Studying Optimal Designs for Multivariate Crossover Trials
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908547960274944 |
|---|---|
| author | Niphadkar, Shubham Mukhopadhyay, Siuli |
| author_facet | Niphadkar, Shubham Mukhopadhyay, Siuli |
| contents | This article discusses $A$-, $D$- and $E$-optimality results for multivariate crossover designs, where more than one response is measured from every period for each subject. The motivation for these multivariate designs comes from a $3 \times 3$ crossover trial that investigates how an oral drug affects biomarkers of mucosal inflammation, by analyzing the various gene profiles from each participant. A multivariate response crossover model with fixed effects including direct and carryover effects, and with heteroscedastic error terms is considered to fit the multiple responses measured. It is assumed all throughout the article that there is no correlation between responses but there is presence of correlation within responses. Corresponding to the direct effects, we obtain the information matrix in a multiple response setup. Various results regarding this information matrix are studied. For $p$ periods and $t$ treatments, orthogonal array design of type $I$ and strength $2$ is proved as $A$-, $D$- and $E$-optimal, when $p=t \geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Studying Optimal Designs for Multivariate Crossover Trials Niphadkar, Shubham Mukhopadhyay, Siuli Methodology This article discusses $A$-, $D$- and $E$-optimality results for multivariate crossover designs, where more than one response is measured from every period for each subject. The motivation for these multivariate designs comes from a $3 \times 3$ crossover trial that investigates how an oral drug affects biomarkers of mucosal inflammation, by analyzing the various gene profiles from each participant. A multivariate response crossover model with fixed effects including direct and carryover effects, and with heteroscedastic error terms is considered to fit the multiple responses measured. It is assumed all throughout the article that there is no correlation between responses but there is presence of correlation within responses. Corresponding to the direct effects, we obtain the information matrix in a multiple response setup. Various results regarding this information matrix are studied. For $p$ periods and $t$ treatments, orthogonal array design of type $I$ and strength $2$ is proved as $A$-, $D$- and $E$-optimal, when $p=t \geq 3$. |
| title | Studying Optimal Designs for Multivariate Crossover Trials |
| topic | Methodology |
| url | https://arxiv.org/abs/2509.16076 |