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Attempts to predict prognosis in cancer patients using high-dimensional genomic data such as gene expression in tumor tissue can be made difficult by the large number of features and the potential complexity of the relationship between features and the outcome. Integrating prior biological knowledge into risk prediction with such data by grouping genomic features into pathways and networks reduces the dimensionality of the problem and could improve prediction accuracy. Additionally, such knowledge-based models may be more biologically grounded and interpretable. Prediction could potentially be further improved by allowing for complex nonlinear pathway effects. The kernel machine framework has been proposed as an effective approach for modeling the nonlinear and interactive effects of genes in pathways for both censored and noncensored outcomes. When multiple pathways are under consideration, one may efficiently select informative pathways and aggregate their signals via multiple kernel learning (MKL), which has been proposed for prediction of noncensored outcomes. In this paper, we propose MKL methods for censored survival outcomes. We derive our approach for a general survival modeling framework with a convex objective function and illustrate its application under the Cox proportional hazards and semiparametric accelerated failure time models. Numerical studies demonstrate that the proposed MKL-based prediction methods work well in finite sample and can potentially outperform models constructed assuming linear effects or ignoring the group knowledge. The methods are illustrated with an application to 2 cancer data sets. [ABSTRACT FROM AUTHOR]

When a moderate number of potential predictors are available and a survival model is fit with regularization to achieve variable selection, providing accurate inference on the predicted survival can be challenging. We investigate inference on the predicted survival estimated after fitting a Cox model under regularization guaranteeing the oracle property. We demonstrate that existing asymptotic formulas for the standard errors of the coefficients tend to underestimate the variability for some coefficients, while typical resampling such as the bootstrap tends to overestimate it; these approaches can both lead to inaccurate variance estimation for predicted survival functions. We propose a two-stage adaptation of a resampling approach that brings the estimated error in line with the truth. In stage 1, we estimate the coefficients in the observed data set and in [Formula: see text] resampled data sets, and allow the resampled coefficient estimates to vote on whether each coefficient should be 0. For those coefficients voted as zero, we set both the point and interval estimates to [Formula: see text] In stage 2, to make inference about coefficients not voted as zero in stage 1, we refit the penalized model in the observed data and in the [Formula: see text] resampled data sets with only variables corresponding to those coefficients. We demonstrate that ensemble voting-based point and interval estimators of the coefficients perform well in finite samples, and prove that the point estimator maintains the oracle property. We extend this approach to derive inference procedures for survival functions and demonstrate that our proposed interval estimation procedures substantially outperform estimators based on asymptotic inference or standard bootstrap. We further illustrate our proposed procedures to predict breast cancer survival in a gene expression study. [ABSTRACT FROM AUTHOR]

Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. [ABSTRACT FROM AUTHOR]