Table 1 The 77 genes grouped by biological sub-process

DNA-damage response BER (no. of NER (no. of MMR (no. of HRR (no. of NHEJ (no. of RECQ (no. of Telomere functioning Mitochondrial DNA (no. of genes¼8) genes¼26) genes¼18) genes¼14) genes¼7) genes¼5) genes¼5) (no. of genes¼9) processes (no. of genes¼12) ATM APEX1 DDB1 (uv- EXO1 LIG1 DCLRE1C BLM ACD (pip) C10orf2 (twinkle) (ape1) ddb1) (artemis) ATR APTX DDB2 (uv- LIG1 MRE11A LIG4 RECQL PIF1 ERCC6 (csb) (aprataxin) ddb2) (recq1) BRIP1 (facj) ERCC6 (csb) ERCC1 MLH1 NBN PRKDC (dna- RECQL4 POT1 ERCC8 (csa) pkcs) (recq4) FANCA (faca) ERCC8 (csa) ERCC2 (xpd) MLH3 RAD50 XRCC4 RECQL5 RECQL4 (recq4) LONP1 (lonp) (recq5) FANCD2 (facd) FEN1 ERCC3 (xpb) MSH2 RAD51 XRCC5 WRN TERF1 NEIL2 (ku80/ku86) H2AFX (h2a.x) HMGB1 ERCC4 (xpf) MSH3 RAD52 TERF2 POLG (polg) (hmg1) TP53 (p53) LIG1 ERCC5 (xpg) MSH6 RAD54L TERF2IP (rap1) POLRMT (mtrpol) (rad54) YBX1 (yb1) LIG3 ERCC6 (csb) PCNA TERT RECQL4 (recq4) NEIL1 ERCC8 (csa) PMS1 WRN SUPV3L1 (suv3) NEIL2 LIG1 PMS2 TFAM (mttfa) NTHL1 PCNA POLD1 (pold) TP53 (p53) OGG1 POLD1 (pold) RFC1 (rfc) YBX1 (yb1) PARP1 POLE (pole) RPA1 (rpa) PCNA RAD23B YBX1(yb1) PNKP (pnk) RFC1 (rfc) POLB RPA1 (rpa) POLD1 (pold) XPA POLE (pole) XPC RECQL4 (recq4) RECQL5 (recq5) RFC1 (rfc) RPA1 (rpa) UNG WRN XRCC1

Abbreviations: BER, base excision repair; HRR, homologous recombinational repair; MMR, mismatch repair; NER, nucleotide excision repair; NHEJ, non-homologous end-joining; RECQ, RecQ helicase activities. Names of gene products are given in parenthesis if different from gene names.

w2(2df)-distribution under the null, ie we used(cid:3)log P as single-marker statistic, where P is the P-value from the trend test). The trend test was included as it is the most applied model in the literature on the genetics of human longevity. In setup III (best-test model), we inspected all possible modes of inheritance simultaneously by combining Cochran–Armitage’s trend test and w2 tests based on assumption-free (2df), recessive (1df) and dominant (1df) models. Thereby we defined the test statistic for each SNP to be the minimum P-value of these four tests (back-transformed so the test statistic equaled (cid:3)log (min 1rir4 Pi), where P1–P4 correspond to the P-values from the four tests, respectively). This procedure is analogous to the MAX test described previously by Freidlin et al.47 The log-transformation used in setups II and III was applied to make the three setups comparable as the enrichment score used by the method of Wang et al39 is sensitive to the scale of the statistics. As the three setups are highly dependent, the enrichment score q- values were calculated (by FDR) individually for each of them.

reflecting the degree of over-representation of associated genes within a sub-process as opposed to the genes outside the sub-process, step 4: was determined by permuting the phenotype labels 10000 times and repeating steps above, hereby generating the enrichment score P-value for each of the sub-processes. Following the recommendations of the authors,39 we used a parameter p ¼ 1 to calculate the enrichment score.

After deriving the enrichment score P-values for each of the nine sub- processes, we used the false discovery rate (FDR) to take the testing of nine sub-processes into account. As described by Wang et al39 for a given sub- process S* (in our case S1–S9) with a normalized enrichment score NES* (NES1-NES9), the FDR was estimated as the proportion of sub-processes with a normalized ES (after permutation) at least as high as NES*, divided by the proportion of sub-processes with a normalized ES (non-permuted) at least as high as the observed NES*. We estimated corresponding enrichment score q-values as the minimal FDR obtainable when declaring a test significant.

Moreover, step 1 was implemented in three different ways referred to setup I, II and III. We applied the three setups to inspect their influence on results. In setup I, we used w2(2df)-statistics (assumption-free model) assessing the difference in genotype frequencies between cases and controls without constraints on the genotypic model. In setup II, Cochran–Armitage’s test statistic was used (suitably transformed to obtain a

RESULTS

The set-based test resulted in an overall P-value of 9.9(cid:2)10(cid:3)5 for the combined set of SNPs. This result supports that variation in

German study population did not show significant results: P-value (self-contained set-based analysis)¼ 0.227 and P-values (competitive gene-set analysis)¼0.468–0.919 (see Supplementary Table 2).

response and DNA repair genes appears to be of for human longevity.

Competitive gene-set analysis of the nine sub-processes

The results of the initial SNP analysis (step 1), using the three different statistical setups, can be seen in Supplementary Table 1. The data can further be found in the GWAS Central data base (www.gwascentral.org). Table 2 shows enrichment score P- and q-values obtained for the nine sub-processes compared to the respective remaining genes of the entire pathway, under the three different statistical setups. We found the results to be consistent with only slight differences; uniformly over the three setups, sub-processes BER, HRR and RECQ showed P-values below 0.05, whereas the remaining sub-processes were non-significant. However, when taking into account the number of sub-processes investigated, only HRR showed a q-value below 0.05 and only in setup II (see Table 2).

DISCUSSION

In this study, we aimed to investigate whether genetic variation in any of the sub-processes of DNA-damage response and DNA repair influences human longevity more than others. This is an important question as the individual sub-processes contribute to different aspects of the maintenance of genetic stability, and therefore have diverse biological roles, which are likely to affect longevity in different manners.

Table 3 Ranking of the genes in the BER, HRR and RECQ sub- processes