Active-set algorithms based statistical inference for shape-restricted generalized additive Cox regression models
基于活动集算法的形状约束广义加性 Cox 回归统计推断AI 解读 ↓
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基于活动集算法的形状约束广义加性 Cox 回归统计推断
- 研究问题
- 如何在 Cox 回归中允许协变量效应具有单调、凸或凹形状，从而放松线性设定并恢复未知的非线性响应关系？
- 方法与思路
- 作者以样条展开表示形状受限的加性函数，使用数据驱动节点，将负对数似然最小化写为凸优化并用活动集算法求解。
- 材料陈述的贡献
- 摘要称，算法可自动删除多余节点；所讨论模型能改善非线性响应恢复，并在相应场景中保持准确的线性效应估计。
- 阅读关注点
- 应核对形状限制与节点选择的实现、模型可识别性、算法收敛依据，以及效应估计和拟合改善的具体比较设计。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未说明推断分布、置信区间构造或性能改善的适用范围。
原文摘要
Recently the shape-restricted inference has gained popularity in statistical and econometric literature in order to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotonic increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modeled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit.