Abstract Large sample datasets have been regarded as the primary basis for innovative discoveries and the solution to missing heritability in genome-wide association studies. However, their computational complexity cannot consider all comprehensive effects and all polygenic backgrounds, which reduces the effectiveness of large datasets. To address these challenges, we included all effects and polygenic backgrounds in a mixed logistic model for binary traits and compressed four variance components into two. The compressed model combined three computational algorithms to develop an innovative method, called FastBiCmrMLM, for large data analysis. These algorithms were tailored to sample size, computational speed, and reduced memory requirements. To mine additional genes, linkage disequilibrium markers were replaced by bin-based haplotypes, which are analyzed by FastBiCmrMLM, named FastBiCmrMLM-Hap. Simulation studies highlighted the superiority of FastBiCmrMLM over GMMAT, SAIGE and fastGWA-GLMM in identifying dominant, small α (allele substitution effect), and rare variants. In the UK Biobank-scale dataset, we demonstrated that FastBiCmrMLM could detect variants as small as 0.03% and with α ≈ 0. In re-analyses of seven diseases in the WTCCC datasets, 29 candidate genes, with both functional and TWAS evidence, around 36 variants identified only by the new methods, strongly validated the new methods. These methods offer a new way to decipher the genetic architecture of binary traits and address the challenges outlined above.