The existence of disparities among communities of diverse racial and economic backgrounds has received considerable attention in last two decades or so. Scholars, bureaucrats, legislators, governing bodies, and numerous other constituents share a sustained concern about the persistent trend of disparity across diverse communities. Today, there is an increasing demand for quantitative tools to analyze such disparity information from high-throughput sources. Simple descriptive statistics that relate to socio-economic, socio-demographic, and socio-health deprivation measures often can mask the important features while analyzing such data. Thus, the exploration of disparity can be better understood by developing sophisticated statistical tools that can extract the salient features from complex data sources. This project will explore innovative multilevel modeling techniques to develop measures that are scientifically more efficient and meaningful for these purposes. Specifically, the research will develop new small area estimation models and estimation techniques that encompass mean-variance relationship, distributional robustness, and multiple comparisons using hierarchical and nonparametric Bayesian approaches. Furthermore, some estimating equation approaches will be developed to study the association between socio-demographic and socio-economic variables with cancer incidence, linked via multilevel generalized linear models. The methods potentially are suitable for analyzing high-dimensional and sparse data.
The statistical development will enrich small area estimation technique in various dimensions. The Dirichlet process-based robust modeling will advance the research on clustering in the context of analyzing socio-economic data. The multiple comparison procedures will enhance the simultaneous inference literature in the context of hierarchical modeling. The methods also will have implications in other areas of research such as education, epidemiology, and genetics. In addition, the project will contribute towards research-based training of graduate students and foster interdisciplinary collaboration.
Small area estimation technique is found to be effective in socal and economic sciences and in social epidemiology. The broder statistical theme of small area estimation is developing shrinkage estimation using random effects models. This project advances the small area estimation research in (i) Confidence interval and mean squared prediction error estimation by jointly shrinking means and variances (ii) Cluetering based shrinkage estimation for large data and semiparameteric approach of curve clustering. The applications are specific to Iowa county crop data, Michigan scholl district MEAP data, and cancer incidence for all 50 states of U.S. The small area estimation is effective when sample sizes are relatively small, however several areas are connected in some sense. The typical models concentrate in "borrowing strength" at the mean level. This project considers "borrowing strength" at the variance level as well. This addition made the models no longer a special case of mixed linear model or general exponential family of distribution. This requires non trivial mathematical development for theiretical validity of the proposed approaches. Through extensive simulations, the research establishes its superiority over existing procedures. Beyond the small area estimation, the implicit statistical procedures were extended to cluster the U.S. states in terms of their cancer incidence trajectories. Specifically a Dirichlet process based clustering approach has been developed to find the change points and do the clustering accordingly. The sgrinkage estimation developed in this project has wide range of implicit applications in genetics, education, business, epidemiology and mobile sensor networks. Some variotions were specifically transformated in engineering and business researchers. Several graduate students from various disciplines were trained through this research activities. The general theme has been disseminated nationally and internationally in disciplinary as weel as in inter-disciplinary audiences.
