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。计数和比例形式的数据、多变量、多层次或聚类寿命数据、高维数据、时空高通量数据经常出现在公共卫生、毒理学、流行病学、医学、遗传学、环境科学等领域。我提出的研究将涉及对复杂数据的分析。在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，数据偶尔会显示混合属性；数据来自混合分布或两个或两个以上种群的混合。因此，我们需要有效的程序来检测与现有模型的偏离，并开发一个有效的模型来拟合数据。此外，我们需要考虑参数、半参数和非参数（函数）回归模型中参数和函数的估计。第二个问题是，通常不能直接观察到感兴趣的故障时间。只有每次故障时间是否在连续两次监控的时间间隔内的信息。在这种情况下，关注的是寿命变量的生存概率和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。第三个问题是需要在不同情况下进行医疗费用估算。在比较不同治疗方法的临床试验、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。本文希望对不同类型的统计审查机制下的终身医疗费用估算问题提出一种处理方法。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.