Optimal two-treatment crossover designs for binary response models

TL;DR

This paper determines optimal two-treatment crossover designs for binary response models by minimizing the variance of treatment contrast estimators, considering logistic regression and working correlation structures.

Contribution

It introduces a method to find optimal crossover designs for binary responses using variance minimization and generalized estimating equations.

Findings

Optimal designs are identified for p=2,3,4 periods.

Design efficiencies are calculated and compared.

Impact of misspecified correlation matrices is analyzed.

Abstract

Optimal two-treatment, $p$ period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of $n$ subjects to $2^p$ possible treatment sequences. An appropriate logistic regression model is postulated and the within subject covariances are modeled through a working correlation matrix. The marginal mean of the binary responses are fitted using generalized estimating equations. The efficiencies of some crossover designs for $p=2,3,4$ periods are calculated. The effect of misspecified working correlation matrix on design efficiency is also studied.