Fast and powerful heritability inference for family-based neuroimaging studies

Heritability estimation has become an important tool for imaging genetics studies. The large number of voxel- and vertex-wise measurements in imaging genetics studies presents a challenge both in terms of computational intensity and the need to account for elevated false positive risk because of the multiple testing problem. There is a gap in existing tools, as standard neuroimaging software cannot estimate heritability, and yet standard quantitative genetics tools cannot provide essential neuroimaging inferences, like family-wise error corrected voxel-wise or cluster-wise P-values. Moreover, available heritability tools rely on P-values that can be inaccurate with usual parametric inference methods. In this work we develop fast estimation and inference procedures for voxel-wise heritability, drawing on recent methodological results that simplify heritability likelihood computations (Blangero et al., 2013). We review the family of score and Wald tests and propose novel inference methods based on explained sum of squares of an auxiliary linear model. To address problems with inaccuracies with the standard results used to find P-values, we propose four different permutation schemes to allow semi-parametric inference (parametric likelihood-based estimation, non-parametric sampling distribution). In total, we evaluate 5 different significance tests for heritability, with either asymptotic parametric or permutation-based P-value computations. We identify a number of tests that are both computationally efficient and powerful, making them ideal candidates for heritability studies in the massive data setting. We illustrate our method on fractional anisotropy measures in 859 subjects from the Genetics of Brain Structure study.