In this work, the PI is to develop a novel approach for identifying optimal and efficient designs under Generalized Linear Models (GLMs) including the fundamental logistic, probit and loglinear models and some other nonlinear models. Specifically, this project intends to achieve the following three objectives: (i) Identify optimal designs for GLMs under non-homogeneous subjects. In this study, optimal designs are derived for models in which the subjects are divided into two or more groups using one or more factors, allowing the intercept or slope to vary from one group to another. Random subject effects can also be allowed for differences among subjects within groups. (ii) Identify optimal designs for GLMs with multiple covariates. There are very few optimality results for GLMs with more than one covariate. The PI will study optimal designs for GLMs when multiple covariates exist. These models can also account for subject heterogeneity. (iii) Identify optimal designs for some other nonlinear models. In nonlinear models, most optimal results were derived under D-optimality for all parameters. The PI will investigate a general approach to identify optimal designs for nonlinear models with three or more parameters under commonly used optimality criteria when all or some of the parameters are of interest. The proposed research will have a tremendous impact because it will fill several gaps in the literature: the models in the proposed research accommodate heterogeneity among subjects and multiple covariates; general solutions for optimal designs of nonlinear models with three parameters will be provided. The technique in the proposed research is innovative in that it yields very general results that go beyond solving problems on a case-by-case basis. It helps to identify the support of locally optimal designs for many of the commonly studied models and can be applied for all the common optimality criteria based on information matrices. It works both with a constrained and unconstrained design region. Furthermore, it can be applied to multistage experiments, where an initial experiment may be used to provide a better idea of the unknown parameters.
GLMs and other nonlinear models have been used in a wide range of social and natural science fields, such as biological sciences, pharmaceutical research, agricultural science, economics, marketing, etc. The results of this study will have a deep impact on the application of GLMs in these fields. For example, when the findings are applied to the design of clinical trials during new drug discovery and development, they will significantly reduce the time, money, and number of patients needed in these trials. In fact, this research can help the U.S. Food and Drug Administration to improve its guidelines for clinical trials. To effectively disseminate the results of this research, the PI will develop a user-friendly software package targeting non-expert users. To successfully integrate research and education, the PI will develop advanced experimental design courses at the University of Missouri-Columbia incorporating findings of this project. Graduate students will be trained to study optimal designs in the new fields, under the PI?s guidance. Finally, the proposed research has the potential to stimulate new research and to provide tools for identifying optimal designs under GLMs or nonlinear models used in other areas, such as longitudinal data analysis and survival analysis.
