Development and Application of Graphical Modeling techniques for Assesshrg the Joint Risks of Contaminants

点击翻译按钮获取中文摘要

The graphical modeling techniques which have been proposed for the analysis of complex causal relationship are developed under the assumption of multivariate normal distribution. Thus they are limited for modeling only linear cause-effect relationships. 'lb remove this restriction we developed in this project graphical modeling techniques based on rank correlation matrix. The method was applied for studying joint risks of environmental contaminants such as Dioxin, PCB and pesticides measuring the amount of these chemicals in breast milks of 120 women and also measuring the thyroid and immune hormone status of infants from those mothers. It was discovered by the method that the odds ratios of thyroid function and Dioxin was 1.65 (p=0.29), but was 7.15 (p=0.02) when adjusted for PCB.We further developed a method of graphical modeling technique that used latent structure models, and also explored the method that may deal with time series data.Theoretical studies were conducted to develop those methods mentioned above ; namely(i)Developed estimation and testing method for comparing two negative binomial distributions by adjusting for confounding variables by stratification.(ii)Developed a method of nonparametric imputation.(iii) Developed a theory to extract information from high dimensional data by modeling the data using various base functions ; developed a Bayes Information criteria to select the models; applied it to not only the graphical modeling but also other statistical methods such as disiminant analysis for DNA data and others.(iv)Developed a theory of graphical modeling for repeated measurements data in one to K multiple comparison setting and developed an approximate confidence intervals for the parameters involved.(v)Developed theory for estimating unknown drift parameter and diffusion parameter of the diffusion process with small diffusion and proved their consisitency and asymptotic normality.