Controlled variable selection in Weibull mixture cure models for high-dimensional data.

Medical breakthroughs in recent years have led to cures for many diseases. The mixture cure model (MCM) is a type of survival model that is often used when a cured fraction exists. Many have sought to identify genomic features associated with a time-to-event outcome which requires variable selection strategies for high-dimensional spaces. Unfortunately, currently few variable selection methods exist for MCMs especially when there are more predictors than samples. This study develops high-dimensional penalized Weibull MCMs, which allow for identification of prognostic factors associated with both cure status and/or survival. We demonstrated how such models may be estimated using two different iterative algorithms. The model-X knockoffs method was combined with these algorithms to control the false discovery rate (FDR) in variable selection. Through extensive simulation studies, our penalized MCMs have been shown to outperform alternative methods on multiple metrics and achieve high statistical power with FDR being controlled. In an acute myeloid leukemia (AML) application with gene expression data, our proposed approach identified 14 genes associated with potential cure and 12 genes with time-to-relapse, which may help inform treatment decisions for AML patients.

Nonlinear variable selection with continuous outcome: a fully nonparametric incremental forward stagewise approach.

We present a method of variable selection for the sparse generalized additive model. The method doesn't assume any specific functional form, and can select from a large number of candidates. It takes the form of incremental forward stagewise regression. Given no functional form is assumed, we devised an approach termed "roughening" to adjust the residuals in the iterations. In simulations, we show the new method is competitive against popular machine learning approaches. We also demonstrate its performance using some real datasets. The method is available as a part of the nlnet package on CRAN (https://cran.r-project.org/package=nlnet).

Forward Stagewise Shrinkage and Addition for High Dimensional Censored Regression.

Despite enormous development on variable selection approaches in recent years, modeling and selection of high dimensional censored regression remains a challenging question. When the number of predictors p far exceeds the number of observational units n and the outcome is censored, computations of existing solutions often become difficult, or even infeasible in some situations, while performances frequently deteriorate. In this article, we aim at simultaneous model estimation and variable selection for Cox proportional hazards models with high dimensional covariates. We propose a forward stage-wise shrinkage and addition approach for that purpose. Our proposal extends a popular statistical learning technique, the boosting method. It inherits the flexible nature of boosting and is straightforward to extend to nonlinear Cox models. Meanwhile it advances the classical boosting method by adding explicit variable selection and substantially reducing the number of iterations to the algorithm convergence. Our intensive simulations have showed that the new method enjoys a competitive performance in Cox models with both p < n and p ≥ n scenarios. The new method was also illustrated with analysis of two real microarray survival datasets.