| With the use of microarrays, the expression of tens of thousands of genes can be examined simultaneously to study the effects following exposure to a single chemical or following exposure to a mixture of chemicals. Measuring gene expression over a range of dose-concentrations (or similarly, over time) can expose similarities across genes and thus provide relationships in gene behavior, aid in determining gene function based on gene expression profiles, and reveal relationships between chemical treatments. We propose an extension to a recently developed gene-screening tool to reduce the dimensionality of a dose-response (or time-course) microarray dataset from tens of thousands of genes down to a subset of the most differentially expressed genes, which takes into account the continuous effect of dose (or time). To explore relationships among the subset of differentially expressed genes, we propose a multivariate model that allows for inter-gene as well as intra-gene correlated measurements. Rao's score test, a goodness-of-fit test for covariance matrices, is developed to test the goodness-of-fit of a parsimonious covariance (correlation) structure, which allows the number of genes in the corresponding covariance matrix to be larger than the number of independent tissue samples. Although, the development of Rao's score test for covariance matrices was motivated by microarray data, it is applicable to non-microarray data as well (e.g., a small clinical trial in which numerous repeated measurements are recorded for each subject). |
