The Hybrid Rat Diversity Panel (HRDP) is a stable and well-characterized set of more than 90 inbred rat strains that can be leveraged for systems genetics approaches to understanding the genetic and genomic variation associated with complex disease. The HRDP exhibits substantial between-strain diversity while retaining substantial within-strain isogenicity, allowing for the precise mapping of genetic variation associated with complex phenotypes and providing statistical power to identify associated variants. In order to robustly identify associated genetic variants, it is important to account for the population structure induced by inbreeding. To this end, we investigate the performance of four plausible approaches towards modeling quantitative traits in the HRDP and quantify their operating characteristics. In particular, we investigate three approaches based on genome-wide mixed model analysis, and one approach based on ordinary least squares linear regression. Towards facilitating study planning and design, we conduct extensive simulations to investigate the power of genetic association analyses in the HRDP, and characterize the impressive attained power. In simulation of eQTL data in the HRDP, we find that a mixed model approach that leverages leave-one-chromosome-out kinship estimation attains the highest power while controlling type I error.