Optimal cross-over designs for full interaction models

TL;DR

This paper develops optimal and efficient experimental designs for repeated measurements considering interactions between carry-over and direct treatment effects, especially when residual effects are limited to one later period.

Contribution

It introduces universally optimal approximate designs and efficient reduced-subject designs for models with interactions, improving upon traditional additive assumptions.

Findings

Derived universally optimal approximate designs.

Proposed efficient designs with fewer subjects.

Addressed bias issues in treatment effect estimation.

Abstract

We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment effects, we consider a model with interactions between carry-over and direct treatment effects. When the aim of the experiment is to study the effects of a treatment used alone, we obtain universally optimal approximate designs. We also propose some efficient designs with a reduced number of subjects.