A General Equivalence Theorem for Crossover Designs under Generalized Linear Models

TL;DR

This paper develops a new general equivalence theorem for crossover designs within generalized linear models, enabling the verification of optimality of designs using generalized estimating equations and constrained optimization.

Contribution

It introduces a novel equivalence theorem tailored for crossover designs under generalized linear models, addressing limitations of traditional methods.

Findings

Derived a general equivalence theorem for these designs.

Identified locally D-optimal crossover designs using GEE.

Provided a framework for optimality verification in complex models.

Abstract

With the help of Generalized Estimating Equations, we identify locally D-optimal crossover designs for generalized linear models. We adopt the variance of parameters of interest as the objective function, which is minimized using constrained optimization to obtain optimal crossover designs. In this case, the traditional general equivalence theorem could not be used directly to check the optimality of obtained designs. In this manuscript, we derive a corresponding general equivalence theorem for crossover designs under generalized linear models.