CONFIDENCE BANDS FOR THE MEDIAN SURVIVAL-TIME AS A FUNCTION OF THE COVARIATES IN THE COX MODEL

• 成果类型: Article
• 署名作者: BURR, D; DOSS, H
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291274
• 发表日期: 1993
• 页码: 1330-1340
• 关键词: regression-model; WEAK-CONVERGENCE; censored-data; large sample; intervals; LIFE

摘要

Let xi(p)(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 xi(p)(x) of xi(p)(x) and develop several families of confidence bands for xi(p)(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n --> infinity, where n is the number of individuals in the study, square-root n (xi(p)(x) - xi(p)(x)) 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.