We propose a ridge-penalized adaptive Mantel test (AdaMant) for evaluating the association of two high-dimensional sets of features. By introducing a ridge penalty, AdaMant tests the association across many metrics simultaneously. We demonstrate how ridge penalization bridges Euclidean and Mahalanobis distances and their corresponding linear models from the perspective of association measurement and testing. This result is not only theoretically interesting but also has important implications in penalized hypothesis testing, especially in high dimensional settings such as imaging genetics. Applying the proposed method to an imaging genetic study of visual working memory in health adults, we identified interesting associations of brain connectivity (measured by EEG coherence) with selected genetic features.

In treating patients diagnosed with early Stage I non-small-cell lung cancer (NSCLC), doctors must choose surgery alone, Adjuvant Cisplatin-Based Chemotherapy (ACT) alone or both. For patients with resected stages IB to IIIA, clinical trials have shown a survival advantage from 4-15% with the adoption of ACT. However, due to the inherent toxicity of chemotherapy, it is necessary for doctors to identify patients whose chance of success with ACT is sufficient to justify the risks. This research seeks to use gene expression profiling in the development of a statistical decision-making algorithm to identify patients whose survival rates will improve from ACT treatment. Using the data from the National Cancer Institute, the lasso method in the Cox-Proportional-Hazards regression model is used as the main method to determine a feasible number of genes that are strongly associated with the treatment-related patient survival. Considering treatment groups separately, the patients are assigned a risk category based on the estimation of survival times. These risk categories are used to develop a Random Forests classification model to identify patients who are likely to benefit from chemotherapy treatment. This model allows the prediction of a new patient's prognosis and the likelihood of survival benefit from ACT treatment based on a feasible number of genomic biomarkers. The proposed methods are evaluated using a simulation study.

The study of genetic influences on brain connectivity, known as connectome genetics, is an exciting new direction of research in imaging genetics. We here review recent results and current statistical methods in this area, and discuss some of the persistent challenges and possible directions for future work.

We propose a statistical framework to investigate whether a given subpopulation lies between two other subpopulations in a multivariate feature space. This methodology is motivated by a biological question from a collaborator: Is a newly discovered cell type between two known types in several given features? We propose two in-betweenness indices (IBI) to quantify the in-betweenness exhibited by a random triangle formed by the summary statistics of the three subpopulations. Statistical inference methods are provided for triangle shape and IBI metrics. The application of our methods is demonstrated in three examples: the classic Iris data set, a study of risk of relapse across three breast cancer subtypes, and the motivating neuronal cell data with measured electrophysiological features.

We propose a ridge-penalized adaptive Mantel test (AdaMant) for evaluating the association of two high-dimensional sets of features. By introducing a ridge penalty, AdaMant tests the association across many metrics simultaneously. We demonstrate how ridge penalization bridges Euclidean and Mahalanobis distances and their corresponding linear models from the perspective of association measurement and testing. This result is not only theoretically interesting but also has important implications in penalized hypothesis testing, especially in high dimensional settings such as imaging genetics. Applying the proposed method to an imaging genetic study of visual working memory in health adults, we identified interesting associations of brain connectivity (measured by EEG coherence) with selected genetic features.