Quality control

After genotype calling, in order to check errors at genotypic level, the datasets were subjected to a bat- tery of quality control (QC) tests. In particular, SNPs were excluded if they had (1) a significant deviation

reduction (MB-MDR) method recently developed by Calle et al. (2010). It is an extension of the popular multifactor dimensionality reduction (MDR) method in which risk categories are defined using a regression model that also allows adjustments for main effects and covariates. By this approach, first, logistic regres- sions analyses are performed to define the nine possible genotypic combinations as high (H), low (L), or no risk (0). Then, these multilocus genotypes of the same risk category are merged and two Wald statistics (WH and WL, one for each risk) with the relevant p values (PH and PL) are obtained. The significance for the epistatic effect is based on the minimum between PH and PL (MIN.P). Finally, the significance of a specified model is assessed through a permutation test on the maximum Wald statistic, imple- mented in the function mbmdr.PermTest of MB-MDR package.

Statistical analyses

Single SNP analysis

In both stages, the chi-square test was used to assess the association between the variability of the analyzed polymorphisms and human longevity. Before to apply the test, each genotypic variable was first coded with respect to dominant, recessive, and heterozygote disad- vantage/advantage model. For each of these models, the corresponding chi-square value was then obtained. The maximum of these three chi-square values ðc2 Þ was MAX used as a measure of association between the polymor- phism and the analyzed phenotype:

In the present study we applied the MB-MDR algo- rithm to the stage 2 dataset. The permutation procedure (10,000 permutations) was applied to the interaction models with a MIN.P<0.05.

where and represent the three chi- DOM REC HET square statistics assuming a dominant, recessive and an heterozygote disadvantage/advantage model of inheri- tance of the analyzed polymorphism. The p value of the proposed test statistics was obtained by the Monte-Carlo procedure described in Ziegler and König (2010). The procedure of ranking the SNPs not according to a single p value but to the minimum of different test statistics allows to obtain more robust results, as reported in Zheng et al. (2007).

Results

Dataset stage

Initially, 317 SNPs from 104 candidate genes (see Supplementary Table S1) were genotyped in 78 cases and 71 controls. After the QC phase, the final number of analyzed polymorphisms in stage 1 was 235. In particular, 49 SNPs were excluded from the analysis because of a significant deviation from HWE. Thirty SNPs were excluded from the analysis because of a MiF value higher than 20 %. Finally, three SNPs were excluded on the basis of MAF criterion (<1 %). The cleaned dataset was then analyzed for association with longevity by using the c2 test.

In the present study, the test (maximum of MAX three different chi-square tests) was used to assess the 0 associations between the selected markers (M 317) and the analyzed phenotype. In the stage 1 the c2 values MAX π were ranked, and a proportion equal to 0.1 (top markers 10 %) of the initial set of SNPs corresponding approx- imately to a p value <0.15 was selected for stage 2 analysis. By following the standard strategy to consider the stage 2 data as a replication study, the same test was used to assess the association between the selected polymorphism and longevity, adopting the Bonferroni- α π corrected significance level /( ·M). markers

Single-locus analysis

The plot reported in Fig. 1 displays the p values com- puted on the basis of the c2 test with respect to the MAX analyzed polymorphisms. Supplementary Table S2 π 0 reports the list of the top-ranked SNPs ( 0.1) markers obtained according to the association results and corresponding approximately to a p value <0.15.

In order to capture second-order SNP SNP interactions, we used the model-based multifactor dimensionality

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showed an increased chance to attain longevity; for the SNP rs2111699 located in GSTZ1 gene, the subjects carrying two copies of the G allele showed an increased chance to survive at very old age.

Dataset stage 2

The 31 selected SNPs were genotyped in the additional 288 cases and 554 controls in the subsequent stage 2. Two SNPs were excluded from the following associa- tion analysis because of a MiF value higher than 20 %. The cleaned dataset was then analyzed for association with longevity by using the c2 test. Table 1 reports MAX the SNPs which we found to have a significant effect on the phenotype in the c2 test with the most likely best MAX model. The complete list of the results obtained for the 29 SNPs of stage 2 is reported in Supplementary ’ Table S3. After the Bonferroni s correction (p value threshold <0.05/29), two of the observed associations remained statistically significant: rs282070 (p value equal to 1.1×10−3) and rs2111699 (p value equal to 1.4×10−3). In particular, for the SNP rs282070, located in MAP3K7 gene, the subjects carrying the C allele

Interaction analysis

Supplementary Table S4 reports the significant second- order interactions results (p<0.05) in the stage 2 dataset from the MB-MDR analysis. In this table for each inter- action model, a permutation testing was performed for each of the top-ranked models (MIN.P<0.05) by permut- ing the outcome variable calling the mbmdr.PermTest function of the mbmdr package (10,000 permutations). By this approach, we found that all these interactions resulted to be significant (p≤ 0.05). However, after a Bonferroni’ s correction for multiple testing no significant differences remained.

Table 1 Significant SNPs obtained according to test in the stage 2 sample MAX