STATISTICAL METHODS FOR RARE AND COMMON VARIANT ASSOCIATION STUDIES

Complex human diseases are a major challenge for biological research. The goal of my research is to develop effective methods for biostatistics in order to create more opportunities for the prevention and cure of human diseases. This dissertation proposes statistical technologies that have the ability of being adapted to sequencing data in family-based designs, and that account for joint effects as well as gene-gene and gene-environment interactions in the GWA studies. The framework includes statistical methods for rare and common variant association studies. Although next-generation DNA sequencing technologies have made rare variant association studies feasible, the development of powerful statistical methods for rare variant association studies is still underway. Chapter 2 demonstrates two adaptive weighting methods for rare variant association studies based on family data for quantitative traits. The results show that both proposed methods are robust to population stratification, robust to the direction and magnitude of the effects of causal variants, and more powerful than the methods using weights suggested by Madsen and Browning [2009]. In Chapter 3, I extended the previously proposed test for Testing the effect of an Optimally Weighted combination of variants (TOW) [Sha et al., 2012] for unrelated individuals to TOW &ndash F, TOW for Family &ndash based design. Simulation results show that TOW &ndash F can control for population stratification in wide range of population structures including spatially structured populations, is robust to the directions of effect of causal variants, and is relatively robust to percentage of neutral variants. In GWA studies, this dissertation consists of a two &ndash locus joint effect analysis and a two-stage approach accounting for gene &ndash gene and gene &ndash environment interaction. Chapter 4 proposes a novel two &ndash stage approach, which is promising to identify joint effects, especially for monotonic models. The proposed approach outperforms a single &ndash marker method and a regular two &ndash stage analysis based on the two &ndash locus genotypic test. In Chapter 5, I proposed a gene &ndash based two &ndash stage approach to identify gene &ndash gene and gene &ndash environment interactions in GWA studies which can include rare variants. The two &ndash stage approach is applied to the GAW 17 dataset to identify the interaction between KDR gene and smoking status.

DEVELOPMENT OF A CONCEPTUAL MODEL AND PARAMETERIZATION OF A MATHEMATICAL MODEL FOR SEDIMENT PHOSPHORUS DIAGENESIS, SORPTION AND RELEASE FROM ONONDAGA LAKE SYRACUSE, NEW YORK

Eutrophication is a persistent problem in many fresh water lakes. Delay in lake recovery following reductions in external loading of phosphorus, the limiting nutrient in fresh water ecosystems, is often observed. Models have been created to assist with lake remediation efforts, however, the application of management tools to sediment diagenesis is often neglected due to conceptual and mathematical complexity. SED2K (Chapra et al. 2012) is proposed as a "middle way", offering engineering rigor while being accessible to users. An objective of this research is to further support the development and application SED2K for sediment phosphorus diagenesis and release to the water column of Onondaga Lake. Application of SED2K has been made to eutrophic Lake Alice in Minnesota. The more homogenous sediment characteristics of Lake Alice, compared with the industrially polluted sediment layers of Onondaga Lake, allowed for an invariant rate coefficient to be applied to describe first order decay kinetics of phosphorus. When a similar approach was attempted on Onondaga Lake an invariant rate coefficient failed to simulate the sediment phosphorus profile. Therefore, labile P was accounted for by progressive preservation after burial and a rate coefficient which gradual decreased with depth was applied. In this study, profile sediment samples were chemically extracted into five operationally-defined fractions: CaCO3-P, Fe/Al-P, Biogenic-P, Ca Mineral-P and Residual-P. Chemical fractionation data, from this study, showed that preservation is not the only mechanism by which phosphorus may be maintained in a non-reactive state in the profile. Sorption has been shown to contribute substantially to P burial within the profile. A new kinetic approach involving partitioning of P into process based fractions is applied here. Results from this approach indicate that labile P (Ca Mineral and Organic P) is contributing to internal P loading to Onondaga Lake, through diagenesis and diffusion to the water column, while the sorbed P fraction (Fe/Al-P and CaCO3-P) is remaining consistent. Sediment profile concentrations of labile and total phosphorus at time of deposition were also modeled and compared with current labile and total phosphorus, to quantify the extent to which remaining phosphorus which will continue to contribute to internal P loading and influence the trophic status of Onondaga Lake. Results presented here also allowed for estimation of the depth of the active sediment layer and the attendant response time as well as the sediment burden of labile P and associated efflux.