DAE 2024 - Session IX

Session IX (May 17, 8:30am-10:00am): Optimal Experimental Design, organized by Abhyuday Mandal

Title: A Supersaturated Screening Design Framework Based on Lasso Support Recovery
Speaker: Kade Young, Eli Lilly
Abstract: Screening experiments utilize n experimental runs to determine which of $p$ factors drive a response. Supersaturated screening designs (SSDs) represent a screening experiment where $n<p+1$. In this case, the full main effects linear model cannot be uniquely estimated with Ordinary Least Squares. Thus, it is common for some type of penalized estimation method, like the lasso, to be used to perform factor screening. This works develops a framework for optimal SSDs based on maximizing the support recovery probability of the lasso and shows that a compound symmetric matrix (a matrix where all off-diagonals are equal) is the ideal structure of lasso information matrices for support recovery. This ideal structure allows for the theoretical justification on why some two-level SSD criteria out-perform others under certain assumptions about the signs of the effects. Additionally, a design construction algorithm is presented that balances two design criteria based on how close a given design's information matrix is to the ideal structure. The performance of these constructed designs are evaluated compared to existing SSD construction methods, and their utility and limitations are discussed.

Title: Approximating Shapley Values by Fractional Factorial Designs
Speaker: Wei Zheng, University of Tennesse
Abstract: Shapley value is a well-known concept in cooperative game theory which provides a fair way to distribute the revenues or costs to each player. Recently, it has been widely applied in various fields such as data science, marketing, genetics. However, the computation of the Shapley value is an NP-hard problem. For a cooperative game with $n$ players, calculating the Shapley value for one player requires calculating the value function for $2^n$ different coalitions, which makes it infeasible to calculate the Shapley value for a large $n$. \revA{In this paper, we propose a fast approximation approach for Shapley values based on fractional factorial designs. When the value function satisfies certain conditions, our approach can obtain true Shapley values by calculating contributions of fewer than $4d^2-4$ different coalitions. For general cases, highly accurate approximations of Shapley values can also be yielded by calculating contributions of additional $O(d^2)$ different coalitions.} Multiple simulations and real case examples demonstrate that, with equivalent computational cost, our method provides significantly more accurate approximations compared with several popular methods.

Title: Nature-inspired Metaheuristics for Designing Innovative Drug Studies
Speaker: Weng Kee Wong, UCLA
Abstract: Nature-inspired metaheuristics is widely used in computer science and engineering but seems greatly underused in pharmaceutical and clinical science research. This class of algorithms is appealing because they are essentially assumptions free, fast and have been shown that they are capable of tackling various types of high dimensional complex optimization problems. We briefly review some exemplary nature-inspired metaheuristic algorithms and show (i) how they can be applied to extend Simon’s 2 stage designs for a Phase II trial with a single alternative hypothesis to one with multiple alternative hypotheses to capture the uncertainty of the efficacy of the drug more accurately, and (ii), how to construct a global clinical trial that can attain the large enrollment target with high probability at minimum cost and subject to multiple linear or nonlinear constraints. We also indicate how metaheuristics can be applied to develop more realistic and flexible adaptive designs for early phase clinical trials.