Universally Optimal Multivariate Crossover Designs

In this article, universally optimal multivariate crossover designs are studied. The multiple response crossover design is motivated by a $3 \times 3$ crossover setup, where the effect of $3$ doses of an oral drug are studied on gene expressions related to mucosal inflammation. Subjects are assigned to three treatment sequences and response measurements on 5 different gene expressions are taken from each subject in each of the $3$ time periods. To model multiple or $g$ responses, where $g>1$, in a crossover setup, a multivariate fixed effect model with both direct and carryover treatment effects is considered. It is assumed that there are non zero within response correlations, while between response correlations are taken to be zero. The information matrix corresponding to the direct effects is obtained and some results are studied. The information matrix in the multivariate case is shown to differ from the univariate case, particularly in the completely symmetric property. For the $g>1$ case, with $t$ treatments and $p$ periods, for $p=t \geq 3$, the design represented by a Type $I$ orthogonal array of strength $2$ is proved to be universally optimal over the class of binary designs, for the direct treatment effects.Comment: 17 Pages, 2 Figure

Likelihood-based missing data analysis in multivariate crossover trials

For gene expression data measured in a crossover trial, a multivariate mixed-effects model seems to be most appropriate. Standard statistical inference fails to provide reliable results when some responses are missing. Particularly for crossover studies, missingness is a serious concern as the trial requires a small number of participants. A Monte Carlo EM (MCEM) based technique has been adopted to deal with this situation. Along with estimation, a MCEM likelihood ratio test (LRTs) is developed for testing the fixed effects in such a multivariate crossover model with missing data. Intensive simulation studies have been carried out prior to the analysis of the gene expression data

Min–max crossover designs for two treatments binary and poisson crossover trials

In this article min–max crossover designs for binary and Poisson crossover trials with two treatments are proposed. Models with and without carryover effects are considered. Min–max designs for periods 2 and 3 are discussed in details. A sensitivity analysis is performed to assess the robustness of proposed designs when compared to existing optimal designs. An equivalence theorem is provided to verify optimality of min–max designs. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature