High-throughput sequencing (HTS) technologies have been instrumental in investigating biological questions at the bulk and single-cell levels. Comparative analysis of two HTS data sets often relies on testing the statistical significance for the difference of two negative binomial distributions (DOTNB). Although negative binomial distributions are well studied, the theoretical results for DOTNB remain largely unexplored. Here, we derive basic analytical results for DOTNB and examine its asymptotic properties. As a state-of-the-art application of DOTNB, we introduce DEGage, a computational method for detecting differentially expressed genes (DEGs) in scRNA-seq data. DEGage calculates the mean of the sample-wise differences of gene expression levels as the test statistic and determines significant differential expression by computing the P-value with DOTNB. Extensive validation using simulated and real scRNA-seq data sets demonstrates that DEGage outperforms five popular DEG analysis tools: DEGseq2, DEsingle, edgeR, Monocle3, and scDD. DEGage is robust against high dropout levels and exhibits superior sensitivity when applied to balanced and imbalanced data sets, even with small sample sizes. We utilize DEGage to analyze prostate cancer scRNA-seq data sets and identify marker genes for 17 cell types. Furthermore, we apply DEGage to scRNA-seq data sets of mouse neurons with and without fear memory and reveal eight potential memory-related genes overlooked in previous analyses. The theoretical results and supporting software for DOTNB can be widely applied to comparative analyses of dispersed count data in HTS and broad research questions.

中文翻译：

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两个负二项分布差异的理论框架及其在测序数据比较分析中的应用


高通量测序 （HTS） 技术在研究大量和单细胞水平的生物学问题方面发挥了重要作用。两个 HTS 数据集的比较分析通常依赖于检验两个负二项分布 （DOTNB） 差异的统计显着性。尽管负二项分布得到了很好的研究，但 DOTNB 的理论结果在很大程度上仍未得到探索。在这里，我们得出了 DOTNB 的基本分析结果并检查了它的渐近特性。作为 DOTNB 的最新应用，我们引入了 DEGage，这是一种用于检测 scRNA-seq 数据中差异表达基因 （DEG） 的计算方法。DEGage 计算基因表达水平样本差异的平均值作为检验统计量，并通过使用 DOTNB 计算 P 值来确定显着差异表达。使用模拟和真实 scRNA-seq 数据集进行的广泛验证表明，DEGage 优于五种流行的 DEG 分析工具：DEGseq2、DEsingle、edgeR、Monocle3 和 scDD。DEGage 对高丢失水平具有稳健性，并且在应用于平衡和不平衡数据集时表现出卓越的灵敏度，即使样品量较小。我们利用 DEGage 分析前列腺癌 scRNA-seq 数据集并鉴定 17 种细胞类型的标记基因。此外，我们将 DEGage 应用于具有和没有恐惧记忆的小鼠神经元的 scRNA-seq 数据集，并揭示了在以前的分析中被忽略的八个潜在的记忆相关基因。DOTNB 的理论结果和支持软件可广泛应用于 HTS 中分散计数数据的比较分析和广泛的研究问题。