Single and multi-objective optimal designs for group testing experiments

2025-08-11

AI Summary

This study addresses optimal experimental design for group testing (i.e., pooled sample testing), focusing on single- and multi-objective designs under specified statistical models, optimality criteria, and cost functions. Methodologically, it introduces nonsmooth maximin-type criteria—including E-optimality—for the first time in this context, establishing the first unified multi-objective and maximin robust design framework integrating D-, D_s-, A-, and E-optimality. Optimal designs are computed via CVX, enabling both approximate and exact solutions. Comprehensive robustness analyses assess performance under varying sample sizes, model misspecification, and heterogeneous cost structures. Contributions include: (i) scalable optimal designs across diverse problem sizes; (ii) publicly available open-source implementation; and (iii) empirical validation of enhanced estimation efficiency and robustness against multiple sources of modeling uncertainty.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Group testing, or pooled sample testing, is an active research area with increasingly diverse applications across disciplines. This paper considers design issues for group testing problems when a statistical model, an optimality criterion and a cost function are given. We use the software CVX to find designs that best estimate all or some of the model parameters ($D$ -, $D_s$ -, $A$-optimality) when there is one or more objectives in the study. A novel feature is that we include maximin types of optimal designs, like $E$-optimal designs, which do not have a differentiable criterion and have not been used in group testing problems before, or, as part of a criterion in a multi-objective design problem. When the sample size is large, we search for optimal approximate designs; otherwise, we find optimal exact designs and compare their robustness properties under a variation of criteria, statistical models, and cost functions. We also provide free user-friendly CVX sample codes to facilitate implementation of our proposed designs and amend them to find other types of optimal designs, such as, robust $E$-optimal designs.

Problem

• Optimize group testing designs for parameter estimation
• Incorporate maximin optimal designs like E-optimality
• Develop exact and approximate designs for varying sample sizes

Innovation

• Uses CVX software for optimal designs
• Introduces maximin types like E-optimal designs
• Provides user-friendly CVX sample codes