Hierarchical False Discovery Rate Control for High-dimensional Survival Analysis with Interactions.

With the development of data collection techniques, analysis with a survival response and high-dimensional covariates has become routine. Here we consider an interaction model, which includes a set of low-dimensional covariates, a set of high-dimensional covariates, and their interactions. This model has been motivated by gene-environment (G-E) interaction analysis, where the E variables have a low dimension, and the G variables have a high dimension. For such a model, there has been extensive research on estimation and variable selection. Comparatively, inference studies with a valid false discovery rate (FDR) control have been very limited. The existing high-dimensional inference tools cannot be directly applied to interaction models, as interactions and main effects are not "equal". In this article, for high-dimensional survival analysis with interactions, we model survival using the Accelerated Failure Time (AFT) model and adopt a "weighted least squares + debiased Lasso" approach for estimation and selection. A hierarchical FDR control approach is developed for inference and respect of the "main effects, interactions" hierarchy. The asymptotic distribution properties of the debiased Lasso estimators are rigorously established. Simulation demonstrates the satisfactory performance of the proposed approach, and the analysis of a breast cancer dataset further establishes its practical utility.

Marginal false discovery rate for a penalized transformation survival model.

Survival analysis that involves moderate/high dimensional covariates has become common. Most of the existing analyses have been focused on estimation and variable selection, using penalization and other regularization techniques. To draw more definitive conclusions, a handful of studies have also conducted inference. The recently developed mFDR (marginal false discovery rate) technique provides an alternative inference perspective and can be advantageous in multiple aspects. The existing inference studies for regularized estimation of survival data with moderate/high dimensional covariates assume the Cox and other specific models, which may not be sufficiently flexible. To tackle this problem, the analysis scope is expanded to the transformation model, which is robust and has been shown to be desirable for practical data analysis. Statistical validity is rigorously established. Two data analyses are conducted. Overall, an alternative inference approach has been developed for survival analysis with moderate/high dimensional data.

Integrative sparse partial least squares.

Partial least squares, as a dimension reduction technique, has become increasingly important for its ability to deal with problems with a large number of variables. Since noisy variables may weaken estimation performance, the sparse partial least squares (SPLS) technique has been proposed to identify important variables and generate more interpretable results. However, the small sample size of a single dataset limits the performance of conventional methods. An effective solution comes from gathering information from multiple comparable studies. Integrative analysis has essential importance in multidatasets analysis. The main idea is to improve performance by assembling raw data from multiple independent datasets and analyzing them jointly. In this article, we develop an integrative SPLS (iSPLS) method using penalization based on the SPLS technique. The proposed approach consists of two penalties. The first penalty conducts variable selection under the context of integrative analysis. The second penalty, a contrasted penalty, is imposed to encourage the similarity of estimates across datasets and generate more sensible and accurate results. Computational algorithms are developed. Simulation experiments are conducted to compare iSPLS with alternative approaches. The practical utility of iSPLS is shown in the analysis of two TCGA gene expression data.