Thanks to the development of microarray technology, gene-expression data are becoming more available, and it has been shown that genomic predictors have a great clinical impact in predicting treatment responses. For instance, pathologic complete response (pCR) is a strong indicator of survival after neoadjuvant chemotherapy for breast cancer patients.
On the other hand, given that genes are grouped into pathways for particular functions and that pathways are not isolated, we have proposed a method to jointly estimate the two-level Gaussian graphical models across heterogeneous classes. While the method has the advantage of controlling sparsity on both pathway and gene level networks, individually, the estimated precision matrices can also be used in quadratic discriminant analysis and its variants.
In this study, we use some real breast cancer data and explore how the proposed estimation method, after incorporating the pathway information into the sparse precision matrix estimation, contributes to predicting breast cancer patients’ treatment responses via quadratic discriminant analysis and its variants.