Statistical Methods for HIV /AIDS Studies

描述（由申请人提供）：在HIV相关疾病的临床或观察性研究中，反应变量（例如，到某个临床或实验室事件的时间、特定病毒或免疫学标记物的水平等）。可以被删除或截断。我们建议调查以下三个一般的，密切相关的删失回归问题，我们经常遇到的艾滋病毒/艾滋病的研究。 1.右删失数据下非比例风险模型的推断方法。我们将开发半参数加速失效时间（AFT）和分位数模型的新的推理程序。我们还将研究一般的AFT和分位数回归与Box-Cox型转换的故障时间。 2.截尾失效时间数据的模型检验与评估。我们将开发AFT，分位数和线性变换模型的模型诊断工具，基于鞅残差的删失数据，用于检查建模假设的各个方面。 3.高维协变量的删失数据回归。 我们将研究当有大量协变量、协变量高度相关或失败次数小于通常认为的谨慎值时，用右删失数据拟合探索性回归模型时，降低估计均方误差的方法。 我们的方法将推广主成分回归的比例风险模型和偏最小二乘和主成分回归的AFT模型的战斗删失数据。

DESCRIPTION (provided by applicant): In a clinical or observational study for HIV-related diseases, the response variable (e.g., the time to a certain clinical or lab based event, the level of a specific viral or immunological marker et al.) may be censored or truncated. We propose to investigate the following three general, closely related censored regression problems, which we encounter frequently in HIV/AIDS research. 1. Inference procedures for nonproportional hazards models for right censored data. We will develop new inference procedures for semi-parametric accelerated failure time (AFT) and quantile models. We will also study the general AFT and quantile regression with the Box-Cox-type of transformation for the failure time. 2. Model checking and evaluation for censored failure time data. We will develop model diagnostic tools for AFT, quantile and linear transformation models with censored data based on martingale residuals for checking various aspects of modeling assumptions. 3. Censored data regression with high-dimensional covariates. We will study methods for reducing mean squared error of estimation when fitting exploratory regression models with right censored data when there are large numbers of covariates, when the covariates are highly correlated, or the number of failures is smaller than commonly thought prudent. Our methods will generalize principal component regression to the proportional hazards model and partial least squares and principal components regression to AFT models for fight censored data.