Summary data based fine-mapping methods require a high-quality correlation estimate. Ideally, the correlation matrix is computed from the same genotype data from which the z-scores originate. In that case, for quantitative traits, the equations in Section 2.1 connecting original genotype-phenotype data and GWAS summary data are exact and hence no information is lost by working with summary data. For case-control data, a normal approximation to the logistic likelihood causes some difference between the two approaches but the difference is expected to be small with current GWAS sample sizes (Pirinen et al., 2013). For some populations, sequencing of many thousands of individuals have either already been carried out or will complete soon. Such reference data allow reliable fine-mapping down to low-frequency variants also when the original genotype data are not available. A more challenging problem is large meta-analyses that combine individuals from varying ancestries. Assuming that the causal variants are included in the data and have the same effect sizes across the ancestral backgrounds, FINEMAP can be run with the sample size weighted SNP correlation matrix. If these assumptions are not met, then a hierarchical model allowing separate SNP correlation structures in each ancestry would perform better (Kichaev and Pasaniuc, 2015).
