Boosting the discriminatory power of sparse survival models via optimization of the concordance index and stability selection.
Boosting the discriminatory power of sparse survival models via optimization of the concordance index and stability selection.
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DOI：
10.1186/s12859-016-1149-8
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发表时间：
2016-07-22
影响因子：
3
通讯作者：
Schmid M
中科院分区：
文献类型：
--
作者：
Mayr A;Hofner B;Schmid M
当构建新的生物标志物或基因特征评分用于事件发生时间结局时，其基本目标是开发一种判别模型，帮助预测患者的预后是差还是好，并确定最有影响力的变量。在实践中，这通常是拟合考克斯模型。然而，就所产生的歧视力而言，这些并不一定是最佳的，而且是基于限制性的假设。我们提出了一种组合的方法来自动选择和拟合稀疏判别模型的潜在高维生存数据的基础上提高一个平滑版本的一致性指数（C指数）。由于该目标函数，所得到的预测模型在区分存活时间较长和较短的患者的能力方面是最佳的。梯度提升算法与稳定性选择方法相结合，以增强和控制其变量选择属性。由此产生的算法根据生存时间的排名拟合预测模型，并自动选择最稳定的预测因子。在大规模的模拟研究中证明了该方法的性能，该方法适用于少量的信息预测因子：C指数提升结合稳定性选择能够从更大的非信息预测因子集合中识别出一小部分信息预测因子，同时控制每个家庭的错误率。在基于基因表达数据发现乳腺癌患者的生物标志物的应用中，稳定性选择产生了更稀疏的模型，并且所得的区分能力高于套索惩罚考克斯回归模型。稳定性选择和C指数增强的组合可用于选择少量信息性生物标志物，并导出关于其区分能力最佳的新预测规则。稳定性选择控制每个家庭的错误率，这使得新的方法也从推理的角度来看有吸引力，因为它提供了一种替代经典的假设检验的单一预测效应。由于统计提升算法的收缩和变量选择特性，后者的测试通常对于通过提升拟合的预测模型是不可行的。本文的在线版本（doi：10.1186/s12859-016-1149-8）包含补充材料，可供授权用户使用。
When constructing new biomarker or gene signature scores for time-to-event outcomes, the underlying aims are to develop a discrimination model that helps to predict whether patients have a poor or good prognosis and to identify the most influential variables for this task. In practice, this is often done fitting Cox models. Those are, however, not necessarily optimal with respect to the resulting discriminatory power and are based on restrictive assumptions. We present a combined approach to automatically select and fit sparse discrimination models for potentially high-dimensional survival data based on boosting a smooth version of the concordance index (C-index). Due to this objective function, the resulting prediction models are optimal with respect to their ability to discriminate between patients with longer and shorter survival times. The gradient boosting algorithm is combined with the stability selection approach to enhance and control its variable selection properties. The resulting algorithm fits prediction models based on the rankings of the survival times and automatically selects only the most stable predictors. The performance of the approach, which works best for small numbers of informative predictors, is demonstrated in a large scale simulation study: C-index boosting in combination with stability selection is able to identify a small subset of informative predictors from a much larger set of non-informative ones while controlling the per-family error rate. In an application to discover biomarkers for breast cancer patients based on gene expression data, stability selection yielded sparser models and the resulting discriminatory power was higher than with lasso penalized Cox regression models. The combination of stability selection and C-index boosting can be used to select small numbers of informative biomarkers and to derive new prediction rules that are optimal with respect to their discriminatory power. Stability selection controls the per-family error rate which makes the new approach also appealing from an inferential point of view, as it provides an alternative to classical hypothesis tests for single predictor effects. Due to the shrinkage and variable selection properties of statistical boosting algorithms, the latter tests are typically unfeasible for prediction models fitted by boosting. The online version of this article (doi:10.1186/s12859-016-1149-8) contains supplementary material, which is available to authorized users.