The BrCa and T2D studies have been described elsewhere (Hunter et al. 2007; Qi et al. 2010). Both studies were restricted to women of European ancestry. Genotyping in the BrCa study was done on the Illumina HumanHap550 chip, while the T2D study was genotyped on the Affymetrix Genome-Wide Human 6.0 array. We imputed missing genotypes separately within each study using MaCH 1.0, which relies on Markov chain haplotyping (http://www.sph.umich.edu/csg/yli/mach/index.html) (Li et al. 2009, 2010). We present results from imputation done separately in the two studies; when the two control groups were pooled first and then the imputation was done, results were similar. The imputations used HapMap Release 22 (NCBI build 36) as a reference panel. For each unmeasured SNP, we considered both a soft call, or dosage, imputation, which gives the expected number of rare alleles given the other SNPs available for that individual and takes values on a continuum between 0 and 2, and a hard call imputation, which gives the best integral guess for the number of rare alleles, either 0, 1, or 2. We had available 1,038
