@article {Hayeck046995, author = {Tristan Hayeck and Noah A. Zaitlen and Po-Ru Loh and Samuela Pollack and Alexander Gusev and Nick Patterson and Alkes L. Price}, title = {Mixed Model Association with Family-Biased Case-Control Ascertainment}, elocation-id = {046995}, year = {2016}, doi = {10.1101/046995}, publisher = {Cold Spring Harbor Laboratory}, abstract = {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 cases and controls 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 χ2 = 1.00), whereas Armitage Trend Test (ATT) and standard mixed model association (MLM) were mis-calibrated (e.g. average χ2 = 0.50-0.67 for MLM). LT-Fam also attained higher power in these simulations, with increases of up to 8\% vs. ATT and 3\% vs. MLM after correcting for mis-calibration. In 1,269 type 2 diabetes cases and 5,819 controls from the CARe cohort, downsampled to induce family-biased ascertainment, LT-Fam was correctly calibrated whereas ATT and MLM were again mis-calibrated (e.g. average χ2 = 0.60-0.82 for MLM). Our results highlight the importance of modeling family sampling bias in case-control data sets with related samples.}, URL = {https://www.biorxiv.org/content/early/2016/04/05/046995}, eprint = {https://www.biorxiv.org/content/early/2016/04/05/046995.full.pdf}, journal = {bioRxiv} }