In previous studies Type 1 diabetes (T1D) has demonstrated a strong association with the HLA region of chromosome 6 [36]. To illustrate our method we consider joint analysis of 19 T1D trios with just over 2000 independent controls. All family and control samples are of European ancestry; for details about the data see Luca et al. [17]. First, we estimated the ancestry of the controls and plotted them against their two most significant axes of genetic variation using SpectralGEM. We then projected the 19 trio probands onto the control's eigenmap using the Nystrom approximation (Supplementary Figure 6). The fullmatch algorithm identified 19 distinct strata, each including exactly one trio proband, and between 19 and 359 controls. We call these unbalanced strata ‘all controls’, to indicate that we matched the full sample of controls. For our analysis we also chose the closest m controls to each case, where m = 5 and 10. For SNPs in the HLA region, we evaluated mCLRs success at detecting association with T1D. From our results it is apparent that as m increases our power to
