Non/semiparametric methods for nonlinear/hazards/cencored regression; Nonparametric monotone empirical Bayes; Non/semiparametric seemingly unrelated regression

当响应是事件发生时间结局（如患者寿命、失败时间）时，数据通常被删失，并涉及时间依赖性协变量。例如，在一项临床试验中，研究人员感兴趣的是评估治疗对HIV-1血清阳性吸毒者生存率的影响，这些吸毒者调整了其他预测协变量，如BMI（身体质量指数）和年龄。一些患者在研究终止时可能仍然存活。因此，对这些患者的生存时间进行删失。另一方面，当患者来自不同的健康中心时，同一中心的患者之间可能存在依赖性。本研究建议的部分目标是开发改进的非/半参数回归模型的固定和混合协变量效应与删失和聚类样本，并调查估计的大样本性能，以及它们的效率和最佳收敛速度。

When the response is the time-to-event outcome such as lifetimes of patients, failure times, the data are often censored and involve time dependent covariates. For example, in a clinical trial, the researchers are interested in evaluating the effect of a treatment on survival in the HIV-1 seropositive drug users adjusted for other predictive covariates such as BMI (body mess index) and age. Some patients may still be alive when the study terminates. Hence, the survival time of these patients are censored. On the other hand, when patients are taken from different health centers, there might be a dependence between patients in the same centers. Part of the objective of this research proposal is to develop improved non/semi-parametric regression models for fixed and mixed covariate effects with censored and clustered samples and to investigate the large sample performance of the estimators as well as their efficiency and the optimal convergence rates.