EFFICIENT ESTIMATION OF THE MAXIMAL ASSOCIATION BETWEEN MULTIPLE PREDICTORS AND A SURVIVAL OUTCOME

This paper develops a new approach to post-selection inference for screening high-dimensional predictors of survival outcomes. Post-selection inference for right-censored outcome data has been investigated in the literature, but much remains to be done to make the methods both reliable and computationally-scalable in high-dimensions. Machine learning tools are commonly used to provide predictions of survival outcomes, but the estimated effect of a selected predictor suffers from confirmation bias unless the selection is taken into account. The new approach involves the construction of semi-parametrically efficient estimators of the linear association between the predictors and the survival outcome, which are used to build a test statistic for detecting the presence of an association between any of the predictors and the outcome. Further, a stabilization technique reminiscent of bagging allows a normal calibration for the resulting test statistic, which enables the construction of confidence intervals for the maximal association between predictors and the outcome and also greatly reduces computational cost. Theoretical results show that this testing procedure is valid even when the number of predictors grows superpolynomially with sample size, and our simulations support this asymptotic guarantee at moderate sample sizes. The new approach is applied to the problem of identifying patterns in viral gene expression associated with the potency of an antiviral drug.

Sure Joint Screening for High Dimensional Cox's Proportional Hazards Model Under the Case-Cohort Design

This study develops a sure joint feature screening method for the case-cohort design with ultrahigh-dimensional covariates. Our method is based on a sparsity-restricted Cox proportional hazards model. An iterative reweighted hard thresholding algorithm is proposed to approximate the sparsity-restricted, pseudo-partial likelihood estimator for joint screening. We rigorously show that our method possesses the sure screening property, with the probability of retaining all relevant covariates tending to 1 as the sample size goes to infinity. Our simulation results demonstrate that the proposed procedure has substantially improved screening performance over some existing feature screening methods for the case-cohort design, especially when some covariates are jointly correlated, but marginally uncorrelated, with the event time outcome. A real data illustration is provided using breast cancer data with high-dimensional genomic covariates. We have implemented the proposed method using MATLAB and made it available to readers through GitHub.

A note of feature screening via a rank-based coefficient of correlation

Feature screening is a useful and popular tool to detect informative predictors for ultrahigh-dimensional data before developing statistical analysis or constructing statistical models. While a large body of feature screening procedures has been developed, most methods are restricted to examine either continuous or discrete responses. Moreover, even though many model-free feature screening methods have been proposed, additional assumptions are imposed in those methods to ensure their theoretical results. To address those difficulties and provide simple implementation, in this paper we extend the rank-based coefficient of correlation to develop a feature screening procedure. We show that this new screening criterion is able to deal with continuous and binary responses. Theoretically, the sure screening property is established to justify the proposed method. Simulation studies demonstrate that the predictors with nonlinear and oscillatory trajectories are successfully retained regardless of the distribution of the response. Finally, the proposed method is implemented to analyze two microarray datasets.

Unified model-free interaction screening via CV-entropy filter

For many practical high-dimensional problems, interactions have been increasingly found to play important roles beyond main effects. A representative example is gene-gene interaction. Joint analysis, which analyzes all interactions and main effects in a single model, can be seriously challenged by high dimensionality. For high-dimensional data analysis in general, marginal screening has been established as effective for reducing computational cost, increasing stability, and improving estimation/selection performance. Most of the existing marginal screening methods are designed for the analysis of main effects only. The existing screening methods for interaction analysis are often limited by making stringent model assumptions, lacking robustness, and/or requiring predictors to be continuous (and hence lacking flexibility). A unified marginal screening approach tailored to interaction analysis is developed, which can be applied to regression, classification, and survival analysis. Predictors are allowed to be continuous and discrete. The proposed approach is built on Coefficient of Variation (CV) filters based on information entropy. Statistical properties are rigorously established. It is shown that the CV filters are almost insensitive to the distribution tails of predictors, correlation structure among predictors, and sparsity level of signals. An efficient two-stage algorithm is developed to make the proposed approach scalable to ultrahigh-dimensional data. Simulations and the analysis of TCGA LUAD data further establish the practical superiority of the proposed approach.

Quantile-Adaptive Sufficient Variable Screening by Controlling False Discovery

Sufficient variable screening rapidly reduces dimensionality with high probability in ultra-high dimensional modeling. To rapidly screen out the null predictors, a quantile-adaptive sufficient variable screening framework is developed by controlling the false discovery. Without any specification of an actual model, we first introduce a compound testing procedure based on the conditionally imputing marginal rank correlation at different quantile levels of response to select active predictors in high dimensionality. The testing statistic can capture sufficient dependence through two paths: one is to control false discovery adaptively and the other is to control the false discovery rate by giving a prespecified threshold. It is computationally efficient and easy to implement. We establish the theoretical properties under mild conditions. Numerical studies including simulation studies and real data analysis contain supporting evidence that the proposal performs reasonably well in practical settings.

High-Dimensional Survival Analysis: Methods and Applications

In the era of precision medicine, time-to-event outcomes such as time to death or progression are routinely collected, along with high-throughput covariates. These high-dimensional data defy classical survival regression models, which are either infeasible to fit or likely to incur low predictability due to over-fitting. To overcome this, recent emphasis has been placed on developing novel approaches for feature selection and survival prognostication. We will review various cutting-edge methods that handle survival outcome data with high-dimensional predictors, highlighting recent innovations in machine learning approaches for survival prediction. We will cover the statistical intuitions and principles behind these methods and conclude with extensions to more complex settings, where competing events are observed. We exemplify these methods with applications to the Boston Lung Cancer Survival Cohort study, one of the largest cancer epidemiology cohorts investigating the complex mechanisms of lung cancer.

Jackknife model averaging for high-dimensional quantile regression

In this paper, we propose a frequentist model averaging method for quantile regression with high-dimensional covariates. Although research on these subjects has proliferated as separate approaches, no study has considered them in conjunction. Our method entails reducing the covariate dimensions through ranking the covariates based on marginal quantile utilities. The second step of our method implements model averaging on the models containing the covariates that survive the screening of the first step. We use a delete-one cross-validation method to select the model weights, and prove that the resultant estimator possesses an optimal asymptotic property uniformly over any compact (0,1) subset of the quantile indices. Our proof, which relies on empirical process theory, is arguably more challenging than proofs of similar results in other contexts owing to the high-dimensional nature of the problem and our relaxation of the conventional assumption of the weights summing to one. Our investigation of finite-sample performance demonstrates that the proposed method exhibits very favorable properties compared to the least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalized regression methods. The method is applied to a microarray gene expression data set.

Gene Screening in High-Throughput Right-Censored Lung Cancer Data

Background

Advances in sequencing technologies have allowed collection of massive genome-wide information that substantially advances lung cancer diagnosis and prognosis. Identifying influential markers for clinical endpoints of interest has been an indispensable and critical component of the statistical analysis pipeline. However, classical variable selection methods are not feasible or reliable for high-throughput genetic data. Our objective is to propose a model-free gene screening procedure for high-throughput right-censored data, and to develop a predictive gene signature for lung squamous cell carcinoma (LUSC) with the proposed procedure.

Methods

A gene screening procedure was developed based on a recently proposed independence measure. The Cancer Genome Atlas (TCGA) data on LUSC was then studied. The screening procedure was conducted to narrow down the set of influential genes to 378 candidates. A penalized Cox model was then fitted to the reduced set, which further identified a 6-gene signature for LUSC prognosis. The 6-gene signature was validated on datasets from the Gene Expression Omnibus.

Results

Both model-fitting and validation results reveal that our method selected influential genes that lead to biologically sensible findings as well as better predictive performance, compared to existing alternatives. According to our multivariable Cox regression analysis, the 6-gene signature was indeed a significant prognostic factor (p-value < 0.001) while controlling for clinical covariates.

Conclusions

Gene screening as a fast dimension reduction technique plays an important role in analyzing high-throughput data. The main contribution of this paper is to introduce a fundamental yet pragmatic model-free gene screening approach that aids statistical analysis of right-censored cancer data, and provide a lateral comparison with other available methods in the context of LUSC.

Interaction screening for high-dimensional heterogeneous data via robust hybrid metrics

A novel model-free interaction screening approach called the hybrid metrics is introduced for high-dimensional heterogeneous data analysis. The metrics established based on the variation of conditional joint distribution function are measurements of interaction that include both size and direction. They are robust and can work with many types of response variables, including continuous, discrete, and categorical variables. We can apply the hybrid metrics to effective interaction selection for classification, response index models, and Poisson regression, among others. When dealing with classification, the hybrid metrics are capable of capturing both nonlinear category-general and category-specific interaction effects, providing us with a comprehensive overview and precise discovery of category information. When faced with a continuous response, the hybrid metrics perform fairly well even if the signal strength is weak, behaving as if the true interactions were known. To facilitate implementation, a fast two-stage procedure which naturally and efficiently enforces both strong and weak heredity is advocated. We further demonstrate their superior performances over popular competitors by exhaustive simulations and a SRBCT real data example. Supplementary materials for this article are available online.

Robust group variable screening based on maximum Lq-likelihood estimation

Variable screening plays an important role in ultra-high-dimensional data analysis. Most of the previous analyses have focused on individual predictor screening using marginal correlation or other rank-based techniques. When predictors can be naturally grouped, the structure information should be incorporated while applying variable screening. This study presents a group screening procedure that is based on maximum Lq-likelihood estimation, which is being increasingly used for robust estimation. The proposed method is robust against data contamination, including a heavy-tailed distribution of the response and a mixture of observations from different distributions. The sure screening property is rigorously established. Simulations demonstrate the competitive performance of the proposed method, especially in terms of its robustness against data contamination. Two real data analyses are presented to further illustrate its performance.

Nonparametric screening and feature selection for ultrahigh-dimensional Case II interval-censored failure time data

For the analysis of ultrahigh-dimensional data, the first step is often to perform screening and feature selection to effectively reduce the dimensionality while retaining all the active or relevant variables with high probability. For this, many methods have been developed under various frameworks but most of them only apply to complete data. In this paper, we consider an incomplete data situation, case II interval-censored failure time data, for which there seems to be no screening procedure. Basing on the idea of cumulative residual, a model-free or nonparametric method is developed and shown to have the sure independent screening property. In particular, the approach is shown to tend to rank the active variables above the inactive ones in terms of their association with the failure time of interest. A simulation study is conducted to demonstrate the usefulness of the proposed method and, in particular, indicates that it works well with general survival models and is capable of capturing the nonlinear covariates with interactions. Also the approach is applied to a childhood cancer survivor study that motivated this investigation.

A new joint screening method for right-censored time-to-event data with ultra-high dimensional covariates

In an ultra-high dimensional setting with a huge number of covariates, variable screening is useful for dimension reduction before applying a more refined method for model selection and statistical analysis. This paper proposes a new sure joint screening procedure for right-censored time-to-event data based on a sparsity-restricted semiparametric accelerated failure time model. Our method, referred to as Buckley-James assisted sure screening (BJASS), consists of an initial screening step using a sparsity-restricted least-squares estimate based on a synthetic time variable and a refinement screening step using a sparsity-restricted least-squares estimate with the Buckley-James imputed event times. The refinement step may be repeated several times to obtain more stable results. We show that with any fixed number of refinement steps, the BJASS procedure retains all important variables with probability tending to 1. Simulation results are presented to illustrate its performance in comparison with some marginal screening methods. Real data examples are provided using a diffuse large-B-cell lymphoma (DLBCL) data and a breast cancer data. We have implemented the BJASS method using Matlab and made it available to readers through Github https://github.com/yiucla/BJASS .

Variable Screening for Near Infrared (NIR) Spectroscopy Data Based on Ridge Partial Least Squares Regression

AIM AND OBJECTIVE

Near Infrared (NIR) spectroscopy data are featured by few dozen to many thousands of samples and highly correlated variables. Quantitative analysis of such data usually requires a combination of analytical methods with variable selection or screening methods. Commonly-used variable screening methods fail to recover the true model when (i) some of the variables are highly correlated, and (ii) the sample size is less than the number of relevant variables. In these cases, Partial Least Squares (PLS) regression based approaches can be useful alternatives.

MATERIALS AND METHODS

In this research, a fast variable screening strategy, namely the preconditioned screening for ridge partial least squares regression (PSRPLS), is proposed for modelling NIR spectroscopy data with high-dimensional and highly correlated covariates. Under rather mild assumptions, we prove that using Puffer transformation, the proposed approach successfully transforms the problem of variable screening with highly correlated predictor variables to that of weakly correlated covariates with less extra computational effort.

RESULTS

We show that our proposed method leads to theoretically consistent model selection results. Four simulation studies and two real examples are then analyzed to illustrate the effectiveness of the proposed approach.

CONCLUSION

By introducing Puffer transformation, high correlation problem can be mitigated using the PSRPLS procedure we construct. By employing RPLS regression to our approach, it can be made more simple and computational efficient to cope with the situation where model size is larger than the sample size while maintaining a high precision prediction.