Determining significant prognostic biomarkers is of increasing importance in many areas of medicine. Scores used in clinical practice often categorize continuous features into binary ones using expert-driven cut-points. Many algorithms have been developed to find one optimal cut-point, but there is often need to determine an optimal number of cut-points and their locations at the same time. However, there exists no standard method to help evaluate how many cut-points are optimal for a given continuous feature in the survival analysis setting. Moreover, most existing methods are univariate, hence not well-suited to high-dimensional frameworks. Here we introduce the binacox, a prognostic method to deal with the problem of detecting multiple cut-points per features in a multivariate setting where a large number of continuous features are available. The method is based on the Cox model and combines one-hot encoding with the binarsity penalty, which uses total-variation regularization together with an extra linear constraint, and enables feature selection. Nonasymptotic oracle inequalities for prediction and estimation with a fast rate of convergence are established. The statistical performance of the method is examined in an extensive Monte Carlo simulation study, and then illustrated on three publicly available genetic cancer datasets. On these high-dimensional datasets, our proposed method significantly outperforms state-of-the-art survival models regarding risk prediction in terms of the C-index, with a computing time orders of magnitude faster. In addition, it provides powerful interpretability from a clinical perspective by automatically pinpointing significant cut-points in relevant variables.

翻译：在许多医学领域,确定重要的预测性生物标志越来越重要。临床实践中使用的分数往往使用专家驱动的切点将连续特征分类为二进制的分数。许多算法的开发是为了找到一个最佳切点,但往往需要同时确定最佳的切点数量及其位置。然而,目前没有标准的方法来帮助评估在生存分析环境中对某个连续特征而言有多少切点是最佳的。此外,大多数现有方法都是单向的,因此不适宜于高维框架。在这里,我们引入了双轨法,这是一种在多变式环境中发现多个切点及其位置的最佳切点。但通常需要同时确定一个最佳的切点及其位置。但是,没有标准的方法来帮助评估在生存分析环境中对某个连续特征进行最优化的切点。此外,大多数现有方法都是单向的,因此不适合高高度框架。在这里,我们引入了双轨法的预测和快速趋同率的预断点,在多变现性数据模型中提供了一种显著的计算方法。