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Counting process-based dimension reduction methods for censored outcomes.

ABSTRACT: We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second, the nonparametric estimation involved adapts to the structural dimension, so our methods circumvent the curse of dimensionality. Asymptotic normality is established for the estimators. We propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that our new approaches exhibit significantly improved performance. The methods are implemented in the [Formula: see text] package [Formula: see text].

SUBMITTER: Sun Q

PROVIDER: S-EPMC6373420 | biostudies-literature | 2019 Mar

REPOSITORIES: biostudies-literature

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Counting process-based dimension reduction methods for censored outcomes.

Sun Qiang Q Zhu Ruoqing R Wang Tao T Zeng Donglin D

Biometrika 20190107 1

We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second, the nonparametric estimation ...[more]

PMID: 30799878

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Project description:BackgroundThe most popular methods for significance analysis on microarray data are well suited to find genes differentially expressed across predefined categories. However, identification of features that correlate with continuous dependent variables is more difficult using these methods, and long lists of significant genes returned are not easily probed for co-regulations and dependencies. Dimension reduction methods are much used in the microarray literature for classification or for obtaining low-dimensional representations of data sets. These methods have an additional interpretation strength that is often not fully exploited when expression data are analysed. In addition, significance analysis may be performed directly on the model parameters to find genes that are important for any number of categorical or continuous responses. We introduce a general scheme for analysis of expression data that combines significance testing with the interpretative advantages of the dimension reduction methods. This approach is applicable both for explorative analysis and for classification and regression problems.ResultsThree public data sets are analysed. One is used for classification, one contains spiked-in transcripts of known concentrations, and one represents a regression problem with several measured responses. Model-based significance analysis is performed using a modified version of Hotelling's T2-test, and a false discovery rate significance level is estimated by resampling. Our results show that underlying biological phenomena and unknown relationships in the data can be detected by a simple visual interpretation of the model parameters. It is also found that measured phenotypic responses may model the expression data more accurately than if the design-parameters are used as input. For the classification data, our method finds much the same genes as the standard methods, in addition to some extra which are shown to be biologically relevant. The list of spiked-in genes is also reproduced with high accuracy.ConclusionThe dimension reduction methods are versatile tools that may also be used for significance testing. Visual inspection of model components is useful for interpretation, and the methodology is the same whether the goal is classification, prediction of responses, feature selection or exploration of a data set. The presented framework is conceptually and algorithmically simple, and a Matlab toolbox (Mathworks Inc, USA) is supplemented.

Project description:MotivationOne of the major goals in large-scale genomic studies is to identify genes with a prognostic impact on time-to-event outcomes which provide insight into the disease process. With rapid developments in high-throughput genomic technologies in the past two decades, the scientific community is able to monitor the expression levels of tens of thousands of genes and proteins resulting in enormous datasets where the number of genomic features is far greater than the number of subjects. Methods based on univariate Cox regression are often used to select genomic features related to survival outcome; however, the Cox model assumes proportional hazards (PH), which is unlikely to hold for each feature. When applied to genomic features exhibiting some form of non-proportional hazards (NPH), these methods could lead to an under- or over-estimation of the effects. We propose a broad array of marginal screening techniques that aid in feature ranking and selection by accommodating various forms of NPH. First, we develop an approach based on Kullback-Leibler information divergence and the Yang-Prentice model that includes methods for the PH and proportional odds (PO) models as special cases. Next, we propose R2 measures for the PH and PO models that can be interpreted in terms of explained randomness. Lastly, we propose a generalized pseudo-R2 index that includes PH, PO, crossing hazards and crossing odds models as special cases and can be interpreted as the percentage of separability between subjects experiencing the event and not experiencing the event according to feature measurements.ResultsWe evaluate the performance of our measures using extensive simulation studies and publicly available datasets in cancer genomics. We demonstrate that the proposed methods successfully address the issue of NPH in genomic feature selection and outperform existing methods.Availability and implementationR code for the proposed methods is available at github.com/lburns27/Feature-Selection.Contactkarthik.devarajan@fccc.edu.Supplementary informationSupplementary data are available at Bioinformatics online.

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Counting process-based dimension reduction methods for censored outcomes.

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Counting process-based dimension reduction methods for censored outcomes.

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