Single SNP Analysis

Genetic matching of controls

with the centenarian and control data, because a large proportion of NECS subjects were immigrants from Europe, and the patterns of immigration at the end of the 19th century may lead to an overrepresentation of some European ethnic groups [83]. In fact, an initial GWAS analysis in which we randomly selected controls from the Illumina repository pointed to substantial stratification (genomic control factor ,1.3). We therefore reduced possible confounding due to population stratification by selecting controls to match the genetic backgrounds of NECS subjects.

and traditional frequentist analyses of four different genetic models: general in which we analyzed the distribution of three genotypes; allelic in which we analyzed the distribution of alleles M versus m; recessive and dominant in which we grouped the genotypes in two groups, either MM/Mm versus mm (dominant for TOP strand allele), or MM versus Mm/mm (recessive for TOP strand allele) respectively. Note that M is the allele in the TOP strand and m is the allele in the BOTTOM strand based on Illumina genotype calling rules. We used a traditional x2 test of independence in a 263 contingency table to test general association, and the x2 test of independence in a 262 contingency table to test additive, dominant and recessive associations.

controls we ran a principal components analysis with the software EIGENSOFT [84], using GWAS SNP data for SNPs common to the NECS and Illumina datasets that had a SNP call rate.0.95 and MAF.0.05. SNPs in strong LD were removed using the program PLINK with a SNP window of 50 and sliding window of 5 SNPs and we removed 1 SNP from each pair of SNPs with r2.0.30 leaving 97,508 SNPs for this analysis. We found that the top several principal components (PCs) correlated to the genetic ancestry and formed a similar pattern to other studies of subjects of European ancestry [84,85]. However, the analysis also showed that the Illumina controls contain many more ethnic groups than the NECS (Figure S1), and the inclusion of these control subjects might therefore inflate false positive associations. We used the clustering algorithm in [65] to group individuals with similar ancestry into the same cluster. The algorithm utilizes k- means clustering to iteratively group individuals into cluster sizes varying from 2 to 30 and then computes a scoring index at each cluster size that accounts for the accuracy of the subjects’ cluster assignments, the stability of k-means clustering from iteration to iteration and the ability of the algorithm to maximize the distance between subjects allocated to different clusters. This analysis identified 20 clusters corresponding to sub-populations with different genetic structure, and Figure S1 shows the details of the clusters and their ethnic labels based on the known mother tongue and ancestry of the cluster members. NECS cases were present in only 16 of the 20 clusters as shown in Table 3 that displays the frequency of NECS cases (row 2), NECS controls (row 3) and Illumina controls (row 4). For example, no centenarians were allocated to cluster 1 or 15 (empty and full red dots in Figure S1 that may represent Franks and Celtics- Alpine ethnicities). To increase the number of controls, we randomly selected additional Illumina controls from those 16 clusters to maintain the same ratio of cases/controls in each cluster. For example, we sampled 4 additional Illumina controls from cluster 2, so that the ratio case/controls in cluster 2 was 21/ 24 = 0.88, and similarly, we sampled 19 additional controls from cluster 9, so that the ratio case/control in cluster 9 was 31/ 35 = 0.88 etc.

With the Bayesian analysis, we scored each SNP association by the Bayes Factor (BF) that can be interpreted as the posterior odds for the association when the null hypothesis of no association and the alternative hypothesis of an association have the same prior probability [86]. Specifically, let H0 and H1 denote the null hypothesis of no association between the SNP and the phenotype and the alternative hypothesis that there is an association between the SNP and the phenotype, and let p(H0) and p(H1) denote the prior probabilities of the two hypotheses. Then, by Bayes’ theorem, the posterior odds of the alternative hypothesis is computed as:

The quantities p(data|H0) and p(data|H1) are the ‘‘marginal likelihoods’’ of the data, given the two hypotheses H0 and H1, and are computed as the solutions to the two integrals

p(data

)~ p(datajh,H

)p(h

)dh ð p(data

)~ p(datajh,H

)p(h

)dh

The quantities p(datajh,H0) and p(datajh,H1) are the traditional likelihood functions under the null and alternative hypotheses, and p(hjH0),p(hjH1) are the prior distributions of the parameters of the two likelihood functions. These parameters are the conditional probabilities of the SNPs alleles in cases and controls and, in the paragraph below, we will provide details of the parameterizations. The ratio p(data|H1)/p(data|H0) is the BF, so that under the assumption that p(H0)= p(H1)= 0.5, the posterior odds equals the BF. The BF can be computed in closed form for all 4 models when appropriate parameterizations are used and missing genotypes are

Table 3. Distribution of NECS cases (row 2), NECS controls (row 3) and Illumina controls (row 4) in clusters of genetic ethnicity (columns).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Cent 0 21 34 79 27 189 6 0 31 102 22 20 3 94 0 15 94 34 0 25 Control 2 20 8 14 30 38 2 1 16 19 18 3 4 12 4 3 29 7 0 12 Illumina 90 310 192 47 278 168 223 104 277 288 200 120 173 132 169 54 266 154 118 250

The table shows the 20 clusters of genetic ethnicity that were discovered using a clustering algorithm described in reference [20]. Note that no centenarians allocated to cluster 1 or 15. These clusters are represented by full red dots in Figure S1 and denote Franks and Celtics- Alpine ethnicities. doi:10.1371/journal.pone.0029848.t003