A penalized structural equation modeling method accounting for secondary phenotypes for variable selection on genetically regulated expression from PrediXcan for Alzheimer's disease.

As the global burden of mental illness is estimated to become a severe issue in the near future, it demands the development of more effective treatments. Most psychiatric diseases are moderately to highly heritable and believed to involve many genes. Development of new treatment options demands more knowledge on the molecular basis of psychiatric diseases. Toward this end, we propose to develop new statistical methods with improved sensitivity and accuracy to identify disease-related genes specialized for psychiatric diseases. The qualitative psychiatric diagnoses such as case control often suffer from high rates of misdiagnosis and oversimplify the disease phenotypes. Our proposed method utilizes endophenotypes, the quantitative traits hypothesized to underlie disease syndromes, to better characterize the heterogeneous phenotypes of psychiatric diseases. We employ the structural equation modeling using the liability-index model to link multiple genetically regulated expressions from PrediXcan and the manifest variables including endophenotypes and case-control status. The proposed method can be considered as a general method for multivariate regression, which is particularly helpful for psychiatric diseases. We derive penalized retrospective likelihood estimators to deal with the typical small sample size issue. Simulation results demonstrate the advantages of the proposed method and the real data analysis of Alzheimer's disease illustrates the practical utility of the techniques. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.