Batch effects were evaluated by (1) comparing distributions of genetic principal components among sequencing centres, which are very similar between European American and African American individuals (Supplementary Figs. 3–5); (2) comparing alternative allele concordance between duplicates among centres, which is high (the largest difference being 4 × 10−4), and the patterns of between- versus within-centre differences, which indicate random errors rather than systematic centre differences (Supplementary Figs. 6–8); and (3) performing tests of association between variants and batches, which show a very small fraction of variants with genome-wide significance (0.004%, Supplementary Figs. 9, 10) (Supplementary Information 1.2). We conclude that batch effects appear to be minor, thus enabling multi-study association testing.