Other possible explanations for incomplete replication include unde- tected population structure, use of under-powered replication samples, and heterogeneity between samples. However, adjustment for potential population stratification via principal components only modestly dimin- ished the associations reported here. Similarly, differential power based on sample size differences does not appear to explain the incomplete rep- lication as the NECS sample was arguably the least well-powered owing to small sample size and skewed case–control ratio. Heterogeneity between samples can occur for a variety of reasons. For example, the GTCT haplotype could tag a functional variant in some samples but not others owing to differential LD patterns. Alternatively, a functional variant tagged by GTCT could correlate with the longevity phenotype only in the NECS and Stage 1 samples; this can result from differential ascertainment of cases or from between-sample differences in environmental exposures (McCarthy et al., 2008). One potential source of heterogeneity is differ- ential ascertainment of LLI, as the minimum age for inclusion varied by

Experimental procedures

Samples

We analyzed one initial (Stage 1) and four follow-up (Stage 2) samples of LLI and younger controls. Samples collected for the Stage 1 study by Elixir Pharmaceuticals were Caucasians primarily of Northern European ances- try. Samples were also obtained from the New England (NECS), French, Southern Italian (SICS), and Ashkenazi Jewish Centenarian Studies. Details of sample collection, as well as steps taken to ensure that the study samples did not overlap, can be found in Supporting information.

meta-analysis test statistic. Permutation tests for two-stage studies are complicated by the fact that only partial genotyping is performed in the second stage of the study. Our strategy for dealing with this was, for per- mutation purposes only, to use MaCH 1.0, along with inferred haplotypes from the HapMap CEU sample, to impute the full 16-SNP haplotypes for all Stage 2 samples. We were then able to perform a full two-stage analy- sis in each permutation as follows:

SNP selection

We downloaded all SNP genotype data for the CEU population from )40 kb to +10 kb of LMNA from the website of the International Hap- Map (International HapMap Consortium 2005): http://www.hapmap.org. These genotype data in raw HapMap format were uploaded to Tagger (http://www.broad.mit.edu/mpg/tagger/), and our multiplex assay design (see Supporting Information for details) was created from the list of tag SNPs to capture all variants of interest in our LMNA region of interest. We used r2 > 0.8 as the threshold for accepting tag SNPs. Ten SNPs were selected in HapMap Phase I, release #16 along with the synonymous cod- ing SNP, rs4641, which was not in HapMap Phase I. Upon release of Hap- Map Phase II, release #19 we selected SNPs in the LMNA region again and added five additional SNPs not tagged (r2 < 0.8) by the previously selected SNPs. Based on Phase II of the HapMap, these 16 SNPs offered comprehensive coverage and representation of common variants in the LMNA region and were genotyped in Stage 1.

1 Randomly reassign case–control status within each of the five samples.

2 Compute trend test statistics for all haplotypes (or SNPs) in the permuted Stage 1 sample.

3 To mimic the selection of six SNPs for genotyping in the Stage 2 samples, as was performed in the original study, select the most signifi- cant 6-SNP haplotype from the (permuted) Stage 1 analysis for follow-up. Perform trend tests of association for all six SNPs and for all haplotypes composed of 2–6 SNP combinations of these six SNPs in the four per- muted Stage 2 samples.

4 Compute meta-analysis statistics for all haplotypes (or SNPs) tested on all five permuted samples; record the value of the most significant meta-analysis test statistic.

For Stage 2 samples, we genotyped the six SNPs from the most signifi- cant 6-SNP haplotype in Stage 1. Additional SNPs from the original 16 were genotyped in some Stage 2 samples based on convenience; these SNPs were tested for association (Table 2), but were not included in the haplotype analysis. Details on SNP genotyping are provided in Supporting information.

We performed 10 000 permutations, and recorded the best meta- analysis test statistic for each permutation. We computed the empirical P-value as the proportion of permutations in which the best statistic from the permutation was greater in magnitude than the best statistic from the original data analysis.

Statistical analysis

We used the MaCH 1.0 haplotype inference and imputation software (Li et al., 2010) to infer 16-SNP haplotypes for all individuals in Stage 1 and 6-SNP haplotypes for all individuals in Stage 2. For individuals with miss- ing genotypes, the most likely genotype was inferred based on haplotype frequencies within the sample. We imputed genotypes for SNP rs1468772 that was not genotyped in the French sample, using MaCH (Li et al., 2010) in conjunction with phased haplotype information from the HapMap CEU sample.

Population stratification

As described in Supporting Information, the Stage 1 and French samples had previously been tested for the presence of population stratification between LLI and control subjects and the Stage 1 sample had been genet- ically matched. There was no evidence of population stratification in the French sample (mean v2 = 1.00 across 57 random microsatellite markers) or in the genetically matched Stage 1 sample (mean v2 = 0.95 across 80 random SNPs) (Geesaman et al., 2003).