Paramatric and nonparrametric inferences for various types of data

几乎每个领域都会出现各种类型的数据。在公共卫生、毒理学、流行病学、医学、遗传学、环境科学等领域，往往会出现以计数和比例、多变量、多层次或聚类式生命周期数据、高维数据、时空高通量数据等形式存在的数据。我提议的研究将涉及复杂数据的分析。数据分析中经常遇到的一个问题是，现有的模型不能解释数据中存在的变化和协变量的影响。此外，数据有时会显示混合的属性；数据来自混合分布或两个或更多总体的混合。因此，我们需要有效的程序来检测与现有模型的偏差，并开发一个有效的模型来适应数据。此外，我们还需要考虑参数、半参数和非参数(函数)回归模型中的参数和函数的估计。第二个问题是，通常不能直接观察到感兴趣的故障时间。只有关于每个故障时间是否在两个连续监测时间的时间间隔内的信息才可用。在这种情况下，关注的是寿命变量的生存概率以及协变量对这些寿命的影响。我们的目标是建立这类数据的回归模型，特别是多元区间截尾数据的回归模型。第三个问题是在不同情况下需要估计医疗成本。在比较不同治疗方法的临床试验中，在卫生经济学和结果研究中，经常分析医疗成本，以评估新治疗方案的经济影响和卫生保健利用的经济价值。我希望提出一种方法来处理在不同类型的统计审查机制下的终身医疗成本的估计。另一个问题是开发有效的方法来分析时间基因表达数据。我将与生物统计学家合作解决这个问题。

Various types of data arise in almost every field. Data in the form of counts and proportions, multivariate, multilevel or clustered lifetime data, high dimensional data, spatial and temporal high throughput data often occur in public health, toxicology, epidemiology, medicine, genetics, environmental science and so on. My proposed research will deal with the analysis of complex data. One frequently encountered problem in data analysis is that the existing models fail to explain the variation that exists in data and the effects of covariates. Also, data occasionally display a mixture of properties; the data are drawn from a mixed distribution or a mixture of two or more populations. We therefore need valid procedures to detect departures from the existing model and develop an effective model to fit the data. Further we need to consider the estimation of parameters and functions in the parametric, semi-parametric and non-parametric (functional) regression models. A second problem is that often the failure times of interest cannot be observed directly. Only information about whether each failure time lies in the time interval of two consecutive monitoring times is available. In this situation, the concern is the survival probability of the lifetime variables and the effects of covariates to these lifetimes. Our goal is to establish the regression models for this kind of data, in particular, for multivariate interval-censored data. A third problem is the need for medical cost estimation in different cases. In clinical trials comparing different treatments, in health economics, and in outcomes research, medical costs are frequently analyzed to evaluate the economical impacts of new treatment options and economic values of health-care utilization. I expect to propose an approach to deal with the estimation of the lifetime medical cost under the different types of statisitical censoring mechanism. Other problem is to develop effective methods to analyze temporal gene expression data. I will collaborate with biostatisticians to work out this problem.