ; D-optimal design ; metaheuristic algorithms ; particle swarm optimization ; D-efficiency

Abstract

Poisson regression models are widely used in modeling count data in social science, epidemiology and bioscience. In toxicity studies, researchers have found D-optimal designs for estimating the model parameters or Poisson models of up to two toxicants and a two way interaction term, but such simple model might be limiting in practice.

We developed a new version of the Particle Swarm Optimization called Ultra-dimensional PSO that deliberately searches for the optimal design among designs with many more points than the number of parameters in the model. This strategy allows us to find D-optimal designs for estimating all model parameters in a 3, 4 and 5-toxicant Poisson models with two-way interactions when the induced design space is unrestricted or restricted, including the situation where our interest is only interested in estimating all the interaction terms. Our work thus generalizes results from Wang et al. (2004) and Russell et al. (2009) in a few ways. We also use simulation studies and provide guidelines for the choice of different tuning parameters in the PSO algorithm for searching such optimal designs.