Recently, one of the most important problems in genetics is the identification of genes associated with complex diseases. A useful design for this proposal corresponds to collect data from extended families and SNPs platforms (Single Nucleotide polymorphism), that represent a high-dimensional sampling of the genome. For gene mapping, how to exploit SNP information in family-based data is still questionable and offers analytical challenges. We highlight the problem of multiple tests and the difficulty of identifying significant individual effect of SNP, since that, in general, this effect is low and does not contribute to the covariance among individuals.In order to select SNPs and to estimate their individual effects, the Polygenic Mixed Model has been used. However, a more efficient alternative strategy is to measure the simultaneous effect of ordered sets of SNPs (haplotype) rather than their individual effects. In this context, the theory associated with the Added Variable Plot (Hilden Minton, 1995) is relevant. This approach allows to split any fixed-effect into components associated with family structure (polygenic random-effect) and general population (residual random-effect). This theory has been investigated in Duarte (2011) considering that one SNP at a time is added to the Mixed Model under different scenarios of simulated data. This project will be carried out considering applications of this methodology to real database and extending the model to include interaction between SNPs (epistasis). Moreover, the proposed model will be extended to Multivariate Mixed Models in order to find genes that influence more than one phenotype simultaneously (pleiotropy).The motivation for this project is the statistical analysis of the data of the Project `` Baependi Heart Study " (FAPESP Process 2007/58150-7).
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