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Linear mixed models for association analysis of quantitative traits with next‐generation sequencing data

We develop linear mixed models (LMMs) and functional linear mixed models (FLMMs) for gene‐based tests of association between a quantitative trait and genetic variants on pedigrees. The effects of a major gene are modeled as a fixed effect, the contributions of polygenes are modeled as a random effect, and the correlations of pedigree members are modeled via inbreeding/kinship coefficients. F ‐statistics and χ 2 likelihood ratio test (LRT) statistics based on the LMMs and FLMMs are constructed to test for association. We show empirically that the F ‐distributed statistics provide a good control of the type I error rate. The F ‐test statistics of the LMMs have similar or higher power than the FLMMs, kernel‐based famSKAT (family‐based sequence kernel association test), and burden test famBT (family‐based burden test). The F ‐statistics of the FLMMs perform well when analyzing a combination of rare and common variants. For small samples, the LRT statistics of the FLMMs control the type I error rate well at the nominal levels α = 0.01 and 0.05 . For moderate/large samples, the LRT statistics of the FLMMs control the type I error rates well. The LRT statistics of the LMMs can lead to inflated type I error rates. The proposed models are useful in whole genome and whole exome association studies of complex traits.