Genetic variants in genome-wide association studies (GWAS) are tested for disease association mostly using simple regression, one variant at a time. Multiple regression can improve power by aggregating evidence from multiple nearby variants. It can also distinguish disease-coupled variants from variants merely correlated with a coupled variant. However, it requires individual genotype data, limiting its applicability when combining several GWAS. Moreover, multiple logistic regression to model binary phenotypes in case-control GWAS requires inefficient sampling schemes to integrate over the variant effect sizes. Our sparse Bayesian multiple LOgistic REgression (B-LORE) method overcomes these two drawbacks. We propose a quasi-Laplace approximation to analytically integrate over variant effect sizes. The resulting marginal likelihood functions of individual GWAS are approximated by multivariate normal distributions. Their means and covariance matrices serve as summary statistics for combining several GWAS. Additionally, B-LORE can integrate functional genomics tracks as priors for each variant's causality. To test our method, we simulated synthetic phenotypes for real genotypes. B-LORE improved the prediction of loci harboring causal variants and the variant fine mapping. We also used B-LORE for a metanalysis of five small GWAS for coronary artery disease (CAD). We pre-selected the top 50 loci with SNPTEST / META, which included 11 loci discovered by a 14-fold larger meta-analysis (CARDIoGRAMplusC4D). While simple regression discovered only 3 of them with genome-wide significance, B-LORE discovered all of them with causal probability > 95%. Of the 12 other loci discovered by B-LORE, 3 are known from other CAD GWAS and 6 are associated with well-known CAD risk-related blood metabolic phenotypes. Software availability: https://github.com/soedinglab/b-lore.