Dataset Information

Interaction Screening for Ultra-High Dimensional Data.

ABSTRACT: In ultra-high dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a data set with n observations and p predictors, the augmented design matrix including all linear and order-2 terms is of size n × (p(2) + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard machines and software tools for storage and analysis. In theory, the interaction selection consistency is hard to achieve in high dimensional settings. Interaction effects have heavier tails and more complex covariance structures than main effects in a random design, making theoretical analysis difficult. In this article, we propose to tackle these issues by forward-selection based procedures called iFOR, which identify interaction effects in a greedy forward fashion while maintaining the natural hierarchical model structure. Two algorithms, iFORT and iFORM, are studied. Computationally, the iFOR procedures are designed to be simple and fast to implement. No complex optimization tools are needed, since only OLS-type calculations are involved; the iFOR algorithms avoid storing and manipulating the whole augmented matrix, so the memory and CPU requirement is minimal; the computational complexity is linear in p for sparse models, hence feasible for p ? n. Theoretically, we prove that they possess sure screening property for ultra-high dimensional settings. Numerical examples are used to demonstrate their finite sample performance.

SUBMITTER: Hao N

PROVIDER: S-EPMC4224119 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Publications

Interaction Screening for Ultra-High Dimensional Data.

Hao Ning N Zhang Hao Helen HH

Journal of the American Statistical Association 20140101 507

In ultra-high dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a data set with n observations and p predictors, the augmented design matrix including all linear and order-2 terms is of size n × (p2 + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard mac ...[more]

PMID: 25386043

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Project description:Background:Building prognostic models of clinical outcomes is an increasingly important research task and will remain a vital area in genomic medicine. Prognostic models of clinical outcomes are usually built and validated utilizing variable selection methods and machine learning tools. The challenges, however, in ultra-high dimensional space are not only to reduce the dimensionality of the data, but also to retain the important variables which predict the outcome. Screening approaches, such as the sure independence screening (SIS), iterative SIS (ISIS) and principled SIS (PSIS) have been developed to overcome the challenge of high dimensionality. We are interested in identifying important single-nucleotide polymorphisms (SNPs) and integrating them into a validated prognostic model of overall survival in patients with metastatic prostate cancer. While the abovementioned variable selection approaches have theoretical justification in selecting SNPs, the comparison and the performance of these combined methods in predicting time-to-event outcomes have not been previously studied in ultra-high dimensional space with hundreds of thousands of variables. Methods:We conducted a series of simulations to compare the performance of different combinations of variable selection approaches and classification trees, such as the least absolute shrinkage and selection operator (LASSO), adaptive least absolute shrinkage and selection operator (ALASSO) and random survival forest (RSF), in ultra-high dimensional setting data for the purpose of developing prognostic models for a time-to-event outcome that is subject to censoring. The variable selection methods were evaluated for discrimination (Harrell's concordance statistic), calibration and overall performance. In addition, we applied these approaches to 498,081 SNPs from 623 Caucasian patients with prostate cancer. Results:When n=300, ISIS-LASSO and ISIS-ALASSO chose all the informative variables which resulted in the highest Harrell's c-index (>0.80). On the other hand, with a small sample size (n=150), ALASSO performed better than any other combinations as demonstrated by the highest c-index and/or overall performance, although there was evidence of overfitting. In analyzing the prostate cancer data, ISIS-ALASSO, SIS-LASSO, and SIS-ALASSO combinations achieved the highest discrimination with c-index of 0.67. Conclusions:Choosing the appropriate variable selection method for training a model is a critical step in developing a robust prognostic model. Based on the simulation studies, the effective use of ALASSO or a combination of methods, such as ISIS-LASSO and ISIS-ALASSO, allows both for the development of prognostic models with high predictive accuracy and a low risk of overfitting assuming moderate sample sizes.

Dataset Information

Interaction Screening for Ultra-High Dimensional Data.

Publications

Interaction Screening for Ultra-High Dimensional Data.

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