  Given genetic variations and various phenotypical traits, such as Magnetic
Resonance Imaging (MRI) features, we consider two important and related tasks
in biomedical research: i)to select genetic and phenotypical markers for
disease diagnosis and ii) to identify associations between genetic and
phenotypical data. These two tasks are tightly coupled because underlying
associations between genetic variations and phenotypical features contain the
biological basis for a disease. While a variety of sparse models have been
applied for disease diagnosis and canonical correlation analysis and its
extensions have bee widely used in association studies (e.g., eQTL analysis),
these two tasks have been treated separately. To unify these two tasks, we
present a new sparse Bayesian approach for joint association study and disease
diagnosis. In this approach, common latent features are extracted from
different data sources based on sparse projection matrices and used to predict
multiple disease severity levels based on Gaussian process ordinal regression;
in return, the disease status is used to guide the discovery of relationships
between the data sources. The sparse projection matrices not only reveal
interactions between data sources but also select groups of biomarkers related
to the disease. To learn the model from data, we develop an efficient
variational expectation maximization algorithm. Simulation results demonstrate
that our approach achieves higher accuracy in both predicting ordinal labels
and discovering associations between data sources than alternative methods. We
apply our approach to an imaging genetics dataset for the study of Alzheimer's
Disease (AD). Our method identifies biologically meaningful relationships
between genetic variations, MRI features, and AD status, and achieves
significantly higher accuracy for predicting ordinal AD stages than the
competing methods.
