Mixed Model Association with Family-Biased Case-Control Ascertainment

Mixed models have become the tool of choice for genetic association studies; however, standard mixed model methods may be poorly calibrated or underpowered under family sampling bias and/or case-control ascertainment. Previously, we introduced a liability threshold-based mixed model association statistic (LTMLM) to address case-control ascertainment in unrelated samples. Here, we consider family-biased case-control ascertainment, where case and control subjects are ascertained non-randomly with respect to family relatedness. Previous work has shown that this type of ascertainment can severely bias heritability estimates; we show here that it also impacts mixed model association statistics. We introduce a family-based association statistic (LT-Fam) that is robust to this problem. Similar to LTMLM, LT-Fam is computed from posterior mean liabilities (PML) under a liability threshold model; however, LT-Fam uses published narrow-sense heritability estimates to avoid the problem of biased heritability estimation, enabling correct calibration. In simulations with family-biased case-control ascertainment, LT-Fam was correctly calibrated (average χ 2 = 1.00-1.02 for null SNPs), whereas the Armitage trend test (ATT), standard mixed model association (MLM), and case-control retrospective association test (CARAT) were mis-calibrated (e.g., average χ 2 = 0.50-1.22 for MLM, 0.89-2.65 for CARAT). LT-Fam also attained higher power than other methods in some settings. In 1,259 type 2 diabetes-affected case subjects and 5,765 control subjects from the CARe cohort, downsampled to induce family-biased ascertainment, LT-Fam was correctly calibrated whereas ATT, MLM, and CARAT were again mis-calibrated. Our results highlight the importance of modeling family sampling bias in case-control datasets with related samples.