Information criteria for detecting change-points in the Cox proportional hazards model
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Cox比例风险模型变点检测的信息准则
- 研究问题
- 当治疗效应延迟出现、风险比可能发生突变时，如何为带变点的Cox模型选择结构，并处理常规AIC惩罚不足的问题？
- 方法与思路
- 作者针对变点模型的非正则性建立偏似然估计的专门渐近理论，再依据AIC的原始推导构造信息准则。
- 材料陈述的贡献
- 摘要称得到显式且可能远大于两倍参数数目的惩罚项，并以数值实验和临床试验说明其与形式化AIC的差异。
- 阅读关注点
- 应核对变点及风险比的参数化方式、偏似然渐近条件、惩罚项推导，以及候选结构与模型选择目标的定义。
- 阅读边界
- 这是预印本，同行评审未核验；摘要未给出惩罚公式、变点间隔要求或数值结果，不能据此确认普遍的选择优势。
原文摘要
The Cox proportional hazards model, commonly used in clinical trials, assumes proportional hazards. However, it does not hold when, for example, there is a delayed onset of the treatment effect. In such a situation, an acute change in the hazard ratio function is expected to exist. This paper considers the Cox model with change-points and derives AIC-type information criteria for detecting those change-points. The change-point model does not allow for conventional statistical asymptotics due to its irregularity, thus a formal AIC that penalizes twice the number of parameters would not be analytically derived, and using it would clearly give overfitting analysis results. Therefore, we will construct specific asymptotics using the partial likelihood estimation method in the Cox model with change-points. Based on the original derivation method for AIC, we propose information criteria that are mathematically guaranteed. If the partial likelihood is used in the estimation, information criteria with penalties much larger than twice the number of parameters could be obtained in an explicit form. Numerical experiments confirm that the proposed criterion is clearly superior in terms of the original purpose of AIC, which is to provide an estimate that is close to the true structure. We also apply the proposed criterion to actual clinical trial data to indicate that it will easily lead to different results from the formal AIC.