Interpretation of genetic risk profiles.

genetic risk profiles for each subject by plotting the posterior probability of EL (p(EL|S ), y axis) against the number of SNPs in k each of 281 SNP sets (x-axis). The trend of the profiles informs about the enrichment of longevity associated variants (LAV)s because the posterior probability of exceptional longevity in a subject, given the SNP set S is greater than that given the SNP k+1 set S if the subjects carries a genotype of the (k+1)th SNP that is k more common in centenarians rather than controls. In fact

Correlation of genetic signatures with aging sub- phenotypes. Difference in survival was tested using log-rank tests implemented in the survival package of R. Only subjects with events or alive without events were included in the analysis.

ethnicity. We tested the association between the genetic signatures in centenarians and the genetic structure determined with the cluster algorithm of the principal components. When we correlate the 26 clusters of genetic signatures to the clusters of different population structures, we did not find any association (the p-value from x2 was 0.3).

p(EL)Pk p(SNP jEL)zp(AL)Pk p(SNP jAL) i~1 i i~1 i

And the inequality is equivalent to

validate the genotyping of the SNPs included in the model, 30 SNPs (.10% of the SNPs in the model) were selected to re- genotype using the TaqMan platform (Applied Biosystems, Carlsbad, CA). This genotyping was performed at Yale University. The samples included 688 centenarians and 221 controls from the NECS that were included in the discovery set and for whom we had available DNA. For each sample, 2.5 ng of DNA was arrayed into 384-well plates and was dried prior to TaqMan genotyping. Thermal cycling was performed using either a BioRad C1000 or S1000 (BioRad, Hercules, CA) and plate reads were done using the CFX Optical Reaction Module (BioRad, Hercules, CA). Genotype calls were made using the BioRad CFX Manager Software for Allelic Discrimination (BioRad, Hercules, CA). Of the 30 SNPs attempted, 28 SNPs were successfully genotyped; one zSNP, rs4802234, did not yield data that could be clustered using the allelic discrimination software for one of the three 384-well plates, and one SNP, rs12629971, had a lower call rate (93%). All TaqMan genotyping was performed blind to the microarray genotypes as the Yale group did not have access to the microarray genotypes.

This can be written as

p(SNP p(EL)Pk i~1 p(SNP ijEL)zp(AL)Pk i~1 p(SNP p(SNP kz1jEL)|p(EL)Pk i~1 p(SNP ijEL)zp(SNP kz1jAL)p(AL)Pk i~1 p(SNP ijAL)

Note that this property is independent of the SNPs in the current SNP set, so changing the order of the nested model may change the overall pattern of the risk profile but not the interpretation in terms of enrichment of longevity associated variants.

Ensemble of genetic risk models. The ensemble of genetic risk models uses 281 nested SNP sets to compute the risk for EL and AL (average longevity), and the overall risk is estimated as the average of all genetic risks:

There were 34 duplicate samples genotyped using TaqMan across the 28 SNPs generating a total of 952 duplicate genotypes, 950 of which had both samples called. Of these 950 duplicate genotypes, 100% of the genotypes were concordant. For the 28 SNPs successfully genotyped, we observed between 1 and 10

discordant genotypes per SNP between the TaqMan genotype and the microarray genotype, yielding concordance rates between 98.88 and 99.89% between genotyping platforms. Our overall discordance rate across all SNPs was ,1%.

and accuracy was .85% was 281. Panel B) displays the specificity for the two types of controls in the discovery set (NECS referent subjects: continuous line; Illumina controls: dashed lines) and shows that there is no difference between the two control sets.

referent subjects: continuous line; Illumina controls: dashed lines) and shows that there is no difference between the two control sets. Panel C) describes the effect of re-ordering the 281 SNPs. Patterns of sensitivity and specificity using the discovery set (left), and randomly generated validation sets (right) when the top 281 SNPs were randomly entered into the nested models (continuous lines: SNPs are ordered by MBF; dashed lines: the same 281 SNPs are randomly arranged). Panel D) describes the effect of random selection on sensitivity and specificity of the nested models. Patterns of sensitivity and specificity using the discovery set (left), and randomly generated validation sets (right) when 281 SNPs were randomly chosen from the top 1,700 most significant SNPs. (continuous lines: SNPs are ordered by MBF; dashed lines: 281 SNPs are randomly selected from the 1700 most significant). The analysis shows that changing the order affects sensitivity and specificity of the model. Furthermore, selecting SNPs at random from the top most significant SNPs gives models that are consistently less specific and less sensitive.

This low rate of discordant genotypes did not affect the results: 23 of the 28 SNPs reached statistical significance in the replicated data, and although 5 SNPs did not reach statistical significance possibly because of the small sample of controls, the allele frequencies from the microarray data and TaqMan data are virtually indistinguishable (Figure S5), suggesting that a 1% genotyping error rate should have no impact on this analysis.

Supporting Information

S1 Population structure of centenarians and