The investigators develop methods for identifying optimal and efficient designs for experiments with categorical data. The project consists of three main parts. (i) Identification of optimal designs for binary data under generalized linear regression models. This part includes consideration of models in which slope and intercept parameters can vary for different groups of subjects and models with a random subject effect. (ii) Identification of optimal allocations of treatments to blocks for comparative studies with binary data. A logistic model is a popular choice for such studies. (iii) Identification of optimal designs for count data under loglinear regression models. In this setting, the investigators focus also on optimal designs for models that can account for subject heterogeneity. This project is innovative in that it uses a new technique that has vast advantages over the commonly used geometric approach.
Categorical responses are very common in designed experiments in many scientific studies, such as drug discovery, clinical trials, social sciences, marketing, etc. Generalized Linear Models (GLMs) are widely used for modeling such data. Using efficient designs for collecting data in such experiments is critically important. It can reduce the sample size needed for achieving a specified precision, thereby reducing the cost, or improve the precision of estimates for a specified sample size. While research on optimal designs for linear models has been systematically developed over more than 30 years, there are very few research publications on optimal designs for GLMs. This project is important both for the introduction of novel theoretical tools and for its impact on applications. For example, the results of the project significantly reduce the time, money, and the number of patients needed in clinical trials, as well as other scientific studies. The results can help the U.S. Food and Drug Administration to improve its guidelines for clinical trials.
