A Family‐Based Joint Test for Mean and Variance Heterogeneity for Quantitative Traits

Traditional quantitative trait locus (QTL) analysis focuses on identifying loci associated with mean heterogeneity. Recent research has discovered loci associated with phenotype variance heterogeneity (vQTL), which is important in studying genetic association with complex traits, especially for identifying gene–gene and gene–environment interactions. While several tests have been proposed to detect vQTL for unrelated individuals, there are no tests for related individuals, commonly seen in family‐based genetic studies. Here we introduce a likelihood ratio test (LRT) for identifying mean and variance heterogeneity simultaneously or for either effect alone, adjusting for covariates and family relatedness using a linear mixed effect model approach. The LRT test statistic for normally distributed quantitative traits approximately follows χ²‐distributions. To correct for inflated Type I error for non‐normally distributed quantitative traits, we propose a parametric bootstrap‐based LRT that removes the best linear unbiased prediction (BLUP) of family random effect. Simulation studies show that our family‐based test controls Type I error and has good power, while Type I error inflation is observed when family relatedness is ignored. We demonstrate the utility and efficiency gains of the proposed method using data from the Framingham Heart Study to detect loci associated with body mass index (BMI) variability.