We develop a post-selection inference method for the Cox proportional hazards model with interval-censored data, which provides asymptotically valid p-values and confidence intervals conditional on the model selected by lasso. The method is based on a pivotal quantity that is shown to converge to a uniform distribution under local alternatives. The proof can be adapted to many other regression models, which is illustrated by the extension to generalized linear models and the Cox model with right-censored data. Our method involves estimation of the efficient information matrix, for which several approaches are proposed with proof of their consistency. Thorough simulation studies show that our method has satisfactory performance in samples of modest sizes. The utility of the method is illustrated via an application to an Alzheimer's disease study.

翻译：本文针对区间删失数据下的Cox比例风险模型，提出了一种后选择推断方法。该方法在lasso模型选择条件下，可提供渐近有效的p值和置信区间。其基础是构造了一个枢轴量，并证明该量在局部备择假设下收敛于均匀分布。该证明可推广至多种回归模型，本文通过将其扩展至广义线性模型和右删失数据下的Cox模型进行了说明。本方法需估计有效信息矩阵，我们提出了多种估计方法并证明了其相合性。充分的模拟研究表明，该方法在中等样本量下表现良好。最后，通过一项阿尔茨海默病研究的实际应用，展示了该方法的实用性。