Universally optimal designs for two interference models

TL;DR

This paper investigates universally optimal experimental designs for two interference models, establishing conditions for optimality, comparing models, and identifying designs that are optimal across both, with implications for complex treatment effect models.

Contribution

It introduces Kushner's linear equations as a necessary and sufficient condition for universal optimality in models with neighbor effects, a novel result for such complex models.

Findings

Derived Kushner's linear equations for optimality

Compared efficiencies between directed and undirected interference models

Identified designs that are optimal for both models

Abstract

A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin [Ann. Statist. 28 (2000) 1728-1742] and Kunert and Mersmann [J. Statist. Plann. Inference 141 (2011) 1623-1632]. Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency under the former model. Designs universally optimal for both models are also identified. Most importantly, this paper provides Kushner'ss type linear equations system as a necessary and sufficient condition for a design to be universally optimal. This result is novel for models with at least two sets of treatment-related nuisance parameters, which are left and right neighbor effects here. It sheds light on other models in deriving asymmetric optimal or efficient designs.