New Statistical Methods For Association Studies And Genomic Predictio

Extended Abstract "Selective genotyping" is a very famous concept in genetics. It was introduced by Lebowitz et al. (1987) and was studied more in details by Lander and Botstein (1989). It consists in genotyping (collecting DNA information at specific positions) only the individuals with extreme phenotypes. Indeed, Lebowitz et al. (1987) noticed that the highest or the lowest observations contain most of the signal on Quantitative Trait Loci (QTL), i.e. genes with quantitative effect on a trait. Today, although the genotyping costs have drastically dropped, selective genotyping is still heavily used (e.g. [1]) since we can optimize the statistical experiment by focusing on extreme individuals instead of "random" individuals. Although "selective genotyping" was introduced in the eighties, biologists are still missing tools to analyze properly data sampled from this experimental design. Indeed, classical methods such as penalized regression (e.g. Lasso [2]) are not dedicated to extreme observations. As a consequence, we introduced recently the SgenoLasso [3], a new L1 penalized regression that models explicitly the extremes. SgenoLasso on the ``Interval Mapping" a famous concept in genetics that consists in scanning the genome by testing the presence of a QTL at each location. From a statistical point of view, SgenoLasso is based on new limiting results on stochastic processes along the genome. SgenoLasso presents all the nice properties of Lasso since we have replaced the problem in a