Adaptive elastic net for group testing.

For disease screening, group (pooled) testing can be a cost-saving alternative to one-at-a-time testing, with savings realized through assaying pooled biospecimen (eg, urine, blood, saliva). In many group testing settings, practitioners are faced with the task of conducting disease surveillance. That is, it is often of interest to relate individuals' true disease statuses to covariate information via binary regression. Several authors have developed regression methods for group testing data, which is challenging due to the effects of imperfect testing. That is, all testing outcomes (on pools and individuals) are subject to misclassification, and individuals' true statuses are never observed. To further complicate matters, individuals may be involved in several testing outcomes. For analyzing such data, we provide a novel regression methodology which generalizes and extends the aforementioned regression techniques and which incorporates regularization. Specifically, for model fitting and variable selection, we propose an adaptive elastic net estimator under the logistic regression model which can be used to analyze data from any group testing strategy. We provide an efficient algorithm for computing the estimator along with guidance on tuning parameter selection. Moreover, we establish the asymptotic properties of the proposed estimator and show that it possesses "oracle" properties. We evaluate the performance of the estimator through Monte Carlo studies and illustrate the methodology on a chlamydia data set from the State Hygienic Laboratory in Iowa City.

Latent Feature Decompositions for Integrative Analysis of Multi-Platform Genomic Data.

Increased availability of multi-platform genomics data on matched samples has sparked research efforts to discover how diverse molecular features interact both within and between platforms. In addition, simultaneous measurements of genetic and epigenetic characteristics illuminate the roles their complex relationships play in disease progression and outcomes. However, integrative methods for diverse genomics data are faced with the challenges of ultra-high dimensionality and the existence of complex interactions both within and between platforms. We propose a novel modeling framework for integrative analysis based on decompositions of the large number of platform-specific features into a smaller number of latent features. Subsequently we build a predictive model for clinical outcomes accounting for both within- and between-platform interactions based on Bayesian model averaging procedures. Principal components, partial least squares and non-negative matrix factorization as well as sparse counterparts of each are used to define the latent features, and the performance of these decompositions is compared both on real and simulated data. The latent feature interactions are shown to preserve interactions between the original features and not only aid prediction but also allow explicit selection of outcome-related features. The methods are motivated by and applied to a glioblastoma multiforme data set from The Cancer Genome Atlas to predict patient survival times integrating gene expression, microRNA, copy number and methylation data. For the glioblastoma data, we find a high concordance between our selected prognostic genes and genes with known associations with glioblastoma. In addition, our model discovers several relevant cross-platform interactions such as copy number variation associated gene dosing and epigenetic regulation through promoter methylation. On simulated data, we show that our proposed method successfully incorporates interactions within and between genomic platforms to aid accurate prediction and variable selection. Our methods perform best when principal components are used to define the latent features.