SEMI PARAMETRIC METHODS FOR CANCER STUDIES

我们建议研究以下有关癌症的统计问题 学习。这项研究的结果将有助于分析 生存数据。 删失数据的中位数和分位数回归模型 我们将开发高效的数值算法来实现 Ying，Jung和魏(1993)提出的计算中位数和分位数的方法 带有删失数据的回归模型；研究删失时的情况 变量依赖于协变量；将这些方法推广到多变量 故障时间数据；探索高度聚集的分位数回归方法 故障时间观测；以及研究模型诊断程序 删失数据下的分位数回归模型。 B.加速失效的半参数方法 时间模型 我们将研究一类新的估计程序，它可以得到 通过标准的数值方法；仔细检查它们的性能和 将它们与魏、英、林(1990)提出的秩估计量进行比较； 求出加速条件下生存函数的置信带 具有特定集合的未来患者的故障时间(AFT)模型 协变量；以及研究AFT模型的模型诊断方法。 C.估计两条生存曲线之间的差异 我们将研究同时构造的非参数方法。 两个生存函数之差的可信区间和 探索Kaplan-Meier估计的适当变换，以获得 适用于小样本量的准确条带。我们将学习非参数方法 它们提供了单个统计信息，用于估计和汇总 两条生存曲线之间的差异。

We propose to study the following statistical problems arising in cancer studies. The results from this research will be useful in analyzing survival data. Median and Quantile Regression Models for Censored Data We will develop efficient numerical aIgorithms to implement the methods proposed by Ying, Jung and Wei (1993) for the median and quantile regression models with censored data; study the case when censoring variables depend on covariates; generalize these methods to multivariate failure time data; explore quantile regression methods for highly clustered failure time observations; and study model diagnostic procedures for the quantile regression model with censored data. B. Semi-parametric Methods for the Accelerated Failure Time Model We will study a class of new estimation procedures which can be obtained through standard numerical methods; carefully examine their performance and compare them to the rank estimators proposed by Wei, Ying and Lin (1990); derive confidence bands for the survival function under the accelerated failure time (AFT) model for future patients with a specific set of covariates; and study model diagnostic methods for the AFT model. C. Estimating the Difference Between Two Survival Curves We will study nonparametric methods for constructing simultaneous confidence intervals of the difference between two survival functions and explore appropriate transformations of the Kaplan-Meier estimates to obtain accurate bands for small sample sizes. We will study nonparametric methods which provide a single statistic for estimating and summarizing the difference between two survival curves.