Our analysis provides further insight about the role of APOE in survival to extreme ages. Although the SNP rs2075650 in TOMM40/APOE is the most significantly association with excep- tional longevity, the value of this SNP to identify who can live to 100 and older appears to be limited. The traces of sensitivity and specificity of the nested genetic models in Figure 4B show that the model with only this SNP has 85% sensitivity to predict exceptional longevity but only 26% specificity in the discovery set. We conducted an ROC analysis to show the poor predictive value of this SNP alone (Figure S19, AUC=0.62). Also, sensitivity and specificity of the model with only this SNP are 85%/26% in the ELIXIR set, and 82%/23% in the second replication set. The traces of sensitivity/ specificity of the models with increasing number of SNPs show that, the predictive accuracy increases only when a substantial number of variants are added to the model that includes rs2075650 (Figure 4B). We also examined the changes in sensitivity/specificity when we removed this SNP from the list of 281, and dropping rs2075650 resulted in a loss of approximately 1% accuracy (88% sensitivity/specificity in the discovery set (AUC=0.95); 55% sensitivity and 58% specificity in the ELIX set (AUC=0.56); and 75% sensitivity and 60% specificity in the additional 60 centenarians and 2863 Illumina controls (AUC=0.73)) These results are summarized in Figure S7. This SNP is only in weak linkage disequilibrium with the two SNPs that define the 3 alleles of APOE but its association with longevity was shown to be dependent on the APOE alleles in [66]. The reason for the low predictive value of rs2075650 alone is that the GG genotype of this SNP is rare in the population (genotype frequency 3%) but virtually absent in centenarians (genotype frequency 0.1%), therefore if someone is a carrier of the GG allele it is unlikely that he will become a centenarian, while predicting the outcome in carriers of the AA or AG genotypes is more difficult without additional genetic data.

Our analysis provides further insight about the role of APOE in survival to extreme ages. Although the SNP rs2075650 in TOMM40/APOE is the most significantly association with excep- tional longevity, the value of this SNP to identify who can live to 100 and older appears to be limited. The traces of sensitivity and specificity of the nested genetic models in Figure 4B show that the model with only this SNP has 85% sensitivity to predict exceptional longevity but only 26% specificity in the discovery set. We conducted an ROC analysis to show the poor predictive value of this SNP alone

While large numbers of longevity associated variants appear to be necessary for extreme survival, we did not observe a substantial difference in the numbers of a large sample of known disease- associated variants carried by centenarians and controls (Figure 10, Table S3). The Leiden Longevity and Leiden 85+ Studies recently produced similar findings for alleles associated with specific age-related diseases amongst 85+ year olds and nonagenarians [69]. Furthermore, only 13 SNPs previously associated with common diseases in genome wide association studies reach statistical significance in the discovery set, and the risk alleles are significantly less frequent in centenarians than in controls (Table S4) [70,71,72,73,74,75].

These preliminary data suggest that exceptional longevity may be the result of an enrichment of longevity associated variants that counter the effect of disease-risk alleles and contribute to the compression of morbidity and/or disability towards the end of very long lives [43].

In our analysis we also found that specific signatures correlated with the prevalence and age of onset of some age-related diseases

and further investigation is needed to understand how and why they predispose for exceptional longevity and for specific, different patterns of aging. The genetic signatures were built by using an ensemble of genetic risk models. The high sensitivity of these predictions in independent samples of centenarians shows that genetic data can indeed predict exceptional longevity without knowledge of any other risk factors. The high sensitivity is consistent with (1) theoretical results that show potentially high predictability of rare and highly heritable traits even when only 50% of the genetic variants that determine the trait are found [36] and (2) the accuracy of genetic risk models that have been developed to predict complex and highly heritable traits [37,38,39,40,41]. To quantify the amount of genetic variance in liability to exceptional longevity that is explained by our model, we used the online calculator http://gump.qimr.edu.au/genroc/ to translate the predictive accuracy measured by the AUC in proportion of explained genetic variance on the liability scale [36]. Based on previous reports and the latest US 2010 Census (http://www.census.gov/prod/cen2010/briefs/c2010br-03.pdf), we estimated that the prevalence of exceptional longevity (living to 100+) is 1 in every 5,000 people, while the sibling relative risk for exceptional longevity ranges between 8 and 17 [9,10]. With these numbers, we estimated that the maximum AUC of a genetic model of exceptional longevity ranges between 0.95 to 0.98 and our genetic model that reaches AUC=0.74 in the second replication set (Figure S7) explains between 12% to 17% of the genetic variance on the liability scale. In the ELIXIR replication set, the AUC of our genetic risk model is 0.58 and this would represent 1–2% of explained genetic variance. Since the ELIXIR set includes more nonagenarians than centenarians, and their prevalence in the population is 0.5% and the sibling relative risk of this trait is approximately 2.5, we repeated the calculations in this scenario and the 0.58 AUC translated into approximately 4% of the genetic variance in the liability scale. These results show that although we