decade of life. Since the distribution of survival times was clearly right skewed (data not shown), a cut-off with respect to time of death was made at December 31st 2000, when approximately half of the males and one third of the females in the cohort had died. Consequently, the early/late death variable was defined as: early=death occurred between 1998 (date at intake) and December 31st 2000 (i.e. individ- uals living to maximum age 95) and late=death occurred after January 1st 2001 (i.e. individuals surviving to age 95+). As the sec- ond variable, we used the number-of-days-lived defined as the exact number of days lived from date of intake in 1998 to either death or the imputed date (the latter is described in Section 2.1.1). For this variable, the assumptions of normal distribution and equal variance were tested in the STATA 11.1 statistical program (Stata Cor- poration, College Station, TX, USA) by Shapiro–Wilk and Breusch– Pagan/Cook–Weisberg tests. Since the variable did not show normal distribution, it was transformed to the square root for a better fit. As- sociation analysis was performed by two-tailed linear (for the number-of-days-lived variable) or logistic (for the early/late death variable) regression in Plink, adjusting for sex and age or stratifying by sex, while adjusting for age.

The 11 SNPs were subsequently analyzed in replication samples of 1613 long-lived and 1104 middle-aged Germans. The MAF of the SNPs in the German and Danish case–control samples are listed in Supplementary Table 3. None of the 11 SNPs formally replicated in the German samples (see Table 3), although rs11571461 (RAD52) did show a non-significant tendency of association in the same direc- tion (95% CI (OR)=[0.927–1.457]).

Replication of the findings from the Danish longitudinal study was performed in Stata 11.1 by analyzing genotype data from the Leiden 85-plus Study using a sex-adjusted Cox proportional hazard model. An additive model was used, and only in cases when inspection of Kaplan–Meier plots indicated a recessive or dominant model, such a model was applied.

3.2. Longitudinal study in the cohort of oldest-old Danes

As for the case–control study, analysis of survival data in the oldest-old Danes revealed more nominally significant associations than would be expected by chance, whether using the categorical early/late death or the numeric number-of-days-lived variables (see Supplementary Table 4). After correcting for multiple testing 2 SNPs were found to be associated with late life survival for both genders combined: carriers of the rare allele of the pro/antioxidant-SNP rs10047589 (TXNRD1) displayed a significant increase in survival when categorizing into early/late death, whereas the rare allele of the pro/antioxidant-SNP rs207444 (XDH) was found to be significant- ly associated with increased number of days lived (see Table 4A). When stratifying by sex, these results were supported in both gen- ders (data not shown). Moreover, when applying the early/late death variable, positive effects of the rare alleles of the GH/IGF-1/ INS-SNP rs26802 (GHRL) and the DNA-repair-SNP rs13320360 (MLH1) on survival were observed in males, while the DNA-repair- SNP rs2509049 (H2AFX) had a negative effect on survival in females. Using number-of-days-lived as the measure of survival, the rare allele of the DNA-repair-SNP rs705649 (XRCC5) positively affected survival in males. The results are summarized in Table 4B.

In order to obtain a quantitative estimate for the differences in mean survival time between individuals homozygous for the com- mon alleles of a SNP found to be associated with the number-of- days-lived variable and individuals being either heterozygous or ho- mozygous for the rare allele at the same SNP, regression analysis was performed for same sex and same age (93 years) individuals and the regression coefficients were used for estimation. Moreover, the relative risks (RRs) of being alive after age 95 (corresponding to the 1st of January 2001) were calculated for the heterozygotes and homozygotes for the rare allele of each SNP found to be associated to the early/late death variable. The RRs between genotype groups were estimated based on the ORs obtained in the logistic regression analysis. All these analyses were performed in STATA 11.1.

For all the analyses, the nominal significance level was set to 0.05. Correction for multiple testing within each pathway was performed by a permutation approach applying max(T) permutation mode set at 10,000 permutations for the analyses carried out in the Plink soft- ware. Correction for multiple testing in analyses performed in the STATA software was done using the Bonferroni approach.

Since we performed the longitudinal analyses as regression ana- lyses, we were able to estimate the quantitative effects of the 6 SNPs, represented by the risk differences (RD) for the SNPs associated with the early/late death variable, and by the additional survival time for the SNPs associated with the number-of-days-lived variable. These estimates indicated rather substantial effects: a maximum RD was seen for rs26802 (GHRL) CC males having a 53% higher chance for being alive after age 95 (corresponding to the 1st of January 2001) as compared to AA homozygotes, while a maximum difference of 1.66 additional years of survival was seen for rs705649 (XRCC5) GG males as compared to rs705649-AA males, who obtained a mean sur- vival time of 2.15 years. The data are summarized in Supplementary Tables 5A and B.

3. Results