Since genome-wide linkage analyses have only been modestly successful in identifying regions that may harbor disease susceptibility genes due to the complex etiology of the disease. To identify the genes for complex traits requires the study of many genes and their interactions. In most Genome wide Association studies, genotyped individuals are usually much less than the number of markers. Thus some systematic statistical approach should be developed to analyze such high dimension data. Based on these concerns, there are many interesting questions cause researcher’s interests. Statistical strategies to

address some of these questions are presented in this dissertation. The main idea in this dissertation is that we combine the merit of allele sharing method to detect linkage at one region and that of liquid association to take the likely interactions from the rest of genome into account. We applied this approach to different datasets and interpret the results in terms of the biology point of view as well as different statistical strategies.