Paramatric and nonparrametric inferences for various types of data

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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.