Novel Statistical Methods with Application to Imaging Genetics

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Imaging genetics is a rapidly evolving field that integrates individual medical images with genetic information to assess the impact of genetic variation on brain function and structure. The long term objective of this proposal is to develop novel statistical methods for imaging genetics studies. With the advent of both advanced imaging as well as genotyping techniques, many large biomedical studies have been conducted to collect imaging and genetic data. Conventional approaches for imaging genetics analysis suffer from issues such as heavy computational cost and algorithmic instability, which requires the development of fast and efficient statistical methods. This proposal will not only enhance methodological and theoretical developments for statistical imaging genetics analysis, but also advance the understanding of the relationship between imaging and genetic data. The proposed project has the following interrelated themes. First, the PI will develop high dimensional tensor response regression models by treating the high dimensional genetic data as scalar predictors and the complex imaging data as a tensor response. The high dimensional tensor response linear regression, quantile regression and semiparametric regression models will be studied. Second, the PI will develop a high dimensional functional response linear regression model, and develop statistical inference procedures in two different directions. For the aforementioned models, the inference procedures only work for the common variants genetic data. The PI will then study the scenario when the rare variants exist, and develop methods that work for this scenario. The statistical methods developed in this proposal are timely and important and will be relevant to many large-scale real data sets, for example the Alzheimer's Disease Neuroimaging Initiative, the Human Connectome Project, the UK Biobank data, the Pediatric Imaging, Neurocognition, and the Genetics and Philadelphia Neurodevelopmental Cohort data. Undergraduate and graduate students as well as postdoctoral researchers will be provided with excellent training to help them to gain valuable skills that increase their chances in the job market or to start their academic career. In order to facilitate the use of the proposed new methods, the PI will implement them in R or Matlab and make software available to the public, along with publishing the corresponding research reports.