Deep conditional independence tests with application to imaging genetics

深度学习是生物医学数据分析的主力，因为它能够利用高度非线性的关联来训练准确的预测模型，特别是对于图像或序列等结构化数据。然而，预测质量本身-这可能会受到混杂的影响-是不够的，以从数据走向了解潜在的生物学。调整潜在混杂影响的独立性统计检验对生物变量在总体水平上的依赖性做出了合理的陈述。然而，目前的统计测试并不是针对结构化数据的应用而定制的。在本项目中，我们开发了条件独立性测试，用于连续标量响应Y与输入/协变量X之间的统计关联，同时以协变量Z为条件，由于与X和Y的依赖性，协变量Z可能会混淆关联。具体来说，我们考虑X和Z中的一个或两个被结构化的情况（特别是图像）。我们的方法使用深度学习将结构化数据X和/或Z映射到连续嵌入上，例如，这可能来自迁移学习。然后，我们在嵌入变量的线性混合效应模型中使用测试，其中随机效应允许在高维中进行简约建模。我们将研究所有开发的测试的理论属性，并提供有效的算法和实现。我们还特别关注有限样本中的良好功效特性，并推导出样本大小和功效calculations.The开发的方法的动机是成像遗传学中的应用，其中条件独立性测试用于将图像中的遗传表型映射到遗传位点，通过调节校正群体结构和相关性的混淆。基于人群的成像允许有效地量化表型，包括疾病生物标志物。虽然目前的全基因组关联研究分析了先验已知的标量生物标志物，如器官大小，但该项目的目标是对图像中任何可遗传表型变异的存在进行无偏测试，以发现新的生物标志物。特别是，我们将使用我们的方法在英国生物银行的2D视网膜眼底图像和3D脑磁共振图像的基因为基础的关联研究。

Deep learning is a workhorse for biomedical data analysis due to its ability to leverage highly nonlinear associations to train accurate prediction models, in particular for structured data such as images or sequences. However, prediction quality alone - which may be influenced by confounding - is insufficient in order to move from data towards understanding the underlying biology. Statistical tests for independence that adjust for potential confounding influences make sound statements about dependencies between biological variables on the population level. Current statistical tests, however, are not tailored towards applications to structured data. In this project, we develop conditional independence tests for statistical association between a continuous scalar response Y and an input/covariate X, while conditioning on covariates Z that may confound the association due to dependencies with both X and Y. Specifically, we consider the cases where one or both of X and Z are structured (in particular images). Our approach uses deep learning to map structured data X and/or Z onto continuous embeddings, which may for example come from transfer learning. We then use tests in linearized mixed effects models on embedded variables, where random effects allow for parsimonious modeling in high dimensions. We will investigate theoretical properties of all developed tests and provide efficient algorithms and implementations. We focus in particular also on good power properties in finite samples and derive sample size and power calculations.The developed methods are motivated by applications in imaging genetics, where conditional independence testing is used to map heritable phenotypes in images to genetic loci, correcting for confounding by population structure and relatedness via conditioning. Population-based imaging allows to efficiently quantify phenotypes, including disease biomarkers. While current genome-wide association studies analyze a priori known scalar biomarkers such as organ sizes, the goal of this project is to enable unbiased testing for the presence of any heritable phenotypic variation in images towards the discovery of novel biomarkers. In particular, we will use our methods for gene-based association studies of 2D retinal fundus images and 3D brain magnetic resonance images in the UK Biobank.