The meta-analysis was carried out by combining study-specific β-estimates using a fixed effects model14 using the inverse of the variance of the study-specific β-estimates to weight the contribution of each study. The variance of each cohort’s β-estimate was multiplied by the GC lambda estimate to correct for observed inflation38. Specifically, βMETA=∑iβi/(λiσi2)∑i1/(λiσi2), σMETA=1∑i1/(λiσi2), ZMETA=βMETAσMETA, where βi βi,σi2 and λi are the β-estimate, β-estimate variance and GC lambda estimate for the ith cohort. This method is appropriate when the same phenotype and measurement scale are used in each cohort and has the advantage that measures of effect size (eβ is an estimate of the Odds Ratio of the risk allele) and its standard error can be calculated. We also repeated the analysis of SQ by combining Z-scores from each cohort weighted by their sample size38 and obtained almost identical results. All meta-analysis was carried out using the SNPMETA program (see URL list). After performing each meta-analysis the overall lambda estimate for each phenotype was: SQ 1.0145, Ever/Never 1.002, Current/Non-Current 0.998. For each SNP we also calculated a p-value for the heterogeneity across the studies38.
