  Approaches for testing sets of variants, such as a set of rare or common
variants within a gene or pathway, for association with complex traits are
important. In particular, set tests allow for aggregation of weak signal within
a set, can capture interplay among variants, and reduce the burden of multiple
hypothesis testing. Until now, these approaches did not address confounding by
family relatedness and population structure, a problem that is becoming more
important as larger data sets are used to increase power.
  Results: We introduce a new approach for set tests that handles confounders.
Our model is based on the linear mixed model and uses two random effects-one to
capture the set association signal and one to capture confounders. We also
introduce a computational speedup for two-random-effects models that makes this
approach feasible even for extremely large cohorts. Using this model with both
the likelihood ratio test and score test, we find that the former yields more
power while controlling type I error. Application of our approach to richly
structured GAW14 data demonstrates that our method successfully corrects for
population structure and family relatedness, while application of our method to
a 15,000 individual Crohn's disease case-control cohort demonstrates that it
additionally recovers genes not recoverable by univariate analysis.
  Availability: A Python-based library implementing our approach is available
at http://mscompbio.codeplex.com
