Linkage disequilibrium approaches to the analysis of gene– gene interactions have been proposed (Zhao et al., 2006), and the modeling of gene–gene interactions using association analy- sis of noncontiguous haplotypes has been implemented (Woo et al., 2006). We took a similar approach. The haplotype fre- quencies for the combination of SNP in APOE, HRAS1, and LASS1 were estimated by an Expectation-Maximization (EM) algorithm implemented in Arlequin (Excoffier et al., 2005). The SD was determined by the parametric bootstrap procedure in Arlequin (100 bootstraps). Those haplotype combinations pres- ent at a frequency of   0.01 or greater in the 20- to59 -year-old group in Georgia and in Louisiana were analyzed further. This cutoff was taken based on the considerations from comparison of statistical and molecular haplotyping for sample sizes as small as 17 (Tishkoff et al., 2000). The frequency estimates in case and control groups were used to generate 2 · 2 contingency tables to test significance of associations of the respective haplo- type combinations with exceptional longevity. Fisher’s exact test was used to assess significance. The sequential Dunn-Sidak pro- cedure was used to adjust the exact P-values for multiple com- parisons of haplotype combinations. The adjustment included seven such combinations independently identified in the Geor- gia and Louisiana samples in the subpopulations of European origin (Table S4). In the African-origin subpopulations, there were seven and three such combinations in these samples, respectively. A stringent criterion of adjusted P < 0.01 (two- sided) was used to identify the potentially interacting combina-

Statistical analysis

There is substantial evidence supporting the hypothesis of asso- ciation with exceptional longevity of variants in the three candi- date genes chosen here for analysis. This information is presented in this paper. APOE has been replicated as a longev- ity-determining gene in numerous studies (Christensen et al., 2006). This gene anchors the interaction described in this report (Fig. 5). The hypothesis we test is related to the role of the apoli- poprotein APOE in lipid and lipoprotein metabolism. The BioSys- tems Database (NCBI) lists 228 genes under the entry ‘Metabolism of Lipids and Lipoproteins.’ APOE and LASS1 are among them. Thus, we assume the prior probability of an inter- action of these genes to be  1.0. It is likely that there are genes involved in lipid and lipoprotein metabolism in addition to the 228, and we conservatively propose there to be 300. We there- fore assume the prior probability of identifying another interact- ing gene, such as HRAS1, to be  300⁄30 000 or  0.01. We set the posterior probability for identification of such a gene at 0.95. Applying Bayes’ theorem, we obtain the likelihood ratio Pr(Data|Association)⁄Pr(Data|NoAssociation) of 1881. These considerations are applicable to the initial test of the association with longevity of the combination of the haplotypes in the three genes in both the Georgia and Louisiana populations. The prior probability increases dramatically in subsequent tests, once the

The two significant haplotype combinations found to be asso- ciated with exceptional longevity in the independent analyses in the Georgia and Louisiana samples were then evaluated in men

Hawley, J. Hayden, K. Hebert, F. Holton, H.-C. Hsu, D. Johann- sen, L. Kawasaki, B. Kimball, C. King-Rowley, M. Konkel, R. Kuhn, K. Landry, C. Lavie, D. LaVie, M. Leblanc, H.-Y. Lin, K. Lopez, B. McEvoy-Hein, J.D. Mountz, E. Olinde, J. Owens, K. Pedersen, A. Pellett, P. Remedios, Y. Robertson, J. Rood, H. Rothschild, R.A. Russell, E. Sandifer, B. Schmidt, R. Schwartz, D.K. Scott, J. Silva, F.N. Standberry, J. Thomson, A. Tiwari, V. Toups, C. Traylor, C. Velasco-Gonzalez, C. Waguespack, X.-Y. Wang, R.H. Wood, Q. Yu, S. Zehr, and P. Zhang.

deficit accumulation in the Louisiana population. The same  0.01 frequency cutoff was applied. This involved adjustment for up to two comparisons, using the sequential Dunn-Sidak procedure. The haplotype combination frequencies differed sig- nificantly in the various samples examined. These haplotype combinations are common in the relevant samples characterized by longevity and⁄or healthy aging. The three-gene haplotype combinations reported here are associated with certain additional healthy-aging phenotypes but not with others (in preparation).

Author contributions

The APOE and APOEÆHRAS1 haplotypes derived from the significant haplotype combinations in the three genes were also evaluated independently for association with exceptional longevity, using the above procedures.

S.M.J., L.W.P., M.A.B., D.A.W., L.J.S., D.B.H., E.R., K.E.C., and M.A.W. designed the research; S.K., L.L., X.B., J.C.J., J.A.W., C.M.L., J.V., L.M., L.J.S., D.B.H., M.V.M., and K.E.C. acquired data; J.A. and J.D. contributed new analytic tools; S.M.J., S.K., J.D., X.B., J.A., M.A.B., D.A.W., C.M.L., J.V., L.M., and L.J.S. analyzed and interpreted data; and S.M.J., S.K., and J.D. prepared the manuscript.

Nonagenarians were classified by tertile according to their deficit accumulation, as described above. The Kaplan–Meier survival was plotted for each tertile. The differences between tertiles were evaluated by the Wilcoxon test (a two-sided P < 0.05 was considered significant). SAS v9.13 software was used for Kaplan–Meier survival analysis.

References

The significance of differences in promoter strength deter- mined using the luciferase reporter assay was evaluated for six independent experiments in which the control (no LASS1 promoter sequences) and the three LASS1 promoter haplo- types were compared. One-way ANOVA was used to first test for any differences, using a criterion of P < 0.05 (two-sided). Then, all pairwise combinations were evaluated in a two- tailed Newman–Keuls test, implemented in STATMOST (DataMost Corp., Sandy, UT, USA). A P-value of < 0.05 was considered significant.