癌症的发展涉及几种重要生物学途径中体细胞突变的积累。描述肿瘤发生过程中途径突变的时间顺序对于理解癌症发展的生物学机制和确定治疗干预的潜在靶标至关重要。已经引入了几种计算和统计方法，用于根据一组患者的突变谱数据估计体细胞突变的顺序。然而，当前方法的一个主要问题是它们没有考虑肿瘤内异质性（ITH），这限制了它们准确辨别途径突变顺序的能力。为了解决这个问题，我们提出了 PATOPAI，一种概率方法，通过结合 ITH 信息以及突变的通路和功能注释信息来估计通路水平上突变的时间顺序。 PATOPAI 使用最大似然方法来估计特定序列中发生途径突变事件的概率，其中它侧重于与肿瘤系统发育结构一致的顺序。对癌症基因组图谱 (TCGA) 的全外显子组测序数据的应用说明了我们的方法能够恢复几种癌症类型中途径突变的时间顺序。

The development of cancer involves the accumulation of somatic mutations in several essential biological pathways. Delineating the temporal order of pathway mutations during tumorigenesis is crucial for comprehending the biological mechanisms underlying cancer development and identifying potential targets for therapeutic intervention. Several computational and statistical methods have been introduced for estimating the order of somatic mutations based on mutation profile data from a cohort of patients. However, one major issue of current methods is that they do not take into account intra-tumor heterogeneity (ITH), which limits their ability to accurately discern the order of pathway mutations. To address this problem, we propose PATOPAI, a probabilistic approach to estimate the temporal order of mutations at the pathway level by incorporating ITH information as well as pathway and functional annotation information of mutations. PATOPAI uses a maximum likelihood approach to estimate the probability of pathway mutational events occurring in a specific sequence, wherein it focuses on the orders that are consistent with the phylogenetic structure of the tumors. Applications to whole exome sequencing data from The Cancer Genome Atlas (TCGA) illustrate our method's ability to recover the temporal order of pathway mutations in several cancer types.