癌症是一种异质性疾病。有限混合回归（FMR）作为一种重要的异质性分析技术，在癌症研究中得到广泛应用，揭示了癌症结果/表型与协变量之间的重要差异。癌症FMR分析基于临床、人口统计学和组学变量。最近，另一种数据来源是组织病理学图像。组织病理学图像长期以来一直用于癌症诊断和分期。最近，已经证明使用自动数字图像处理管道提取的高维组织病理学图像特征对于建模癌症结果/表型是有效的。组织病理学成像环境交互作用分析已经得到进一步发展，以扩展癌症建模和基于组织病理学成像的分析范围。在癌症FMR分析的重要性和对更有效方法仍然有强烈需求的情况下，本文采用自然的下一步并基于低维临床/人口统计学/环境变量、高维成像特征及其交互开展了癌症FMR分析。与许多现有研究相辅相成，我们开发了一种贝叶斯方法，以适应高维度、筛选噪声、识别信号和尊重“主要效应、交互作用”变量选择层次。我们还开发了有效的计算算法，模拟显示提议方法的优势性能。在肺鳞状细胞癌的癌症基因组图谱数据分析中，我们得出了与替代方法不同的有趣结论。© 作者2021。由牛津大学出版社出版。保留所有权利。有关权限，请发送电子邮件至：journals.permissions@oup.com。

Cancer is a heterogeneous disease. Finite mixture of regression (FMR)-as an important heterogeneity analysis technique when an outcome variable is present-has been extensively employed in cancer research, revealing important differences in the associations between a cancer outcome/phenotype and covariates. Cancer FMR analysis has been based on clinical, demographic, and omics variables. A relatively recent and alternative source of data comes from histopathological images. Histopathological images have been long used for cancer diagnosis and staging. Recently, it has been shown that high-dimensional histopathological image features, which are extracted using automated digital image processing pipelines, are effective for modeling cancer outcomes/phenotypes. Histopathological imaging-environment interaction analysis has been further developed to expand the scope of cancer modeling and histopathological imaging-based analysis. Motivated by the significance of cancer FMR analysis and a still strong demand for more effective methods, in this article, we take the natural next step and conduct cancer FMR analysis based on models that incorporate low-dimensional clinical/demographic/environmental variables, high-dimensional imaging features, as well as their interactions. Complementary to many of the existing studies, we develop a Bayesian approach for accommodating high dimensionality, screening out noises, identifying signals, and respecting the "main effects, interactions" variable selection hierarchy. An effective computational algorithm is developed, and simulation shows advantageous performance of the proposed approach. The analysis of The Cancer Genome Atlas data on lung squamous cell cancer leads to interesting findings different from the alternative approaches.© The Author 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.