could be extended and/or improved to include for example different parametric models, or different types of cluster analyses to discover genetic signatures. We conducted extensive simulation studies to compare our approach to logistic regression that use the genetic data, or a summary of the genetic data in a genetic risk score. Our analyses show that when all SNPs have an additive effect, using a Bayesian classifier or a logistic regression model with a weighted genetic risk score perform equivalently. However, when the genetic effects include different models of inheritance, such as a combination of dominant/recessive/general associations, then a Bayesian classifier is more robust than logistic regression with a weighed genetic risk score. In either case, the approach we chose guarantees robustness as indicated in simulation studies (Clustering by genetics ancestry using genome-wide single nucleotide polymorphisms and incorporating genetic ancestry into genetic prediction models, Doctoral dissertation by Nadia Solovieff, May 2011, available upon request). Further- more, many other ‘‘machine-learning type’’ approaches exist that can be used to generate genetic risk models, and years of comparative evaluations in the machine learning community have shown that there is no clear winner, but different problems require different solutions [61]. In our search for genetic predictors of exceptional longevity, Bayesian classifiers appear to perform reasonably well and can be extended to more general directed graphical models to include interactions between SNPs and between genes and environmental factors [62]. Our approach for selecting predictive features appears to work well in this application. However other search procedures for feature selection need to be explored and may produce even better predictive accuracy.

For 17 of the 28 centenarians in cluster C26 who lack almost all the longevity associated variants discovered in this study, we had information about familial longevity. Twenty-five percent (n= 5) had .50% of siblings who survived past the age of 90 and some had evidence for longevity as shown in some pedigrees in Figure S18. This could indicate that such families have more private or rare variants not captured by either the genotyping or the model.

Discussion

Though living to very old age runs strongly in families, it is also a very complex phenomenon with many different patterns of survival that include disease-free survival but also survival with various age-related diseases. Given this complexity, it is extremely unlikely that a single or few genes confer this survival advantage, but rather it is likely that many genes are involved. To capture this genetic complexity we developed an approach that uses genetic risk modeling for in-silico genetics. Our approach includes 3 steps: 1) a single SNP analysis to identify and rank SNPs that are significantly associated with exceptional longevity, 2) genetic risk modeling based on nested Bayesian classifiers that produce genetic risk profiles and 3) cluster analysis of the profiles to discover genetic signatures and correlate these to different survival patterns or subphenotypes of exceptional longevity.

Limitations

Although we elected to work with na¨ıve Bayesian classifiers, many alternative approaches to genetic risk modeling exist and our method

Survival distributionsSurvival distributions1.00.80.60.40.20.Q9-—<       — Signature C1— Signature C295 700 105Age at death     — Signature C1——~ Signature C26Age at death  Survival distributions=o0.8 L0.60.40.2  — Signature R1—— Signature R20.095 400-405 410-~—«145~—~*120Survival distributions Age at death  — Signature R1— Signature R15   Age at death

Figure 9. Correlation of genetic signatures with lifespan. Panel A: Some genetic signatures are associated with significantly different life- span. For example the most predictive signature (C1) comprises centenarians with significant longer survival compared to centenarians with signatures C2 or C26. (p-value 0.01 and 0.02) More examples are in Figure S15. Panel B: The two most predictive genetic signatures and the least predictive signature in the centenarians of the merged replications sets show consistent results. The comparison between survival of centenarians with the most predictive signature R1 and the least predictive signature R15 reaches statistical significance, (p-value=0.003) while the comparison between survival distributions of centenarians with signatures R1 and R2 does not reach statistical significance (p-value 0.10). doi:10.1371/journal.pone.0029848.g009

There are aspects of our method that are based on heuristics. For example, our choice of the number of SNPs to be used in the genetic risk modeling is based on a heuristic rule. The choice of the optimal number of features to be used in a classifier is a well- known problem, with no simple solution [44] and to limit the effect of a sub-optimal selection we used an ensemble of classifiers to gain robustness. This approach is known to produce better classifiers than one single model [63]. Our heuristic search orders SNPs by maximum Bayes factor. Our secondary analyses show that random reordering of the 281 SNPs decreases the specificity slightly and selecting SNPs at random from the most significant 1700 SNPs gives models that are less predictive in independent sets (Figure S4 and S8). If other investigators apply this approach to other domains, they may want to conduct similar secondary