Optimal designs for network experimentation with unstructured treatments

Abstract

Experiments involving connected units are prevalent across various scientific disciplines. In such settings, an experimental unit may interact with others, leading to potential contamination effects, referred to in this study as network adjustments, which influence the responses of neighboring units. This paper addresses the design problem for connected experimental units subjected to unstructured treatments under linear models, explicitly incorporating network adjustments to account for correlated responses. We employ alphabetic optimality criteria to identify efficient designs that enhance the precision of treatment effect estimation and the accuracy of quantifying network adjustments. Theoretical conditions and practical guidelines for optimal designs are developed and validated through numerical simulations and application to a real-world network. Our findings demonstrate that the proposed approach delivers highly efficient designs while maintaining low computational complexity.