UCLA

Implementing optimal design can provide the most accurate statistical inference with minimal cost. However, optimal designs for high-dimensional models or complicated nonlinear models can be hard to find. I propose a novel swarm algorithm, called competitive swarm optimizer with mutated agents (CSO-MA), to search for optimal designs for high-dimensional and complicated nonlinear models that are useful for biomedical studies. They include logistic models, Poisson-type models with multiple interacting covariates and some factors may have correlated random effects. I first show the proposed algorithm outperforms several state-of-the-art algorithms using benchmark functions commonly used in the engineering literature. I then show it can either perform as efficiently as some current algorithms used in statistics for finding optimal designs or outperform several of its competitors. Additionally, I find some of the claimed optimal designs in the literature are not optimal by showing CSO-MA-generated designs have higher statistical efficiency. Since the bulk of design work in the literature concerns low-dimensional models, my work has the potential to break new ground, especially in the era of big data, where, increasingly, it is more realistic to use more complex models to reflect reality.

The proposed algorithm is a general-purpose optimization algorithm, so it is flexible and can find exact and approximate designs, with and without constraints. In particular, it can efficiently search for different types of optimal designs, including Bayesian optimal designs, which are especially challenging to find when there are multiple factors and there are multi-dimensional integrals involved in the optimization problem. The results from my research will provide new, more realistic and better quality statistical experimental designs for biomedical researchers at a minimal cost.