Accurate estimation of heritability in genome wide studies using random effects models

Motivation: Random effects models have recently been introduced as an approach for analyzing genome wide association studies (GWASs), which allows estimation of overall heritability of traits without explicitly identifying the genetic loci responsible. Using this approach, Yang et al. (2010) have demonstrated that the heritability of height is much higher than the ~10% associated with identified genetic factors. However, Yang et al. (2010) relied on a heuristic for performing estimation in this model. Results: We adopt the model framework of Yang et al. (2010) and develop a method for maximum-likelihood (ML) estimation in this framework. Our method is based on Monte-Carlo expectationmaximization (MCEM; Wei et al., 1990), an expectation-maximization algorithm wherein a Markov chain Monte Carlo approach is used in the E-step. We demonstrate that this method leads to more stable and accurate heritability estimation compared to the approach of Yang et al. (2010), and it also allows us to find ML estimates of the portion of markers which are causal, indicating whether the heritability stems from a small number of powerful genetic factors or a large number of less powerful ones.