A scientific review on advances in statistical methods for crossover design

TL;DR

This paper provides a comprehensive review of the evolution, applications, and methodological advancements in statistical methods for crossover designs, emphasizing the AB-BA design and extensions to complex responses.

Contribution

It offers an extensive synthesis of historical developments, inference methods, and open problems in crossover design, highlighting recent advances and future research directions.

Findings

Review of statistical inference methods for crossover designs

Discussion of extensions to multivariate and categorical responses

Identification of open problems in the field

Abstract

A comprehensive review of the literature on crossover design is needed to highlight its evolution, applications, and methodological advancements across various fields. Given its widespread use in clinical trials and other research domains, understanding this design's challenges, assumptions, and innovations is essential for optimizing its implementation and ensuring accurate, unbiased results. This article extensively reviews the history and statistical inference methods for crossover designs. A primary focus is given to the AB-BA design as it is the most widely used design in literature. Extension from two periods to higher-order designs is discussed, and a general inference procedure for continuous response is studied. Analysis of multivariate and categorical responses is also reviewed in this context. A bunch of open problems in this area are shortlisted.