In each of the NHS and the WGHS GWA studies separately, we performed linear regression to analyze the association between each of the SNPs (coded as counts of minor alleles) and age at menarche or age at natural menopause as continuous variables using PLINK software29. SNPs with low minor allele frequency (MAF) (<1%) in either the NHS or the WGHS samples were excluded from analysis. To control for potential confounding by population stratification, we adjusted for the top principal components of genetic variation chosen for each study after excluding any clearly non-Caucasian admixed individuals (see Supplementary Methods online). In the NHS analysis, controlling for breast cancer case-control status made no material difference to the GWAS results. To combine evidence for association with age at menarche or age at natural menopause and calculate a summary effect size across the NHS and the WGHS, we used fixed effect joint analysis; and heterogeneity in effect size across two studies was assessed using the Q- test30.
