Controlling the false discovery rate by a Latent Gaussian Copula Knockoff procedure

The penalized Lasso Cox proportional hazards model has been widely used to identify prognosis biomarkers in high-dimension settings. However, this method tends to select many false positives, affecting its interpretability. In order to improve the reproducibility, we develop a knockoff procedure that consists on wrapping the Lasso Cox model with the model-X knockoff, resulting in a powerful tool for variable selection that allows for the control of the false discovery rate in the presence of finite sample guarantees. In this paper, we propose a novel approach to sample valid knockoffs for ordinal and continuous variables whose distributions can be skewed or heavy-tailed, which employs a Latent Mixed Gaussian Copula model to account for the dependence structure between the variables, leading to what we call the Latent Gaussian Copula Knockoff (LGCK) procedure. We then combine the LGCK method with the Lasso coefficient difference (LCD) statistic as the importance metric. To our knowledge, our proposal is the first knockoff framework for jointly considering ordinal and continuous data in a non-Gaussian setting and a survival context. We illustrate the proposed methodology’s effectiveness by applying it to a real lung cancer gene expression dataset.