Detecting PCOS susceptibility loci from genome-wide association studies via iterative trend correlation based feature screening.

BACKGROUND: Feature screening plays a critical role in handling ultrahigh dimensional data analyses when the number of features exponentially exceeds the number of observations. It is increasingly common in biomedical research to have case-control (binary) response and an extremely large-scale categorical features. However, the approach considering such data types is limited in extant literature. In this article, we propose a new feature screening approach based on the iterative trend correlation (ITC-SIS, for short) to detect important susceptibility loci that are associated with the polycystic ovary syndrome (PCOS) affection status by screening 731,442 SNP features that were collected from the genome-wide association studies. RESULTS: We prove that the trend correlation based screening approach satisfies the theoretical strong screening consistency property under a set of reasonable conditions, which provides an appealing theoretical support for its outperformance. We demonstrate that the finite sample performance of ITC-SIS is accurate and fast through various simulation designs. CONCLUSION: ITC-SIS serves as a good alternative method to detect disease susceptibility loci for clinic genomic data.

Regularized Quantile Regression and Robust Feature Screening for Single Index Models.

We propose both a penalized quantile regression and an independence screening procedure to identify important covariates and to exclude unimportant ones for a general class of ultrahigh dimensional single-index models, in which the conditional distribution of the response depends on the covariates via a single-index structure. We observe that the linear quantile regression yields a consistent estimator of the direction of the index parameter in the single-index model. Such an observation dramatically reduces computational complexity in selecting important covariates in the single-index model. We establish an oracle property for the penalized quantile regression estimator when the covariate dimension increases at an exponential rate of the sample size. From a practical perspective, however, when the covariate dimension is extremely large, the penalized quantile regression may suffer from at least two drawbacks: computational expediency and algorithmic stability. To address these issues, we propose an independence screening procedure which is robust to model misspecification, and has reliable performance when the distribution of the response variable is heavily tailed or response realizations contain extreme values. The new independence screening procedure offers a useful complement to the penalized quantile regression since it helps to reduce the covariate dimension from ultrahigh dimensionality to a moderate scale. Based on the reduced model, the penalized linear quantile regression further refines selection of important covariates at different quantile levels. We examine the finite sample performance of the newly proposed procedure by Monte Carlo simulations and demonstrate the proposed methodology by an empirical analysis of a real data set.

Ultrahigh dimensional time course feature selection.

Statistical challenges arise from modern biomedical studies that produce time course genomic data with ultrahigh dimensions. In a renal cancer study that motivated this paper, the pharmacokinetic measures of a tumor suppressor (CCI-779) and expression levels of 12,625 genes were measured for each of 33 patients at 8 and 16 weeks after the start of treatments, with the goal of identifying predictive gene transcripts and the interactions with time in peripheral blood mononuclear cells for pharmacokinetics over the time course. The resulting data set defies analysis even with regularized regression. Although some remedies have been proposed for both linear and generalized linear models, there are virtually no solutions in the time course setting. As such, a novel GEE-based screening procedure is proposed, which only pertains to the specifications of the first two marginal moments and a working correlation structure. Different from existing methods that either fit separate marginal models or compute pairwise correlation measures, the new procedure merely involves making a single evaluation of estimating functions and thus is extremely computationally efficient. The new method is robust against the mis-specification of correlation structures and enjoys theoretical readiness, which is further verified via Monte Carlo simulations. The procedure is applied to analyze the aforementioned renal cancer study and identify gene transcripts and possible time-interactions that are relevant to CCI-779 metabolism in peripheral blood.

Feature Screening for Interval-Valued Response with Application to Study Association between Posted Salary and Required Skills.

It is important to quantify the differences in returns to skills using the online job advertisements data, which have attracted great interest in both labor economics and statistics fields. In this paper, we study the relationship between the posted salary and the job requirements in online labor markets. There are two challenges to deal with. First, the posted salary is always presented in an interval-valued form, for example, 5k-10k yuan per month. Simply taking the mid-point or the lower bound as the alternative for salary may result in biased estimators. Second, the number of the potential skill words as predictors generated from the job advertisements by word segmentation is very large and many of them may not contribute to the salary. To this end, we propose a new feature screening method, Absolute Distribution Difference Sure Independence Screening (ADD-SIS), to select important skill words for the interval-valued response. The marginal utility for feature screening is based on the difference of estimated distribution functions via nonparametric maximum likelihood estimation, which sufficiently uses the interval information. It is model-free and robust to outliers. Numerical simulations show that the new method using the interval information is more efficient to select important predictors than the methods only based on the single points of the intervals. In the real data application, we study the text data of job advertisements for data scientists and data analysts in a major China's online job posting website, and explore the important skill words for the salary. We find that the skill words like optimization, long short-term memory (LSTM), convolutional neural networks (CNN), collaborative filtering, are positively correlated with the salary while the words like Excel, Office, data collection, may negatively contribute to the salary.

Correlation-based joint feature screening for semi-competing risks outcomes with application to breast cancer data.

Ultrahigh-dimensional gene features are often collected in modern cancer studies in which the number of gene features p is extremely larger than sample size n. While gene expression patterns have been shown to be related to patients' survival in microarray-based gene expression studies, one has to deal with the challenges of ultrahigh-dimensional genetic predictors for survival predicting and genetic understanding of the disease in precision medicine. The problem becomes more complicated when two types of survival endpoints, distant metastasis-free survival and overall survival, are of interest in the study and outcome data can be subject to semi-competing risks due to the fact that distant metastasis-free survival is possibly censored by overall survival but not vice versa. Our focus in this paper is to extract important features, which have great impacts on both distant metastasis-free survival and overall survival jointly, from massive gene expression data in the semi-competing risks setting. We propose a model-free screening method based on the ranking of the correlation between gene features and the joint survival function of two endpoints. The method accounts for the relationship between two endpoints in a simply defined utility measure that is easy to understand and calculate. We show its favorable theoretical properties such as the sure screening and ranking consistency, and evaluate its finite sample performance through extensive simulation studies. Finally, an application to classifying breast cancer data clearly demonstrates the utility of the proposed method in practice.

Feature Screening via Distance Correlation Learning.

This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance correlation (DC-SIS, for short). The DC-SIS can be implemented as easily as the sure independence screening procedure based on the Pearson correlation (SIS, for short) proposed by Fan and Lv (2008). However, the DC-SIS can significantly improve the SIS. Fan and Lv (2008) established the sure screening property for the SIS based on linear models, but the sure screening property is valid for the DC-SIS under more general settings including linear models. Furthermore, the implementation of the DC-SIS does not require model specification (e.g., linear model or generalized linear model) for responses or predictors. This is a very appealing property in ultrahigh dimensional data analysis. Moreover, the DC-SIS can be used directly to screen grouped predictor variables and for multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the DC-SIS performs much better than the SIS in various models. We also illustrate the DC-SIS through a real data example.