Cancers are routinely classified into subtypes according to various features, including histopathological characteristics and molecular markers. Previous genome-wide association studies have reported heterogeneous associations between loci and cancer subtypes. However, it is not evident what is the optimal modeling strategy for handling correlated tumor features, missing data, and increased degrees-of-freedom in the underlying tests of associations. We propose to test for genetic associations using a mixed-effect two-stage polytomous model score test (MTOP). In the first stage, a standard polytomous model is used to specify all possible subtypes defined by the cross-classification of the tumor characteristics. In the second stage, the subtype-specific case-control odds ratios are specified using a more parsimonious model based on the case-control odds ratio for a baseline subtype, and the case-case parameters associated with tumor markers. Further, to reduce the degrees-of-freedom, we specify case-case parameters for additional exploratory markers using a random-effect model. We use the Expectation-Maximization algorithm to account for missing data on tumor markers. Through simulations across a range of realistic scenarios and data from the Polish Breast Cancer Study (PBCS), we show MTOP outperforms alternative methods for identifying heterogeneous associations between risk loci and tumor subtypes. The proposed methods have been implemented in a user-friendly and high-speed R statistical package called TOP (https://github.com/andrewhaoyu/TOP).

中文翻译：

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一种混合模型方法，用于对包含肿瘤特征的癌症风险的遗传关联进行强有力的测试。

癌症通常根据各种特征（包括组织病理学特征和分子标志物）分为亚型。以前的全基因组关联研究报告了基因座和癌症亚型之间的异质关联。然而，在关联的基础测试中处理相关肿瘤特征、缺失数据和增加自由度的最佳建模策略是什么并不明显。我们建议使用混合效应两阶段多分模型评分测试 (MTOP) 来测试遗传关联。在第一阶段，使用标准的多分模型来指定由肿瘤特征的交叉分类定义的所有可能的亚型。在第二阶段，基于基线亚型的病例-对照优势比以及与肿瘤标志物相关的病例-病例参数，使用更简洁的模型指定特定亚型的病例-对照优势比。此外，为了降低自由度，我们使用随机效应模型为其他探索性标记指定案例参数。我们使用期望最大化算法来解释肿瘤标志物的缺失数据。通过对波兰乳腺癌研究 (PBCS) 的一系列现实场景和数据的模拟，我们表明 MTOP 在识别风险位点和肿瘤亚型之间的异质关联方面优于替代方法。所提出的方法已在名为 TOP (https://github.com/andrewhaoyu/TOP) 的用户友好且高速的 R 统计包中实现。