The increasing availability of single-cell data revolutionizes the understanding of biological mechanisms at cellular resolution. For differential expression analysis in multi-subject single-cell data, negative binomial mixed models account for both subject-level and cell-level overdispersions, but are computationally demanding. Here, we propose an efficient NEgative Binomial mixed model Using a Large-sample Approximation (NEBULA). The speed gain is achieved by analytically solving high-dimensional integrals instead of using the Laplace approximation. We demonstrate that NEBULA is orders of magnitude faster than existing tools and controls false-positive errors in marker gene identification and co-expression analysis. Using NEBULA in Alzheimer’s disease cohort data sets, we found that the cell-level expression ofAPOEcorrelated with that of other genetic risk factors (includingCLU, CST3, TREM2, C1q, andITM2B) in a cell-type-specific pattern and an isoform-dependent manner in microglia. NEBULA opens up a new avenue for the broad application of mixed models to large-scale multi-subject single-cell data.

Alzheimer’s disease (AD) is the most common cause of dementia in the elderly and the sixth leading cause of death in the United States. AD is mainly considered a complex disorder with polygenic inheritance. Despite discovering many susceptibility loci, a major proportion of AD genetic variance remains to be explained. We investigated the genetic architecture of AD in four publicly available independent datasets through genome-wide association, transcriptome-wide association, and gene-based and pathway-based analyses. To explore differences in the genetic basis of AD between males and females, analyses were performed on three samples in each dataset: males and females combined, only males, or only females. Our genome-wide association analyses corroborated the associations of several previously detected AD loci and revealed novel significant associations of 35 single-nucleotide polymorphisms (SNPs) outside the chromosome 19q13 region at the suggestive significance level of p < 5E–06. These SNPs were mapped to 21 genes in 19 chromosomal regions. Of these, 17 genes were not associated with AD at genome-wide or suggestive levels of associations by previous genome-wide association studies. Also, the chromosomal regions corresponding to 8 genes did not contain any previously detected AD-associated SNPs with p < 5E–06. Our transcriptome-wide association and gene-based analyses revealed that 26 genes located in 20 chromosomal regions outside chromosome 19q13 had evidence of potential associations with AD at a false discovery rate of 0.05. Of these, 13 genes/regions did not contain any previously AD-associated SNPs at genome-wide or suggestive levels of associations. Most of the newly detected AD-associated SNPs and genes were sex specific, indicating sex disparities in the genetic basis of AD. Also, 7 of 26 pathways that showed evidence of associations with AD in our pathway-bases analyses were significant only in females. Our findings, particularly the newly discovered sex-specific genetic contributors, provide novel insight into the genetic architecture of AD and can advance our understanding of its pathogenesis.