arXiv subjects

Shubham Niphadkar

Publications and source records attributed to Shubham Niphadkar.

3 recordsLinked to original sources

arXiv2025

Studying Optimal Designs for Multivariate Crossover Trials

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 $p=t \geq 3$.

stat.ME↗

arXiv2024

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 $\rm{I}$ orthogonal array of strength $2$ is proved to be universally optimal over the class of binary designs, for the direct treatment effects.

stat.ME↗

arXiv2024

Efficient designs for multivariate crossover trials

This article aims to study efficient/trace optimal designs for crossover trials with multiple responses recorded from each subject in the time periods. A multivariate fixed effects model is proposed with direct and carryover effects corresponding to the multiple responses. The corresponding error dispersion matrix is chosen to be either of the proportional or the generalized Markov covariance type, permitting the existence of direct and cross-correlations within and between the multiple responses. The corresponding information matrices for direct effects under the two types of dispersions are used to determine efficient designs. The efficiency of orthogonal array designs of Type $I$ and strength $2$ is investigated for a wide choice of covariance functions, namely, Mat($0.5$), Mat($1.5$) and Mat($\infty$). To motivate these multivariate crossover designs, a gene expression dataset in a $3 \times 3$ framework is utilized.

stat.ME↗