While meta-analyzing retrospective cancer patient cohorts, an investigation of differences in the expressions of target oncogenes across cancer subtypes is of substantial interest because the results may uncover novel tumorigenesis mechanisms and improve screening and treatment strategies. Weighting methods facilitate unconfounded comparisons of multigroup potential outcomes in multiple observational studies. For example, Guha et al. (2022) introduced concordant weights, allowing integrative analyses of survival outcomes by maximizing the effective sample size. However, it remains unclear how to use this or other weighting approaches to analyze a variety of continuous, categorical, ordinal, or multivariate outcomes, especially when research interests prioritize uncommon or unplanned estimands suggested by post hoc analyses; examples include percentiles and moments of group potential outcomes and pairwise correlations of multivariate outcomes. This paper proposes a unified meta-analytical approach accommodating various types of endpoints and fosters new estimators compatible with most weighting frameworks. Asymptotic properties of the estimators are investigated under mild assumptions. For undersampled groups, we devise small-sample procedures for quantifying estimation uncertainty. We meta-analyze multi-site TCGA breast cancer data, shedding light on the differential mRNA expression patterns of eight targeted genes for the subtypes infiltrating ductal carcinoma and infiltrating lobular carcinoma.

翻译：在回顾性分析癌症患者队列的荟萃分析中，探究不同癌症亚型之间目标癌基因表达差异具有重要意义，因为其结果可能揭示新的肿瘤发生机制，并改进筛查与治疗策略。加权方法有助于在多观察性研究中实现多组潜在结局的无混杂比较。例如，Guha等人（2022）提出了一致权重方法，通过最大化有效样本量实现生存结局的整合分析。然而，如何利用该方法或其他加权技术分析连续型、分类型、有序型或多元结局仍不明确，尤其当研究焦点关注事后分析中提出的非普通或非预设的估计量（如各组潜在结局的百分位数和矩、多元结局的成对相关性）时。本文提出一种统一元分析方法，可兼容多种类型结局变量，并催生适用于大多数加权框架的新型估计量。在温和假设下研究了估计量的渐近性质。针对欠采样组，我们设计了用于量化估计不确定性的小样本程序。通过对多中心TCGA乳腺癌数据进行荟萃分析，揭示了浸润性导管癌与浸润性小叶癌两种亚型中八个靶基因的差异mRNA表达模式。