Confidence Bands for the Median Survival Time as a Function of the Covariates in the Cox Model
针对Cox模型，提出中位生存时间作为协变量函数的估计量，并开发了两种置信带构建方法（基于高斯过程模拟和自助法），通过模拟和斯坦福心脏移植数据验证。
Abstract Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then estimate this covariance structure from the data, and simulate many Gaussian processes with this estimated covariance structure. The critical constants required for the construction of the confidence bands are obtained from the simulated processes. Another type of bands is obtained by bootstrapping. We obtain an asymptotic theory for both types of bands. Simulation studies are used to compare the two types of bands. The methods are illustrated on the Stanford Heart Transplant Data.