Semi-parametric generalized estimating equations for repeated measurements in cross-over designs

TL;DR

This paper introduces a semi-parametric generalized estimating equations model for cross-over designs with repeated measures, effectively capturing treatment, time, and carry-over effects using splines, and demonstrating improved performance over standard models.

Contribution

It develops a novel semi-parametric GEE approach incorporating splines for non-parametric effects in cross-over designs, with theoretical properties and practical implementation.

Findings

Model outperforms standard models when carry-over or temporal effects are present.

Solution analogous to weighted least squares facilitates diagnostics.

Applied successfully to blood pressure and insulin data in rabbits.

Abstract

A model for cross-over designs with repeated measures within each period was developed. It is obtained using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a non-parametric component to model time and carry-over effects; the estimation approach for the non-parametric component is based on splines. A simulation study was carried out to explore the model properties. Thus, when there is a carry-over effect or a functional temporal effect, the proposed model presents better results than the standard models. Among the theoretical properties, the solution is found to be analogous to weighted least squares. Therefore, model diagnostics can be made adapting the results from a multiple regression. The proposed methodology was implemented in the data sets of the crossover experiments that motivated the approach of this work: systolic blood pressure and insulin in rabbits.