Ultrahigh-dimensional Survival Data Research Articles

Generalized Jaccard feature screening for ultra-high dimensional survival data

<p>To identify critical genomes that influence a cancer patient's survival time, feature screening methods play a vital role in this biomedical field. Most of the current research relies on a fixed survival function model, which limits its universality in practical applications. In this paper, we propose the Generalized Jaccard coefficient (GJAC), which extends the traditional Jaccard coefficient from comparing binary vectors' similarity to calculating the correlation between the general vectors. The larger the GJAC value, the higher the sample similarity. Using the GJAC, we introduce a novel model-free screening method to select the active set of covariates in ultra-high dimensional survival data. Through Monte Carlo simulations, GJAC-Sure Independence Screening (GJAC-SIS) shows a higher accuracy, lower errors, and an excellent applicability in different types of survival data compared with other existing model-free feature screening methods in survival data. Additionally, in the real cancer datasets (DLBCL), GJAC-SIS can screen out two additional important genomes, which are certified in the real biomedical experiment, while the other five methods can't. As a result, GJAC-SIS achieves a high screening precision, delivers a more effective screening outcome, and has a better utility and universality.</p>

Model-free conditional screening for ultrahigh-dimensional survival data via conditional distance correlation.

How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model-free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large-B-cell lymphomastudy S1.

Variable screening for varying coefficient models with ultrahigh-dimensional survival data

In this article, we develop a variable screening method for varying coefficient hazards models of single-index form. The proposed method can be viewed as a natural survival extension of conditional correlation screening. An appealing feature of the proposed method is that it is applicable to many popularly used survival models, including the varying coefficient additive hazards model and the varying coefficient Cox model. The proposed method enjoys the sure screening property, and the number of the selected covariates can be bounded by a moderate order. Simulation studies demonstrate that our method performs well, and an empirical example is also presented.

Conditional screening for ultrahigh-dimensional survival data in case-cohort studies.

The case-cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In many such studies, the number of covariates is very large, and the goal of the research is to identify active covariates which have great influence on response. Since the introduction of sure independence screening (SIS), screening procedures have achieved great success in terms of effectively reducing the dimensionality and identifying active covariates. However, commonly used screening methods are based on marginal correlation or its variants, they may fail to identify hidden active variables which are jointly important but are weakly correlated with the response. Moreover, these screening methods are mainly proposed for data under the simple random sampling and can not be directly applied to case-cohort data. In this paper, we consider the ultrahigh-dimensional survival data under the case-cohort design, and propose a conditional screening method by incorporating some important prior known information of active variables. This method can effectively detect hidden active variables. Furthermore, it possesses the sure screening property under some mild regularity conditions and does not require any complicated numerical optimization. We evaluate the finite sample performance of the proposed method via extensive simulation studies and further illustrate the new approach through a real data set from patients with breast cancer.

Censored mean variance sure independence screening for ultrahigh dimensional survival data

Feature screening has become an indispensable statistical modeling tool for ultrahigh dimensional data analysis. This article introduces a new model-free marginal feature screening approach for ultrahigh dimensional survival data with right censoring. The new procedure could be used for survival data with both ultrahigh dimensional categorical and continuous covariates. Motivated by Cui et al. (2015), a censored mean variance index (cMV) is proposed to measure the dependence between a survival outcome and a categorical covariate. Then a slice-and-fuse method is exploited to modify the cMV index adaptive to continuous covariates. The sure independence screening based on the censored mean variance index (cMV-SIS) is proposed to identify the important covariates for ultrahigh dimensional data with censored survival outcomes. It enjoys many appealing merits inherited in the mean variance index. It is model-free and thus robust to model misspecification. It is also robust to heavy tails and outliers in covariates. Moreover, the sure screening properties are theoretically investigated for both categorical and continuous covariates under some mild technical conditions. Extensive numerical simulations and a real data example have demonstrated the competitive performances of the proposed feature screening method.

Model-free feature screening via distance correlation for ultrahigh dimensional survival data

With the explosion of ultrahigh dimensional data in various fields, many sure independent screening methods have been proposed to reduce the dimensionality of data from a large scale to a relatively moderate scale. For censored survival data, the existing screening methods mainly adopt the Kaplan–Meier estimator to handle censoring, which may not perform well for heavy censoring cases. In this article, we propose a novel sure independent screening procedure based on distance correlation after standardizing marginal variables for ultrahigh dimensional survival data. It is a model-free approach and does not involve the Kaplan–Meier estimator, thus its performance is much more robust than the existing methods. Furthermore, our proposed method enjoys other advantages: it avoids the complication to specify an actual model from large number of covariates; it enjoys the sure screening property and the ranking consistency under some mild regularity conditions; it does not require any complicated numerical optimization, so the corresponding calculation is very simple and fast. Extensive numerical studies demonstrate that the proposed method has favorable exhibition over the existing methods. As an illustration, we apply the proposed method to a gene expression data set.

Model free feature screening for ultrahigh dimensional covariates with right censored outcomes

This paper is concerned with feature screening for the ultrahigh dimensional survival data. We propose a new feature screening procedure by extending the method of Zhu et al. via inverse probability censoring weighting. The proposed procedure enjoys two appealing merits. First, it does not need to specify any model assumption between the response and the covariates. Thus, it is robust to the model mis-specification. Second, our procedure is robust in the presence of outliers or extreme values since it only uses the rank of censored outcomes. We establish the sure screening property under some regular conditions. The simulations and analysis of the real data demonstrate that our procedure exhibits favorably in comparison with the existing competitors.

Model-free slice screening for ultrahigh-dimensional survival data

For ultrahigh-dimensional data, independent feature screening has been demonstrated both theoretically and empirically to be an effective dimension reduction method with low computational demanding. Motivated by the Buckley–James method to accommodate censoring, we propose a fused Kolmogorov–Smirnov filter to screen out the irrelevant dependent variables for ultrahigh-dimensional survival data. The proposed model-free screening method can work with many types of covariates (e.g. continuous, discrete and categorical variables) and is shown to enjoy the sure independent screening property under mild regularity conditions without requiring any moment conditions on covariates. In particular, the proposed procedure can still be powerful when covariates are strongly dependent on each other. We further develop an iterative algorithm to enhance the performance of our method while dealing with the practical situations where some covariates may be marginally unrelated but jointly related to the response. We conduct extensive simulations to evaluate the finite-sample performance of the proposed method, showing that it has favourable exhibition over the existing typical methods. As an illustration, we apply the proposed method to the diffuse large-B-cell lymphoma study.

The Lq- NORM LEARNING FOR ULTRAHIGH-DIMENSIONAL SURVIVAL DATA: AN INTEGRATIVE FRAMEWORK.

In the era of precision medicine, survival outcome data with high-throughput predictors are routinely collected. Models with an exceedingly large number of covariates are either infeasible to fit or likely to incur low predictability because of overfitting. Variable screening is key in identifying and removing irrelevant attributes. Recent years have seen a surge in screening methods, but most of them rely on some particular modeling assumptions. Motivated by a study on detecting gene signatures for multiple myeloma patients' survival, we propose a model-free L q -norm learning procedure, which includes the well-known Cramér-von Mises and Kolmogorov criteria as two special cases. The work provides an integrative framework for detecting predictors with various levels of impact, such as short- or long-term impact, on censored outcome data. The framework naturally leads to a scheme which combines results from different q to reduce false negatives, an aspect often overlooked by the current literature. We show that our method possesses sure screening properties. The utility of the proposal is confirmed with simulation studies and an analysis of the multiple myeloma study.

Conditional distance correlation sure independence screening for ultra-high dimensional survival data

In this article, we propose a new conditional feature screening procedure for ultra-high dimensional survival data via the conditional distance correlation. Compared with the existing methods, the proposed conditional feature screening approach has two key advantages. First, it is model-free and thus robust to model misspecification. Second, it is robust to heavy tails or extreme values in both of the covaraites and response. The sure screening property of suggested means is well established under rather mild assumptions. Simulation studies are carried out to examine and compare the performance of the advised procedure with its competitors, while a real data example is analyzed to illustrate the proposed approach.

Feature screening for ultrahigh-dimensional survival data when failure indicators are missing at random

In modern statistical applications, the dimension of covariates can be much larger than the sample size, and extensive research has been done on screening methods which can effectively reduce the dimensionality. However, the existing feature screening procedure can not be used to handle the ultrahigh-dimensional survival data problems when failure indicators are missing at random. This motivates us to develop a feature screening procedure to handle this case. In this paper, we propose a feature screening procedure by sieved nonparametric maximum likelihood technique for ultrahigh-dimensional survival data with failure indicators missing at random. The proposed method has several desirable advantages. First, it does not rely on any model assumption and works well for nonlinear survival regression models. Second, it can be used to handle the incomplete survival data with failure indicators missing at random. Third, the proposed method is invariant under the monotone transformation of the response and satisfies the sure screening property. Simulation studies are conducted to examine the performance of our approach, and a real data example is also presented for illustration.

Conditional-quantile screening for ultrahigh-dimensional survival data via martingale difference correlation

Using the so-called martingale difference correlation (MDC), we propose a novel censored-conditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity (which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDC-based conditional quantile screening, as considered in Shao and Zhang (2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.

Nonparametric independence feature screening for ultrahigh-dimensional survival data

With the explosion of digital information, high-dimensional data is frequently collected in prevalent domains, in which the dimension of covariates can be much larger than the sample size. Many effective methods have been developed to reduce the dimension of such data recently, however, few methods might perform well for survival data with censoring. In this article, we develop a novel nonparametric feature screening procedure based on ultrahigh-dimensional survival data by incorporating the inverse probability weighting scheme to tackle the issue of censoring. The proposed method is model-free and hence can be implemented for extensive survival models. Moreover, it is robust to heterogeneity and invariant to monotone increasing transformations of the response. The sure screening property and ranking consistency property are also established under mild conditions. The competence and robustness of our method is further confirmed through comprehensive simulation studies and an analysis of a real data example.

A new nonparametric screening method for ultrahigh-dimensional survival data

For ultrahigh-dimensional data, sure independent screening methods can effectively reduce the dimensionality while ensuring that all the active variables can be retained with high probability. However, most existing screening procedures are developed for ultrahigh-dimensional complete data and cannot be applicable to censored survival data. To address the new challenges from censoring, a novel model-free screening method was proposed through the Kolmogorov–Smirnov test statistic that is specially tailored to the ultrahigh-dimensional survival data. The sure screening property was established under some mild regularity conditions, and its superior performance over existing screening methods is demonstrated by our extensive simulation studies. A real data example of gene expression is used to illustrate the application of the proposed fully nonparametric screening procedure.

Censored cumulative residual independent screening for ultrahigh-dimensional survival data.

For complete ultrahigh-dimensional data, sure independent screening methods can effectively reduce the dimensionality while retaining all the active variables with high probability. However, limited screening methods have been developed for ultrahigh-dimensional survival data subject to censoring. We propose a censored cumulative residual independent screening method that is model-free and enjoys the sure independent screening property. Active variables tend to be ranked above the inactive ones in terms of their association with the survival times. Compared with several existing methods, our model-free screening method works well with general survival models, and it is invariant to the monotone transformation of the responses, as well as requiring substantially weaker moment conditions. Numerical studies demonstrate the usefulness of the censored cumulative residual independent screening method, and the new approach is illustrated with a gene expression data set.

Correlation rank screening for ultrahigh-dimensional survival data

With the recent explosion of ultrahigh-dimensional data, extensive work has been carried out for screening methods which can effectively reduce the dimensionality. However, censored survival data which often arise in clinical trials and genetic studies have been left greatly unexplored for ultrahigh-dimensional scenarios. A novel feature screening procedure is proposed for ultrahigh-dimensional survival data. Also established are the ranking consistency and the sure independent screening properties. Compared with the existing methods, the proposed screening procedure is invariant to the monotone transformation, known or unknown, of the response. Moreover, it can be readily applied to ultrahigh-dimensional complete data when the censoring rate is zero. Simulation studies demonstrate that the proposed procedure exhibits favorably in comparisons with the existing ones. As an illustration, the proposed method is applied to the mantle cell lymphoma study.