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Motivated by genome-wide association studies, we consider a standard linearmodel with one additional random effect in situations where many predictorshave been collected on the same subjects and each predictor is analyzedseparately. Three novel contributions are (1) a transformation between thelinear and log-odds scales which is accurate for the important genetic case ofsmall effect sizes; (2) a likelihood-maximization algorithm that is an order ofmagnitude faster than the previously published approaches; and (3) efficientmethods for computing marginal likelihoods which allow Bayesian modelcomparison. The methodology has been successfully applied to a large-scaleassociation study of multiple sclerosis including over 20,000 individuals and500,000 genetic variants.

Efficient computation with a linear mixed model on large-scale data sets with applications to genetic studies