Set-based variance component tests have been identified as a way to increase power in association studies by aggregating weak individual effects. However, the choice of test statistic has been largely ignored even though it may play an important role in obtaining optimal power. We compared a standard statistical test-a score test-with a recently developed likelihood ratio (LR) test. Further, when correction for hidden structure is needed, or gene-gene interactions are sought, state-of-the art algorithms for both the score and LR tests can be computationally impractical. Thus we develop new computationally efficient methods.