Abstract 2089: Vanishing deviance problem in high-dimensional penalized Cox regression

Abstract

Abstract Penalized regression models, such as LASSO and elastic net, have been well-established for high-dimensional variable sections. For the analysis of censored survival outcomes, the penalized Cox regression model has been widely used. The parameter tuning in the penalized regression is often implemented based on the cross-validation (CV) via the “one standard error rule” (1se rule), resulting in a more parsimonious model. However, in a high-dimensional Cox regression model, a common observation is that the CV plot for tuning parameters against partial-likelihood deviance is often not U-shaped but L-shaped. In this case, the model selection will fail with either the “1se” or the“min” rule. We observed that this phenomenon is quite universal in the setting of high-dimensional prognostic biomarker selection, in which the standard CV steps often result in no or very few features included in the final model. We refer to this phenomenon as the “vanishing deviance” (VD) problem. In this study, we investigated this problem in more depth and demonstrated the issue and potential solution using real data from pan-cancer analysis of prognostic lncRNA biomarkers. To discover the cause behind the VD problem, we conducted an extensive set of simulations by varying sample sizes, feature dimensions, censoring rates, number of true biomarkers, and significance levels of true signals.Our results indicated that the main cause of the VD problem can be related to the limited sample size in the cancer omics dataset and a large number of true (or highly associated) biomarkers or signals underlying. To this end, we propose computational solutions that can alleviate the problem and we implemented them in the R package called CoxHive. We verified the performance of our solution based on both simulation studies and the analyses of the pan-cancer gene expression data. This software tool will greatly facilitate biomarker selection (including genomic and imaging biomarkers) in the high-dimensional setting. Citation Format: Sijie Yao, Tingyi Li, Biwei Cao, Xuefeng Wang. Vanishing deviance problem in high-dimensional penalized Cox regression [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 2089.