Figure 2. Distribution of age of last contact or age at death of centenarians included in the study. NECS: centenarians of the discovery set, ELIX: nonagenarians and centenarians from the ELIX replication set, NECS 2: additional NECS replication set of 60 centenarians. The y-axis reports the density, and the x-axis reports the age, in group of 2 years. The frequency of subjects with ages between x and x+2 is 2*density*(sample size). doi:10.1371/journal.pone.0029848.g002

when the null hypothesis of no association and the alternative hypothesis of an association have the same prior probability [24], and then we used the maximum BF (MBF) as a measure of statistical significance. Figure S2 shows the error rate of decision rules based on several thresholds for MBF. The matching strategy appeared to remove confounding by stratification because we did not observe any inflation of associations and the genomic control factor in allelic association was 0.99 (Figure S3). We also conducted additional analyses described below to investigate whether residual confounding by population stratification could bias the results and found no evidence of bias.

significant associations and all SNPs were independent (Figure S2). The clusters of associations in chromosomes 8, 9 and 21 in Figure 3 point to interesting regions, although they fail to reach genome wide significance. Several authors have argued that SNPs that do not reach genome wide significance may be biologically important by virtue of their joint effect [33,34,35,36], and have successfully built risk models that can predict genetic susceptibility to several complex traits that are highly heritable [37,38,39,40,41]. We similarly explored the hypothesis that different sets of SNPs that are associated with exceptional longevity, although with moderate effects, may jointly characterize the genetic predisposi- tion to exceptional longevity [42,43] and therefore provide a model for in silico analysis that can suggest targets and genetic paths to exceptional longevity.

The Manhattan plot (Figure 3) displays the log10(MBF) for each tested SNP. This analysis identified a single SNP in APOE/ TOMM40 as irrefutably genome-wide significant (P,10e-8, Table 1). The association was replicated in the ELIX set, and was maintained when we used 867 referent subjects included in a GWAS of Parkinson’s disease as alternative controls (Table 1).

we had to make several decisions about the class of models to work with, how to determine the number of SNPs to be included in the model, and the overall search strategy. We chose to compute the genetic risk associated with a set of SNPs using a simple but effective Bayesian classification model, also known as the na¨ıve Bayes classifier (Figure 4A) [44]. This approach –also used in [39] to accurately predict the susceptibility to carotid atherosclerosis – classifies a subject as predisposed to exceptional longevity if the posterior probability of exceptional longevity, given genotypes of a set of SNPs, exceeds the posterior probability of average longevity (Figure 4A). The advantage of this method is that there is virtually no upper limit to the number of SNPs that can be used for classification, and it can be used for risk prediction even if the data used for the analysis are from a case control study. We designed a forward search procedure to discover a sufficient number of predictive SNPs (Figure 4A). The procedure builds a series of

The apolipoprotein E (APOE) is associated with human [25,26,27]. SNP rs2075650 occurs in an intron of TOMM40 but is a strong proxy of the SNPs that define the APOE alleles This SNP has been associated with Alzheimer’s disease [29,30] and lipid levels [31,32].

Genetic Risk Modeling

In the single SNP analysis, we observed a substantial enrichment for significant associations which do not meet the stringent threshold for genome wide significance. For example, 112 SNPs were associated with exceptional longevity with log10(MBF).2 against an estimated error rate of 4 in 100,000 independent tests and hence 8–10 false positive associations expected by chance in ,250,000 tested SNPs if there were no

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Figure 3. The Manhattan plot displays the maximum log10(Bayes Factor) (y-axis) for each of the analyzed SNPs in the discovery set. The Manhattan plot displays the maximum log10(Bayes Factor) (y-axis) for each of the analyzed SNPs in the discovery set. The SNPs are ordered by chromosome (alternate color bands) and, within chromosome, by physical position (x-axis). We tested the association of each SNP with exceptional longevity using general, allelic, dominant and recessive models and the y-axis reports the maximum log10(Bayes factor) observed for each SNP. The SNP rs2075650 in APOE/TOMM40 reached irrefutable genome wide significance (log10(MBF)=7.9 and p-value,e-10). Figure S3 shows the Manhattan plot and QQ plot for the additive model using logistic regression. doi:10.1371/journal.pone.0029848.g003