Distribution-on-Scalar Single-Index Quantile Regression Model for Handling Tumor Heterogeneity

This article develops a distribution-on-scalar single-index quantile regression modeling framework to investigate the relationship between cancer imaging responses and scalar covariates of interest while tackling tumor heterogeneity. Conventional association analysis methods typically assume that the imaging responses are well-aligned after some preprocessing steps. However, this assumption is often violated in practice due to imaging heterogeneity. Although some distribution-based approaches are developed to deal with this heterogeneity, major challenges have been posted due to the nonlinear subspace formed by the distributional responses, the unknown nonlinear association structure, and the lack of statistical inference. Our method can successfully address all the challenges. We establish both estimation and inference procedures for the unknown functions in our model. The asymptotic properties of both estimation and inference procedures are systematically investigated. The finite-sample performance of our proposed method is assessed by using both Monte Carlo simulations and a real data example on brain cancer images from TCIA-GBM collection.

本文提出了一种标量分布单指标分位数回归建模框架，旨在探究癌症影像响应与目标标量协变量之间的关系，同时解决肿瘤异质性问题。传统关联分析方法通常假设影像响应经过预处理步骤后可实现良好对齐，但这一假设在实际中常因影像异质性而不成立。尽管已有部分基于分布的方法用于应对此类异质性，但由于分布响应形成的非线性子空间、未知的非线性关联结构以及统计推断手段的缺失，仍面临诸多挑战。本文提出的方法可有效解决上述所有挑战。我们为模型中的未知函数建立了估计与推断流程，并系统研究了该流程中估计与推断的渐近性质。通过蒙特卡洛模拟及TCIA-GBM数据集的脑癌影像真实数据实例，对所提方法的有限样本性能进行了评估。