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：我们针对区间删失数据下的Cox比例风险模型开发了一种后选择推断方法，该方法能在基于lasso选择模型的条件约束下，提供渐近有效的p值和置信区间。该方法基于一个枢轴量，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其他回归模型，这一点通过将其延伸至广义线性模型及右删失数据下的Cox模型得到了验证。本方法涉及有效信息矩阵的估计，我们提出了多种估计方法并证明了其一致性。充分的模拟研究表明，该方法在中等样本量的数据中表现令人满意。通过一项阿尔茨海默病研究的实际应用，进一步展示了该方法的实用性。