To test gene–gene interaction contributed by ADA (22G>A) and TNF-a ((cid:2)308G>A; (cid:2)238G>A) SNPs we applied the Generalized- Multifactor Dimensionality Reduction (GMDR) method (version 0.7) [29]. This method uses the same data-reduction strategy as the original MDR method [30], but score-based statistics using maximum-likelihood estimates is introduced to classify multifac- tor cells into two different groups [29]. Furthermore, the GMDR method, unlike the original MDR method [31], better handles data with unequal numbers of cases and controls, as occurs in our study. As in MDR, the best n-locus model is selected based on the highest training accuracy, and the maximum Balanced Testing Accuracy (TBA) and Cross Validation Consistency (CVC) are used to deter- mine the overall best epistasis model. TBA is calculated using the formula (sensitivity + specificity)/2 to yield an unbiased estimate for unbalanced case-control studies. Lastly, the v2 and sign tests determine whether the factors are significantly associated with the phenotype of interest. In particular, a significant v2 test reveals that the SNP or interaction between SNPs is associated with pheno- type tested, while a significant sign test suggests that the best

Table 1

ADA (rs73598374) and TNF-a (rs1800629; rs361525) genotype frequencies in age classes studied. Values showing significant differences are shown in bold.

Gene SNP Sex Genotypes Groups Comparison 1 Comparison 2 (age class 2 vs. age class 1) (age class 3 vs. age class 1 age class 2 age class 3 O.R. 95% C.I. P value O.R. 95% C.I. Males Males Males (<66 years, N = 144) (66–88 years, N = 261) (>88 years, N = 97) Females Females Females (<73 years, N = 191) (73–91 years, N = 285) (>91 years, N = 93) ADA 22G>A M A⁄+ 161 (11.1%) 511 (19.5%) 7 (7.2%) 1.943 1.063–3.551 0.320 0.036 G⁄/G⁄ 128 (88.9%) 210 (80.5%) 90 (92.8%) 0.515 0.282–0.941 3.122 F A⁄+ 431 (22.5%) 471 (16.5%) 14 (15.1%) 0.680 0.428–1.079 0.897 0.120 G⁄/G⁄ 148 (77.5%) 238 (83.5%) 79 (84.9%) 1.471 0.927–2.335 1.114 TNFa (cid:2)308G>A M A⁄+ 282 (19.4%) 523 (19.9%) 13 (13.4%) 1.031 0.618–1.721 0.622 1.000 G⁄/G⁄ 116 (80.6%) 209 (80.1%) 84 (86.6%) 0.970 0.581–1.620 1.608 F A⁄+ 312 (16.2%) 521 (18.3%) 14 (15.1%) 1.152 0.707–1.877 0.794 0.623 G⁄/G⁄ 160 (83.8%) 233 (81.7%) 79 (84.9%) 0.868 0.533–1.415 1.259 TNFa (cid:2)238G>A M A⁄+ 13 (9.0%) 371 (14.2%) 161 (16.5%) 1.665 0.854–3.245 1.196 0.156 G⁄/G⁄ 131 (91.0%) 224 (85.8%) 81 (83.5%) 0.601 0.308–1.171 0.836 F A⁄+ 311 (16.2%) 33 (11.6%) 121 (12.9%) 0.676 0.398–1.147 1.131 0.170 G⁄/G⁄ 160 (83.8%) 252 (88.4%) 81 (87.1%) 1.480 0.872–2.511 0.884

ADA age class 1: males vs. females: P = 0.0087 (Fisher’s exact test). O.R., odds ratio. Number in superscript refers to No. of minor allele homozygous genotype.

The haplotype association tests carried out on TNF-a promoter SNPs does not show any significant association with human-life expectancy (Table 2); considering age class 1, it is noteworthy that males show lower frequency of TNF-a (cid:2)308⁄G/(cid:2)238⁄A haplotype compared to females (4.5% vs. 8.2%, P = 0.082). Although LD analy- sis does not show any statistical significant D0 value, age classes 2 and 3 display higher D0 values compared to age classes 1, while r2 value is 0.00 in each age class (Table 2).

model with one or more SNPs is significantly better than the null model. Two-tail P values are reported. Bonferroni’s correction for multiple testing was not performed since we are assessing specific questions on genes previously tested for association with human longevity, and we are not searching for associations without a pri- ori hypotheses [32].

3. Results

3.2. Gene–gene interaction analysis

3.1. Association analyses

The genotype distributions of the three SNPs in the age classes are reported in Table 1. The genotype distributions are all in Hardy–Weinberg Equilibrium. Of the three SNPs studied, only the ADA 22G>A SNP is significantly associated with human life-expec- tancy in males (Table 1), considering each age class comparison (comparison 1, O.R. 1.943, P = 0.036; comparison 2, O.R. 0.320, P = 0.0056) or its genotype frequency distribution along the three age classes (v2 = 10.66, P = 0.0048). Logistic regression also con- firmed the results obtained through contingency tables (ADA males: comparison 1, b = (cid:2)0.637, P = 0.39; comparison 2, b = 1.145, P = 0.007). Of note, the frequency of ADA⁄22A carriers is significantly different between males and females in age class 1 (Males 11.1% vs. Females 22.5%, P = 0.0087).

Table 3 shows the results of GMDR analysis conducted on males and females separately considering the two comparison carried out between age classes. In comparison 1, a significant two-loci interaction occurs in females between ADA 22G>A and TNF-a (cid:2)238G>A SNPs, with a CVC of 10/10 and a TBA of 0.550 (Sign Test P = 0.011) (Table 3, Fig. 1). The odds ratio for this two-loci attribute constructed by GMDR is 1.584 (P = 0.022), while ADA 22G>A single locus attribute association does not reach statistical significance (O.R. = 1.471, P = 0.100). The three GMDR models obtained on males show a borderline non-signifi- cant gene–gene interaction (each model, Sign Test P = 0.055), although the derived attributes result significantly associated with enhanced life-expectancy (Table 3). Interestingly, as shown

Table 2

TNF-a (rs1800629; rs361525) haplotype frequencies along the three age classes.