Weperformedassociationtestsinallfivesamplesandcombinedthesam- ples in a meta-analysis using R (R Development Core Team 2011). We per- formed all SNP and haplotype association tests as Cochran–Armitage tests (Cochran,1954;Armitage,1955)foralineartrendbetweenthenumberof copies of a reference allele (0, 1, or 2) and the likelihood that an individual belongstothecaseorcontrolgroup.WefirsttestedeachSNPorhaplotype for association with centenarian status. We computed meta-analysis statistics for all followed-up SNPs and haplotypes as the weighted sum of z-statistics from the trend tests. The weights for sample i were defined as qffiffiffi 5 n P

For theStage1sample,wealsogenotypedAIMsfrom apublishedpanel specific to European genetic substructure (Tian et al., 2008); genotyping and quality control are described in Supporting Information. We used R to compute principal components and to identify the most important principal components via a Tracy–Widom test (Patterson et al., 2006). To perform an analysis adjusted for population stratification, we included the topprincipalcomponents as covariatesintheoriginalanalysis.

Principal components based on genotypes from the 370K Illumina SNP chip (collected as part of a separate study – Sebastiani et al., 2012) were available for a subset of the NECS sample. We used EIGENSTRAT (Price et al., 2006) to compute the principal components and identified the principal components that were most informative based on visual inspection of a scree plot. To perform an analysis adjusted for population stratification, we included the top principal components as covariates in the original analysis.

To account for the testing of multiple correlated SNPs and haplotypes in Stage 1, we performed permutation tests by (i) randomly permuting case–control status and (ii) recomputing the test statistics for all SNPs and haplotypes. Based on 10 000 permutations, we then computed adjusted P-values that reflected the probability of observing each result by chance alone. To establish whether our most extreme P-value was significantly different than what would be expected if no true association existed, we computed an empirical P-value as the proportion of permutations in which a more extreme result was observed in any of the SNPs or haplo- types analyzed. To establish whether a significant excess of haplotypes with P < a was observed for a given a-level, we computed empirical P-values as the proportion of permutations in which we observed as many haplotypes with P < a as in our original data.

Acknowledgments

This work has been supported by the intramural program of the National Human Genome Research Institute and by grants from Glenn Award for Research in Biological Mechanisms of Aging (N.B.), the NIH PO1 AG027734 (N.B.), the NIH⁄NIA Longevity Consortium U19 AG023122 (G.A., T.P), the NIH⁄NIA R56 AG027216 (C.B.), and NIH⁄NHLBI R01 HL87681-01 (N.S.). We thank Drs. Gilles Thomas,

To account for multiple testing in the two-stage analysis, we performed permutation tests in R to obtain an empirical P-value for the best observed

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