Grant: Discovery Grants Program - Individual

During the last two decades genetics has experienced a revolution that has generated many challenging mathematical and statistical problems. During this time, gene mapping has been one of the most active areas of research in human genetics. The technological advances in molecular biology and genetics have made it possible to gather very large amounts of data about the structure and regulation of genes, which has turned out to be very useful in the understanding of many simple genetic disorders. However, the genetic mapping of complex diseases is still bounded by methodological limitations. Censored phenotypes, such as age-at-onset (specially late-onset), survival, as well as the longitudinal traits  are considered to be complex quantitative traits and, as for most of the statistical modeling of major genes that affect quantitative variation, they can be framed in the context of a statistical analysis of mixtures and hidden models constrained by the Mendelian laws of inheritance. Current methods for age-at-onset traits use variations of the Cox's proportional hazards model with frailties. However, implicit in this approach is the assumption that all individuals are predisposed (in the sense that if they live long enough, they will get the disease) and what is really modeled are modifiers of susceptibility. In many situations this may not be a realistic model since an increased number of long-term survivors (thus an increased number of late-censored observations) could be taken as evidence that those censored individuals are more likely not predisposed. The main objective of the research outlined in the present proposal is to couple mixture modeling with event history data theory to address the inference about the contribution of predisposing genes and modifier genes in time-to-event traits. The statistical methods to be developed during the tenure of this proposal will be of utility for gene mapping as well as helping us to gain a better understanding of the role of population genetic processes in the modeling of complex traits with onset in adult life.