Genetic markers with rare variants are spread out in the genome, making it necessary and difficult to consider them in genetic association studies. Consequently, wisely combining rare variants into "composite" markers may facilitate meaningful analyses. In this paper, we propose a novel approach of analyzing rare variant data by incorporating the least absolute shrinkage and selection operator technique. We applied this method to the Genetic Analysis Workshop 17 data, and our results suggest that this new approach is promising. In addition, we took advantage of having 200 phenotype replications and assessed the performance of our approach by means of repeated classification tree analyses. Our method and analyses were performed without knowledge of the underlying simulating model. Our method identified 38 markers (in 65 genes) that are significantly associated with the phenotype Affected and correctly identified two causal genes, SIRT1 and PDGFD.