A correlation structure for the analysis of Gaussian and non-Gaussian responses in crossover experimental designs with repeated measures

TL;DR

This paper introduces a new family of correlation structures for analyzing crossover experimental designs with repeated measures, applicable to both Gaussian and non-Gaussian responses, improving modeling flexibility and accuracy.

Contribution

It proposes a novel correlation structure using Kronecker products for GEE analysis in crossover designs, with an estimation procedure and theoretical properties.

Findings

Superior performance in quasi-likelihood criterion

Enhanced efficiency over standard models

Better explanation of complex correlation patterns

Abstract

In this study, we propose a family of correlation structures for crossover designs with repeated measures for both, Gaussian and non-Gaussian responses using generalized estimating equations (GEE). The structure considers two matrices: one that models between-period correlation and another one that models within-period correlation. The overall correlation matrix, which is used to build the GEE, corresponds to the Kronecker between these matrices. A procedure to estimate the parameters of the correlation matrix is proposed, its statistical properties are studied and a comparison with standard models using a single correlation matrix is carried out. A simulation study showed a superior performance of the proposed structure in terms of the quasi-likelihood criterion, efficiency, and the capacity to explain complex correlation phenomena/patterns in longitudinal data from crossover designs